**Feature Papers in Eng 2022**

Editor

**Antonio Gil Bravo**

MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin

*Editor* Antonio Gil Bravo Universidad P´ublica de Navarra Spain

*Editorial Office* MDPI St. Alban-Anlage 66 4052 Basel, Switzerland

This is a reprint of articles from the Special Issue published online in the open access journal *Eng-Advances in Engineering* (ISSN 2673-4117) (available at: https://www.mdpi.com/journal/eng/ special issues/FP in Eng 2022).

For citation purposes, cite each article independently as indicated on the article page online and as indicated below:

LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. *Journal Name* **Year**, *Volume Number*, Page Range.

**ISBN 978-3-0365-7530-8 (Hbk) ISBN 978-3-0365-7531-5 (PDF)**

© 2023 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications.

The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND.

## **Contents**




## **About the Editor**

#### **Antonio Gil Bravo**

Antonio Gil Bravo (Full Professor of Chemical Engineering, Universidad Publica de Navarra, ´ Spain): Professor Gil earned his BS and MS in Chemistry at the University of Basque Country (San Sebastian), before receiving his PhD in Chemical Engineering at University of Basque Country (San ´ Sebastian). He undertook postdoctoral research at the Universit ´ e catholique de Louvain (Belgium), ´ working on Spillover and Mobility of Species on Catalyst Surfaces. The research interests of Professor Gil can be summarized as covering the following topics: the evaluation of the porous and surface properties of solids; pillared claysl gas adsorption; energy and CO2 storage; pollutant adsorption; environmental technologies; environmental management; preparation, characterization and catalytic performance of metal supported nanocatalysts; and industrial waste valorization.

## *Editorial* **Special Issue: Feature Papers in** *Eng* **<sup>2022</sup>**

**Antonio Gil Bravo**

INAMAT2, Science Department, Public University of Navarra, Campus of Arrosadia, Building Los Acebos, E-31006 Pamplona, Spain; andoni@unavarra.es

The aim of this second *Eng* Special Issue is to collect experimental and theoretical re-search relating to engineering science and technology. The general topics published in *Eng* are as follows: electrical, electronic and information engineering; chemical and materials engineering; energy engineering; mechanical and automotive engineering; industrial and manufacturing engineering; civil and structural engineering; aerospace engineering; biomedical engineering; geotechnical engineering and engineering geology; and ocean and environmental engineering. This editorial is an overview of the selected representative studies on these topics.

This book contains 33 papers, including 2 *Review* papers and 1 *Communication*, published by several authors interested in new cutting-edge developments in the field of engineering. Recently, a subcategory of nanotechnology—nano- and microcontainers—has developed rapidly, with unexpected results. Nano- and microcontainers refer to hollow spherical structures in which the shells can be organic or inorganic. These containers can be filled with substances released when excited and can be used in corrosion healing, cancer therapy, cement healing, antifouling, etc. In the first review, the author summarizes the various innovative technologies that have beneficial effects on improving people's lives [1].

Jombo and Zhang [2] report that traditional means of monitoring the health of industrial systems involve the use of vibration and performance monitoring techniques, among others. In these approaches, contact-type sensors, such as accelerometers, proximity probes, pressure transducers and temperature transducers, are installed on the machine to monitor its operational health parameters. However, these methods fall short when additional sensors cannot be installed on the machine due to cost, space constraint or sensor reliability concerns. On the other hand, the use of an acoustic-based monitoring technique provides an improved alternative, as acoustic sensors (e.g., microphones) can be implemented quickly and cheaply in various scenarios and do not require physical contact with the machine. The collected acoustic signals contain relevant operating health information about the machine, yet they can be sensitive to background noise and changes in machine operating condition. These challenges are being addressed from the industrial applicability perspective for acoustic-based machine condition monitoring.

Solar generation has increased rapidly worldwide in recent years, and it is projected to continue to grow exponentially. A problem exists in that the increase in solar energy generation will increase the probability of grid disturbances. The study presented by Soto et al. [3] focuses on analyzing the grid disturbances caused by the massive integration into the transmission line of utility-scale solar energy loaded onto the balancing authority high-voltage transmission lines in four regions of the United States electrical system: (1) California, (2) Southwest, (3) New England, and (4) New York. A statistical analysis of the equality of means was carried out to detect changes in the energy balance and peak power. The results show that, when comparing the difference between hourly net generation and demand, energy imbalance occurs in the regions with the highest solar generation: California and Southwest. No significant difference was found in any of the four regions in relation to the energy peaks. The results imply that regions with greater utility-level solar energy adoption must conduct greater energy exchanges with other

**Citation:** Gil Bravo, A. Special Issue: Feature Papers in *Eng* 2022. *Eng* **2023**, *4*, 1156–1166. https://doi.org/ 10.3390/eng4020067

Received: 11 April 2023 Accepted: 12 April 2023 Published: 14 April 2023

**Copyright:** © 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

regions to reduce potential disturbances to the grid. It is essential to bear in mind that, as the installed solar generation capacity increases, the potential energy imbalances created in the grid increase.

The Jiles–Atherton model is commonly used in the hysteresis description of ferromagnetic, ferroelectric, magneto strictive and piezoelectric materials. However, the determination of model parameters is not straightforward because the model involves numerical integration and the solving of ordinary differential equations, both of which are error-prone. As a result, stochastic optimization techniques have been used to explore the vast ranges of these parameters in an effort to identify the parameter values that minimize the error differential between experimental and modelled hysteresis curves. Because of the timeconsuming nature of these optimization techniques, Khemani et al. [4] explored the design space of the parameters using a space-filling design. This design provides a narrower range of parameters to look at with optimization algorithms, thereby reducing the time required to identify the optimal Jiles–Atherton model parameters. The authors also indicate that this procedure can be carried out without using expensive hysteresis measurement devices, provided that the desired transformer's secondary voltage is known.

Nuclear energy is currently in the spotlight as a future energy source all over the world amidst the global warming crisis. In the current state of miniaturization, through the development of advanced reactors, such as small modular reactors (SMRs) and microreactors, a fission battery was created, inspired by the idea that nuclear energy can be used by ordinary people using the "plug-and-play" concept, such as chemical batteries. As for the design requirements, fission batteries must be economical, standardized, installed, unattended and reliable. Furthermore, the commercialization of reactors is regulated by national bodies, such as the United States (U.S.) Nuclear Regulatory Commission (NRC). At the international level, the International Atomic Energy Agency (IAEA) oversees the safe and peaceful use of nuclear power. However, regulations currently face a significant gap in terms of their applicability to advanced non-light water reactors (non-LWRs). Therefore, Lee and Diaconeasa [5] investigated the regulatory gaps in the licensing of fission batteries concerning safety in terms of siting, autonomous operation and transportation and suggested response strategies to supplement them. To determine the applicability of the current licensing framework to fission batteries, the authors reviewed the U.S. NRC Title 10, Code of Federal Regulations (CFR) and IAEA INSAG-12. To address siting issues, the authors also explored the non-power reactor (NPR) approach for site restrictions and the permit-by-rule (PBR) approach for excessive time burdens. In addition, they discussed how the development of an advanced human–system interface augmented with artificial intelligence and monitored by personnel for fission batteries may enable successful exemptions from the current regulatory operation staffing requirements. Finally, they also indicated that no transportation regulatory challenge exists.

Sharafeldin et al. [6] present in an interesting study that intersections are commonly recognized as crash hot spots on roadway networks. Therefore, intersection safety is a major concern for transportation professionals. Identifying and quantifying the impact of crash-contributing factors are crucial to planning and implementing the appropriate countermeasures. This study covered an analysis of nine years of intersection crash records in the State of Wyoming to identify the contributing factors to crash injury severity at intersections. The study involved an investigation of the influence of roadway (intersection) and environmental characteristics on crash injury severity. The results demonstrated that several parameters related to intersection attributes (pavement friction, urban location, roadway functional classification, guardrails and right shoulder width) and two environmental conditions (road surface condition and lighting) influence the injury severity of intersection crashes. This study also identified the significant roadway characteristics influencing crash severity and explored the key role of pavement friction, which is a commonly omitted variable.

In Ref. [7], Andersen et al. present the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for the treatment of crud deposition as a constraint while optimizing the light-water reactor core loading pattern. A neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated by the authors. The analysis showed that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence shows that boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the employed methods provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

For the first time, Zayed et al. [8] study the Fokas–Lenells equation in polarizationpreserving fibers with multiplicative white noise in the Itô sense. Four integration algorithms were applied by the authors, namely, the method of modified simple equation (MMSE), the method of sine-cosine (MSC), the method of Jacobi elliptic equation (MJEE) and ansatze involving hyperbolic functions.

The next study evaluated unsupervised anomaly detection methods in multispectral images obtained with a wavelength-independent synthetic aperture sensing technique called Airborne Optical Sectioning (AOS) [9]. With a focus on search-and-rescue missions that apply drones to locate missing or injured persons in a dense forest and require real-time operation, the authors evaluated the runtime vs. quality of these methods. Furthermore, they also showed that color anomaly detection methods that normally operate in the visual range always benefit from an additional far infrared (thermal) channel.

Tebuthiuron is a selective herbicide for woody species and is commonly manufactured and sold as a granular formulation. In an interesting study, the authors of [10] investigated the use of infrared spectroscopy for a quality analysis of tebuthiuron granules, specifically the prediction of moisture content and tebuthiuron content. A comparison of different methods showed that near-infrared spectroscopy showed better results than mid-infrared spectroscopy, while a handheld NIR instrument (MicroNIR) showed slightly improved results over a benchtop NIR instrument (Antaris II FT-NIR Analyzer). The best-performing models gave an R2CV of 0.92 and an RMSECV of 0.83% *w*/*w* for moisture content, and an R2CV of 0.50 and an RMSECV of 7.5 mg/g for tebuthiuron content. This analytical technique could be used to optimize the manufacturing process and to reduce the costs of post-manufacturing quality assurance.

Thixotropic behavior describes a time-dependent rheological behavior characterized by reversible changes. Fresh cementitious materials often require thixotropic behavior to ensure sufficient workability and proper casting without vibration. Non-thixotropic behavior induces a workability loss. Cementitious materials cannot be considered as an ideal thixotropic material due to cement hydration, which leads to irreversible changes. However, in some cases, cement paste may demonstrate thixotropic behavior during the dormant period of cement hydration. The aim of the work presented by El Bitouri and Azêma [11] was to propose an approach able to quantify the contribution of cement hydration during the dormant period and to examine the conditions under which the cement paste may display thixotropic behavior. The proposed approach consists of a succession of stress growth procedures that allow the static yield stress to be measured. For an inert material, such as a calcite suspension, the structural build-up is due to the flocculation induced by attractive Van der Waals forces. This structural build-up is reversible. For cement paste, there is a significant increase in the static yield stress due to cement hydration. The addition of superplasticizer allows the thixotropic behavior to be maintained during the first hours due to its retarding effect. However, an increase in the superplasticizer dosage leads to a decrease in the magnitude of the Van der Waals forces, which can erase the thixotropic behavior.

Biometrics deals with the recognition of humans based on their unique physical characteristics. It can be based on facial, iris, fingerprint or DNA identification. In Ref. [12], Hafeez et al. considered the iris as a source of biometric verification as it is a unique part of the eye that can never be altered, and it remains the same throughout an individual's life. The authors proposed an improved iris-recognition system including image registration as a main step, as well as an edge-detection method for feature extraction. This PCA-based method was also proposed as an independent iris-recognition method based on a similarity score. The experiments conducted using the developed database demonstrate that the first proposed system reduced the computation time to 6.56 s, and it improved the accuracy to 99.73, while the PCA-based method has less accuracy than this system.

The increasing implementation of distributed renewable generation lead to the need for Citizen Energy Communities. Citizen Energy Communities may be able to be active market players and to solve local imbalances. The liberalization of the electricity sector caused wholesale and retail competition, which is a natural evolution of electricity markets. In retail competition, retailers and communities compete to sign bilateral contracts with consumers. In wholesale competition, producers, retailers and communities can submit bids to spot markets, where the prices are volatile, or can sign bilateral contracts to hedge against spot price volatility. To participate in those markets, communities have to rely on risky consumption forecasts, hours ahead of real-time operation. So, as Balance Responsible Parties, they may pay penalties for real-time imbalances. This paper proposed and tested a new strategic bidding process in spot markets for communities of consumers. The strategic bidding process is composed of a forced forecast methodology for day-ahead and shortrun trends for intraday forecasts of consumption. This paper developed by Algarvio [13] also presents a case study where energy communities submit bids to spot markets to satisfy their members using the strategic bidding process. The results show that bidding at short-term markets leads to lower forecast errors than bidding at long and medium-term markets. Better forecast accuracy leads to better fulfillment of a community's programmed dispatch, resulting in lower imbalances and control reserve needs for power system balance. Furthermore, by being active market players, energy communities may save around 35% in their electrical energy costs when compared with retail tariffs.

Corn is an example of an agricultural grain with a specific combustibility level and can promote smoldering fires during storage. The interesting contribution of the study in Ref. [14] conducted an experimental design to numerically evaluate how three parameters, namely particle size, moisture, and air ventilation, influence the smoldering velocity. The work methodology was based on Minitab's experimental design, which defined the number of experiments. First, a pile of corn was heated by a hot plate, and a set of thermocouples registered all temperature variations. Then, a full-factorial experiment was implemented in Minitab to analyze the smoldering, which provided a mathematical equation to represent the smoldering velocity. The results indicate that particle size is the most influential factor in the reaction, with 35% and 45% variation between the dried and wet samples. Moreover, comparing the effect of moisture between corn flour and corn powder samples, variations of 19% and 31% were observed; additionally, analyzing the ventilation as the only variant, the authors noticed variations of 15% and 17% for dried and wet corn flour, respectively, and 27% and 10% for dried and wet corn powder, respectively.

Currently, tissue product producers try to meet consumers' requirements to retain their loyalty. In perforated products, such as toilet paper, these requirements involve the paper being portioned along the perforation line and not outside of it. Thus, it becomes necessary to enhance the behavior of the perforation line in perforated tissue papers. The study presented by Costa Vieira et al. [15] aimed to verify if the perforation line for 0◦ (the solution found in commercial perforated products) is the best solution to maximize the perforation efficiency. A finite element (FE) simulation was used by the authors to validate the experimental data, where the deviations from the experiments were 5.2% for the case with a 4 mm perforation length and 8.8% for a perforation of 2 mm, and to optimize the perforation efficiency using the genetic algorithm while considering two different cases. In the first case, the blank distance and the perforation line angle were varied, with the best configuration being achieved with a blank distance of 0.1 mm and an inclination angle of 0.56◦. For the second case, the blank distance was fixed to 1.0 mm and the only variable to be optimized was the inclination angle of the perforation line. It was found that the best angle inclination was 0.67◦. In both cases, it was verified that a slight inclination in the perforation line will favor partitioning and, therefore, the perforation efficiency.

Telecommunication companies collect a deluge of subscriber data without retrieving substantial information. An exploratory analysis of these types of data will facilitate the prediction of varied information that can be geographical, demographic, financial or other. Predictions can therefore be an asset in the decision-making process of telecommunications companies, but only if the information retrieved follows a plan with strategic actions. An exploratory analysis of subscriber data was implemented in this research to predict subscriber usage trends based on historical time-stamped data [16]. The predictive outcome was unknown but approximated using the data at hand. The author used 730 data points selected from Insights Data Storage (IDS). These data points were collected from the hourly statistic traffic table and subjected to exploratory data analysis to predict the growth in subscriber data usage. The Auto-Regressive Integrated Moving Average (ARI-MA) model was used for the forecasting. In addition, the author used the normal Q-Q, correlogram and standardized residual metrics to evaluate the model. This model showed a *p*-value of 0.007. This result supports the hypothesis predicting an increase in subscriber data growth. The ARIMA model predicted a growth of 3 Mbps, with a maximum data usage growth of 14 Gbps. In the experiment, ARIMA was compared with the Convolutional Neural Network (CNN) and achieved the best results with the UGRansome data. The ARIMA model performed better, with an execution speed that was faster by a factor of 43 for more than 80,000 rows. On average, it takes 0.0016 s for the ARIMA model to execute one row and 0.069 s for the CNN to execute the same row, thus making the ARIMA 43× (0.0690.0016) faster than the CNN model. These results provide a road map for predicting subscriber data usage so that telecommunication companies can be more productive in improving their Quality of Experience (QoE). This study provides a better understanding of the seasonality and stationarity involved in subscriber data usage's growth, exposing new network concerns and facilitating the development of novel predictive models.

Barbosa et al. [17] performed 2D micrometric mapping of different elements in different grain size fractions of the soil of a sample using the X-ray microfluorescence (μ-XRF) technique. The sample was collected in the vicinity of São Domingos, an old mine of massive sulphide minerals located in the Portuguese Iberian Pyrite Belt. As expected, elemental high-grade concentrations of distinct metals and metalloids dependent on the existing natural geochemical anomaly were detected. The authors developed a clustering and k-means statistical analysis considering red–green–blue (RGB) pixel proportions in the produced 2D micrometric image maps, allowing the authors to identify elementary spatial distributions in 2D. The results evidence how elemental composition varies significantly at the micrometric scale per grain-size class and how chemical elements present irregular spatial distributions due to direct dependence on the distinct mineral spatial distributions. Due to this fact, the elemental compositions are more different in coarser grain-size classes, whereas the grinding-milled fraction does not always represent the average of all partial grain-size fractions. Despite the complexity of the performed analysis, the achieved results evidence the suitability of μ-XRF in characterizing natural, heterogeneous, granular soils samples at the micrometric scale, being a very promising high-resolution investigation technique.

In Ref. [18], the author proposed an efficient method of identifying important neurons that are related to an object's concepts by mainly considering the relationship between these neurons and their object concept or class. He first quantified the activation values among neurons, based on which histograms of each neuron were generated. Then, the obtained histograms were clustered to identify the neurons' importance. A network-wide holistic approach was also introduced to efficiently identify important neurons and their influential connections to reveal the pathway of a given class. The influential connections, as well as their important neurons, were carefully evaluated to reveal the sub-network of each object's concepts. The experimental results on the MNIST and Fashion MNIST datasets show the effectiveness of the proposed method.

Safety reporting has long been recognized as critical to reducing safety occurrences by identifying issues early enough such that they can be remedied before an adverse outcome. The study in Ref. [19] examines safety occurrence reporting amongst a sample of 92 New Zealand civilian uncrewed aircraft users. An online survey was created to obtain the types of occurrences that these users have had, how (if at all) these are reported, and why participants did or did not report using particular systems. This work focused on seven types of occurrences that have been highlighted by the Civil Aviation Authority of New Zealand as being reportable using the CA005RPAS form, the template for reporting un-crewed aircraft occurrences to authorities. The number of each type of occurrence was recorded, as well as what percentage of occurrences were reported using the CA005RPAS form, reported using an internal reporting system or not reported. Qualitative questions were used by the authors to understand why participants did or did not report using particular systems. The categorical and numerical data were analyzed using Chi-Squared Tests of Independence, Kruskal–Wallis H Tests and Mann–Whitney U Tests. The qualitative data were analyzed using thematic analysis. The findings reveal that 85.72% of reportable safety occurrences went unreported by pilots, with only 2.74% of occurrences being selfreported by pilots using the CA005RPAS form. The biggest reason for not reporting was that the user did not perceive the occurrence as being serious enough, with not being aware of reporting systems and not being legally required to report also being major themes. Significant differences were also observed by the authors between user groups, thus leading to suggestions on policy changes to improve safety occurrence reporting, such as making reporting compulsory, setting minimum training standards, having an anonymous and non-punitive reporting system, and working with member-based organizations.

Using surrogate safety measures is a common method to assess safety on roadways. Surrogate safety measures allow for a proactive safety analysis; the analysis is performed prior to crashes occurring. This allows for safety improvements to be implemented proactively to prevent crashes, and the associated injuries and property damage. Existing surrogate safety measures primarily rely on data generated by microsimulations, but the advent of connected vehicles has allowed for the incorporation of data from actual cars into safety analyses with surrogate safety measures. In the study by Khanal and Edelmann [20], commercially available connected vehicle data were used to develop crash-prediction models for crashes at intersections and segments in Salt Lake City, Utah. Harsh braking events were identified and counted within the area of influence, inclusive of sixty intersections and thirty segments, and then used to develop crash-prediction models. Other intersection characteristics were considered as regressor variables in the models, such as the intersection's geometric characteristics, connected vehicle volumes, and the presence of schools and bus stops in the vicinity. Statistically significant models were developed by the authors, and these models may be used as a surrogate safety measure to analyze intersection safety proactively. The findings are applicable to Salt Lake City, but similar research methods may be employed by other researchers to determine whether these models are applicable in other cities and to determine how the effectiveness of this method endures through time.

Buried charges pose a serious threat to both civilians and military personnel. It is well established that soil properties have a large influence on the magnitude and variability of loading from explosive blasts in buried conditions. In Ref. [21], work was undertaken to improve techniques for processing pressure data from discrete measurement apparatuses; this was performed by testing truncation methodologies and the area integration of impulses, accounting for the particle size distribution (PSD) of the soils used in testing. Two experimental techniques were investigated by Waddoups et al. to allow for a comparison between a global impulse capture method and an area-integration procedure from a Hopkinson Pressure Bar array. This paper explores an area-limiting approach, based on particle

size distribution, as a possible approach to derive a better representation of the loading on the plate, thus demonstrating that the spatial distribution of a loading over a target can be related to the PSD of the confining material.

The rapidly increasing number of drones in the national airspace, including those for recreational and commercial applications, has raised concerns regarding misuse. Autonomous drone-detection systems offer a probable solution to overcoming the issue of potential drone misuse, such as drug smuggling, violating people's privacy, etc. However, detecting drones can be difficult, due to similar objects being in the sky, such as airplanes and birds. In addition, automated drone detection systems need to be trained with ample amounts of data to provide high accuracy. Real-time detection is also necessary, but this requires highly configured devices such as a graphical processing unit (GPU). The work in Ref. [22] sought to overcome these challenges by proposing a one-shot detector called You Only Look Once version 5 (YOLOv5), which can train the proposed model using pre-trained weights and data augmentation. The trained model was evaluated using mean average precision (mAP) and recall measures. The model achieved a 90.40% mAP, a 21.57% improvement over our previous model that used You Only Look Once version 4 (YOLOv4), and was tested on the same dataset.

The paper in Ref. [23] introduces a novel approach to leveraging features learned from both supervised and self-supervised paradigms, to improve image classification tasks, specifically for vehicle classification. Two state-of-the-art self-supervised learning methods, DINO and data2vec, were evaluated and compared by the authors for their representation learning of vehicle images. The former contrasts local and global views, while the latter uses masked prediction on multiple layered representations. In the latter case, supervised learning is employed to finetune a pretrained YOLOR object detector for detecting vehicle wheels, from which definitive wheel positional features are retrieved. The representations learned from these self-supervised learning methods were combined with the wheel positional features for the vehicle classification task. Particularly, a random wheel masking strategy was utilized to finetune the previously learned representations in harmony with the wheel positional features during training of the classifier. The experiments made by the authors show that the data2vec-distilled representations, which are consistent with our wheel masking strategy, outperformed the DINO counterpart, resulting in a celebrated Top-1 classification accuracy of 97.2% for classifying the 13 vehicle classes defined by the Federal Highway Administration.

Many current bioinformatics algorithms have been implemented in parallel programming codes. Some of them have already reached the limits imposed by Amdahl's law, but many can still be improved. Blaszynski and Bielecki [24] presented an approach that allows for the generation of a high-performance code for calculating the number of RNA pairs. The approach allows for the generation of a parallel tiled code with maximum-dimension tiles, which for the discussed algorithm, is in 3D. The experiments carried out on two modern multi-core computers, an Intel(R) Xeon(R) Gold 6326 (2.90 GHz, 2 physical units, 32 cores, 64 threads and 24 MB Cache) and Intel(R) i7(11700KF (3.6 GHz, 8 cores, 16 threads and 16 MB Cache), demonstrate a significant increase in performance and scalability of the generated parallel tiled code. For the Intel(R) Xeon(R) Gold 6326 and Intel(R) i7, target code speedup increased linearly with an increase in the number of threads. The approach presented in this paper to generate a target code can be used by programmers to generate target parallel tiled codes for other bioinformatics codes for which the dependence patterns are similar to those of the code implementing the counting algorithm.

Malware classification is a well-known problem in computer security. Hyperparameter optimization (HPO) using covering arrays (CAs) is a novel approach that can enhance machine learning classifier accuracy. The tuning of machine learning (ML) classifiers to increase classification accuracy is needed nowadays, especially with newly evolving malware. Four machine learning techniques were tuned using cAgen, a tool for generating covering arrays. The results included in Ref. [25] show that cAgen is an efficient approach to achieving the optimal parameter choices for ML techniques. Moreover, the covering array shows significant promise, especially cAgen with regard to the ML hyperparameter optimization community, malware detector community and overall security testing.

Musical timbre is a phenomenon of auditory perception that allows for the recognition of musical sounds. The recognition of musical timbre is a challenging task because the timbre of a musical instrument or sound source is a complex and multifaceted phenomenon that is affected by a variety of factors, including the physical properties of the instrument or sound source, the way it is played or produced, and the recording and processing techniques used. Gonzalez and Prati [26] explored an abstract space with 7 dimensions formed by the fundamental frequency and FFT-Acoustic Descriptors in 240 monophonic sounds from the Tinysol and Good-Sounds databases, corresponding to the 4th octave of the transverse flute and clarinet. This approach allowed the authors to unequivocally define a collection of points and, therefore, a timbral space (Category Theory) that allows for different sounds of any type of musical instrument with its respective dynamics to be represented as a single characteristic vector. The geometric distance allows for studying the timbral similarity between audios of different sounds and instruments or between different musical dynamics and datasets. Additionally, a machine learning algorithm that evaluates timbral similarities through Euclidean distances in the abstract space of seven dimensions was proposed by them. The authors conclude that the study of timbral similarity through geometric distances allowed us to distinguish between audio categories of different sounds and musical instruments, between the same type of sound and an instrument with different relative dynamics, and between different datasets.

When studying horizontally inhomogeneous media, it is necessary to apply tensor modifications of electromagnetic soundings. The use of tensor measurements is of particular relevance in near-surface electrical prospecting because the upper part of the geological section is usually more heterogeneously than the deep strata. In the Enviro-MT system designed for the controlled-source radiomagnetotelluric (CSRMT) sounding method, two mutually perpendicular horizontal magnetic dipoles (two vertical loops) are used for tensor measurements. In Ref. [27], a variant of the CSRMT method with two horizontal electrical dipole sources (two transmitter lines) was proposed. The advantage of such sources is an extended frequency range of 1–1000 kHz in comparison with a frequency range of 1–12 kHz for the Enviro-MT system, the greater operational distance (up to 3–4 km compared to 600–800 m), and the ability to measure the signal at the fundamental frequency and its subharmonics. To implement tensor measurements with the equipment of the CSRMT method described in this work, a technique inducing time-varying polarization of the electromagnetic field (rotating field) was developed by the authors based on the use of two transmitters with slightly different current frequencies and two mutually perpendicular transmitter lines grounded at the ends. In this way, the authors made it possible to change the direction of the electrical and magnetic field polarization continuously. This approach allows for the realization of a technique for tensor measurements using a new modified CSRMT method. In permafrost areas, hydrogenic taliks are widespread. These local objects are important in the context of the study of environmental changes in the Arctic and can be successfully explored using the tensor CSRMT method. For numerical modeling, a 2D model of the talik was used. The results of the interpretation of the synthetic data showed the advantage of bimodal inversion using the CSRMT curves of both TM and TE modes compared with separate inversion of the TM and TE curves. These new data demonstrate the prospects of the tensor CSRMT method in the study of permafrost regions. The problems that can be solved using the CSRMT method in the Arctic permafrost regions are also presented and discussed.

The sugar and alcohol sectors are dynamic as a result of climate alterations, the introduction of sugarcane varieties and new technologies. Despite these factors, Brazil stands out as the main producer of sugarcane worldwide, being responsible for 45% of the production of fuel ethanol. Several varieties of sugarcane have been developed in the past few years to improve features of the plant. This, however, led to the challenge of which variety producers should choose to plant on their property. In order to support this process, the research in Ref. [28] aims to test the application of the analytic hierarchy process (AHP) method to support producers in selecting which sugarcane variety to plant on their property. To achieve this goal, the authors relied on a single case study performed on a rural property located inland of São Paulo state, the main producer state in Brazil. The results demonstrate the feasibility of the used approach, specifically owing to the adaptability of the AHP method.

With the rapid development of modern technologies, autonomous or robotic construction sites are becoming a new reality in civil engineering. Despite various potential benefits of the automation of construction sites, there is still a lack of understanding of their complex nature when combining physical and cyber components in one system. A typical approach to describing complex system structures is to use tools of abstract mathematics, which provide a high level of abstraction, allowing for a formal description of the entire system while omitting non-essential details. Therefore, in Ref. [29], autonomous construction is formalized using categorical ontology logs enhanced by abstract definitions of individual components of an autonomous construction system. In this context, followed by a brief introduction to category theory and ologs, exemplary algebraic definitions were given as a basis for the olog-based conceptual modelling of autonomous construction systems. As a result, any automated construction system can be described without providing exhausting detailed definitions of the system components. Existing ologs can be extended, contracted or revised to fit the given system or situation. To illustrate the descriptive capacity of ologs, a lattice of representations was presented by the authors. The main advantage of using the conceptual modelling approach presented in this paper is that any given real-world or engineering problem could be modelled with a mathematically sound background.

Hypotrochoidal profile contours have been produced in industrial applications in recent years using two-spindle processes, and they are considered effective high-quality solutions for form-fit shaft and hub connections. This study presented by Ziaei [30] mainly concerns analytical approaches to determining the stresses and deformations in hypotrochoidal profile shafts due to pure bending loads. The formulation was developed according to bending principles using the mathematical theory of elasticity and conformal mappings. The loading was further used to investigate the rotating bending behavior. The stress factors for the classical calculation of maximum bending stresses were also determined for all those profiles presented and compiled into the German standard DIN3689-1 for practical applications. The results were compared with the corresponding numerical and experimental results, and very good agreement was found. This study contributes to further refinement of the current DIN3689 standard.

Shell structures have a rich family of boundary layers including internal layers. Each layer has its own characteristic length scale, which depends on the thickness of the shell. Some of these length scales are long, something that is not commonly considered in the literature. In Ref. [31], three types of long-range layers are demonstrated over an extensive set of simulations. The author indicates that the observed asymptotic behavior is consistent with theoretical predictions. These layers are shown to also appear on perforated structures underlying the fact these features are properties of the elasticity equations and not dependent on effective material parameters. The simulations were performed using a high-order finite element method implementation of the Naghdi-type dimensionally reduced shell model. Additionally, the effect of the perforations on the first eigenmodes is discussed. Finally, one possible model for buckling analysis is outlined.

Any stretch of coastline requires protection when the rate of erosion exceeds a certain threshold and seasonal coastal drift fluctuations fail to restore balance. Coast erosion can be caused by natural, synthetic or a combination of events. Severe storm occurrences, onshore interventions liable for sedimentation, wave action on the coastlines and rising sea levels caused by climate change are instances of natural factors. The protective methods used to counteract or prevent coastal flooding are categorized as hard and soft engineering techniques. The paper in Ref. [32] is based on extensive reviews and analyses of scientific publications. In order to establish a foundation for the selection of appropriate adaptation

measures for coastal protection, this study compiled the literature on a combination of both natural and artificial models using mangrove trees and polymer-based models' configurations and their efficiency in coastal flooding. Mangrove roots occur naturally and cannot be manipulated, unlike artificial model configuration, which can be structurally configured with different hydrodynamic properties. Artificial models may lack the real structural features and hydrodynamic resistance of the mangrove root that it depicts, and this can reduce its real-life application and accuracy.

In the final manuscript [33], presented as a communication, the author indicates that unmanned aircraft systems (UASs), commonly referred to as drones, are an emerging technology that has changed the way that many industries conduct business. Precision agriculture is one industry that has consistently been predicted to be a major locus of innovation for UASs. However, this has not been the case globally. The agricultural aircraft sector in the United States was used as a case study to consider different metrics in evaluating UAS adoption, including a proposed metric, the normalized UAS adoption index. In aggregate, UAS operators only make up 5% of the number of agricultural aircraft operators. However, the annual number of new UAS operators exceeded that of manned aircraft operators in 2022. When used on a state-by-state basis, the normalized UAS adoption index shows that there are regional differences in UAS adoption, with western and eastern states having higher UAS adoption rates and central states having significantly lower UAS adoption rates. This has implications for UAS operators, manufacturers and regulators as this industry continues to develop at a rapid pace.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**


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### *Review* **All-Purpose Nano- and Microcontainers: A Review of the New Engineering Possibilities**

**George Kordas**

Self-Healing Structural Materials Laboratory, World-Class Scientific Center of the Federal State Autonomous Educational Institution of Higher Education, Peter the Great St. Petersburg Polytechnic University, 195251 St. Petersburg, Russia; gckordas@gmail.com

**Abstract:** Recently, a subcategory of nanotechnology—nano-, and microcontainers—has developed rapidly, with unexpected results. By nano- and microcontainers, we mean hollow spherical structures whose shells can be organic or inorganic. These containers can be filled with substances released when given an excitation, and fulfill their missions of corrosion healing, cancer therapy, cement healing, antifouling, etc. This review summarizes the scattered innovative technology that has beneficial effects on improving people's lives.

**Keywords:** nanocontainers; microcontainers; self-healing; cancer; antibacterial; PCM; antifouling; corrosion

#### **1. Introduction**

The encapsulation of substances in a protective shell has recently become necessary because of the enormous technological possibilities in medicine [1], materials [2], energy [3], antifouling [4], antimicrobials [5], implants [6], the environment [7], etc. As a result, significant progress has also been made in manufacturing containers [8]. The primary method of their four-step production is firstly, the creation of the core; secondly, the coating of the core with the active shell; thirdly, the removal of the core; and finally, encapsulation with the active material. Reference is made here to production because containers can be produced differently, which is not mentioned in this article, e.g., LDH [9,10]. The present review covers the latest development in this technology via four-step production and gives examples of its industrial application. In this paper, we talk about organic and inorganic nanospheres in which each species is better suited to specific applications. CeMo (MBT or 8-HQ) nanospheres are inhibitors for applications in corrosion because they act simultaneously as a cathodic and anodic corrosion inhibitor. This property cannot be derived from the organic nanospheres that are best suited for cancer-fighting applications where we need artificially intelligent nanocontainers to diagnose and fight cancer. Intelligence cannot be obtained by inorganic nanospheres that are better suited to nontherapeutic applications, except for FeO nanospheres, to which hyperthermia can be applied to improve cancer treatment. Here, we can use the EPR effect to enter cancer via hyperthermia to cause destruction. The choice is made according to the problem we want to solve and the expected results. In addition, there are more applications of the nanocontainers not included in this publication, such as storage of hydrogen, food storage, cosmetic storage, etc., which will be the subject of another extensive review.

#### **2. Materials and Methods**

#### *2.1. Inorganic Containers*

In producing inorganic nanocontainers, we first produced a polystyrene core with well-known conditions in the bibliography. The polystyrene core's size determines the nanocontainers' final size. An earlier publication investigated the parameters affecting the polystyrene core's size [11]. Terminating the polystyrene core at a negative charge is

**Citation:** Kordas, G. All-Purpose Nano- and Microcontainers: A Review of the New Engineering Possibilities. *Eng* **2022**, *3*, 554–572. https://doi.org/10.3390/ eng3040039

Academic Editor: Antonio Gil Bravo

Received: 28 October 2022 Accepted: 25 November 2022 Published: 30 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

essential to deposit the metal oxides' salts on it [8]. Then, the sol–gel method deposited the metal oxide coatings, e.g., Ce(acac)3. The third stage involved the removal of polystyrene through combustion at 600 ◦C. Finally, we obtained a shell consisting of CeO2 [8], CeMo [12], TiO2 [13,14], CeOTiO2 [11], Fe2O3 [7], SiO2CaO [15], SiO2Na2O [6] and SiO2P2O5Na2O [6], depending on the alkoxides we used. In the final phase, the nanocontainers entered a vacuum chamber, where we received the maximum vacuum value. Then, we broke it with the materials dissolved in alcohols entering the chamber from a funnel, corrosion inhibitors, filling up the nanocontainers with the desired substance. In one case, paraffin entered the SiO2 to create phase-change materials [3]. There are cases where the core of SiO2 [16] nanocontainers consists of super absorbent polymers (SAP) suited for cement "self-healing" [17,18].

#### *2.2. Organic Containers*

One uses organic nanocontainers to treat cancer and other diseases [19,20]. The core is composed of PMMA, on which three walls are constructed: one is sensitive to temperature, the second is sensitive to pH, and the third is sensitive to redox. The polymeric nanocontainers are loaded with commercial drugs, such as doxorubicin. The containers are grafted with targeting groups to get bonded to cancer. Furthermore, the nanocontainers are grafted with gadolinium for MRI probes, iron oxide for hyperthermia, Fitch for locating them by fluorescent spectroscopy, etc. The literature has named this system quadrupole stimuliresponsive targeted nanocontainer or Nano4XX (XX = Dox, Daun, Cis, etc.) platforms. The synthesis of such platforms was the subject of several publications in recent literature [1,19]. Figure 1 shows the Nano4XX (XX = Dox, Daun, Cis, etc.) platform and the molecules one uses to produce them [21].

**Figure 1.** Quadrupole stimuli-responsive targeted nanocontainers loaded with cancer therapeutic drugs to treat cancer: the Nano4XX (Dox, Cis, etc.) platform.

#### **3. Discussion**

#### *3.1. Corrosion*

Protection against the corrosion of metals is performed by chemical methods designed to replace chromium salts. Several ways have evolved into different metals that offer entirely satisfactory protection. These coatings are, however, passive. They become active when introduced into these nanocontainers filled with inhibitors. With the stimulation caused by corrosion, the inhibitors are released, and thus interrupt the corrosion. This phenomenon is called "self-healing" [22] and is observed in all metals and nanocontainers. [11,13,23–28] Cerium molybdate hollow nanocontainers filled with

2-mercaptobenzothiazole incorporated into epoxy coating deposited onto galvanized steel samples show outstanding inhibition potential after a prolonged corrosion activity. The anodic and cathodic currents determined by SVET showed values close to the noise levels after 20 h of the exhibition to the salt solution until the end of the experiment in 50 h [22]. We attributed the corrosion activity to the organic inhibitor and inorganic inhibitor release of cerium ions from the nanocontainers. Figure 2 shows the SVET measurements of the sample to demonstrate the case.

**Figure 2.** Evolution of the total anodic and cathodic current of the sample containing CeMo (MBT).

Today, the technology of nanocontainers is evolving "intelligence" onto them, containing valves sensitive to the pH change of the environment. With this innovation, we hope for a better and more controlled performance of nanocontainers in stimuli due to corrosion. In a recent paper, mesoporous silicon nanocontainers were prepared and filled with benzotriazole (BTA) corrosion inhibitors. Nanocontainers contain nanovalves consisting of cucurbit [6] uril (CB [6]) rings attached to the surface of the nanocontainers. They do not undergo a corrosion inhibitor release when the pH is neutral. However, the release rate increases with increasing pH values in an alkaline solution. These nanocontainers respond to the pH, but how much better do they work compared to simple nanocontainers? Especially in commercial paints need to be studied better, but such a study is very innovative. Figure 3 shows their function.

**Figure 3.** Nanovalves sensitive to pH incorporated onto the surface of silica nanocontainers.

A recent review explains in great detail the state of the art of this technology [2]. We refer the reader to an update from this publication if they want to be informed more about the recent development.

#### *3.2. Antifouling*

When a metal surface encounters the marine environment, it is then quickly covered by a biofilm of microorganisms and further evolves from invertebrate animals that eventually corrode [29]. The result is that ships develop turbulences on their surface, increasing cruising friction, resulting in decreased vessel efficiency, which at the exact same time increases fuel requirements, and ultimately, increases air pollutants. One realizes that this has enormous economic consequences [30]. To avoid this problem, one can use antifouling coatings containing biocides and copper oxide. In this way, one stops the adhesion of organisms to the surfaces for some time. Most biocides effectively target the microorganisms created in the beginning: bacteria, algae, and barnacles. Biocides can be developed by looking for natural compounds that act as antifouling agents [31–39]. The sea has organisms that defend against biological pollution [40,41]. There are a large number of metabolites at sea that have the potential to grow as antifouling agents.

One such compound is bromosphaerol, isolated in algae cultivated in the marine area of Palaiokastritsas in Corfu. These algae were grown in greenhouse conditions to give large quantities, of which bromosphaerol was chemically isolated. Bromospaerol was encapsulated in copper oxide and zinc oxide nanocontainers to examine the biological aspects of behavior within commercial antifouling paints [4,29]. For this purpose, we used the antifouling bases of the paints of the Wilkens and Re-Turn companies, where we incorporated a small number of CuO and ZnO nanocontainers filled with bromosphaerol. We also used the bases of the two companies and the anticorrosion paints without impurities. We added a small amount of CeMo (8-HQ) to the anticorrosion paint. Figure 4 shows the paint configuration we obtained using basic commercial paints.

**Figure 4.** Paint configuration for lab testing and used for real-ship paint testing.

Figure 5a,b show the FRA of the two paints, one (a) consisting of the primer, anticorrosion with CeMo (8HQ) layer, and antifouling paint with CuO (Bromosphaerol); and the other (b) the Wilkens commercial paint. Both samples were exposed to the sea for three months. The FRA curves for the samples were the same before exposure to the seawater. On the contrary, the commercial paint's FRA dropped drastically, while our nanocontainer paint's FRA performed much better.

Figure 6 shows the FRA of another two paints, one (a) doped with CuO (S.N.) + ZnO (S.N.) and the other (b) with CuO (S.N.). Rp is about 1010 Ω before exposure of the samples to seawater. However, Rp improves for the samples immersed for three months in seawater. This behavior is known as the "self-healing" phenomenon.

The technology is useful when confirmed in practice. However, it was not easy to convince a paint-trading company to paint commercial ships before, firstly because it is dangerous for new technology not to meet the five-year guarantee given by commercial paints, and secondly, because the financial risk is significant if the new technology does not succeed. However, this was made possible by two companies, one Wilkens and the other Re-Turn, which intervened, and they painted a section of two ships, one traveling to the Adriatic sea and the other to different oceans, with speeds of 14 knots, for one year. Figure 7 shows the sections of the ships painted. It was a pleasant surprise in both cases to see the same results for the parts we painted with the technology of nanocontainers filled with bromophenol. The ships traveled in different marine conditions for a year, and the paints from our laboratory performed better than the commercial paints of the two companies [4,29,42].

**Figure 5.** FRA of paints ((**a**) nanocontainer technology and (**b**) commercial paint) before and after immersing the samples in seawater for three paints.

**Figure 6.** FRA of the paints: (**a**) top layer consisting of CuO (S.N.) and the ZnO (S.N.) nanocontainers, and (**b**) top layer consisting of CuO (S.N.) nanocontainers.

In a recent paper, Al2O3 and CuO nanoparticles were incorporated as a pigment using linseed alkyd resin as a binder. The samples were immersed in seawater for 120 days, and the properties were studied with modern spectroscopic techniques where a semantic improvement was observed in the antifouling of steel plates using Al2O3 and CuO compared to bare paint. The contact angle increased dramatically, suggesting that the paint

becomes more hydrophobic [43]. These new results confirm the impact of nanocontainers on Wilkens and Re-Turn commercial paints [2,4,24,26,29].

**Figure 7.** The segments of the two ships painted by our nanotechnology.

A relatively recent publication produced a fluorine-free superhydrophobic coating based on the TiO2 rosin-inoculated nanoparticles. The results were excellent regarding water repellency, which was attributed to the synergistic amplification between natural adhesives and hydrophobic TiO2 nanoparticles. In addition, the results have shown that such coatings will have great potential to cope with some of the antifouling paints [44].

#### *3.3. Antibacterial*

Organic and inorganic spheres are the subject of intense scientific activity due to their applications in biology, medicine, photocatalysis, etc. Heterogeneous polymerization methods prepare organic spheres [45–47]. Empty containers are interesting for coatings due to their lower density and optical properties. These can be coated with inorganic shells to modify their properties [48–53]. Photocatalysis uses empty titanium spheres to reduce Cr(VI) to Cr(III), working as an electron acceptor that finally precipitates as solid waste [53]. It is known that TiO2 appears in nature as brucite (orthorhombic), anatase (quadratic), and rutile (quadratic). Of these three phases, anatase is the most active in photocatalysis. Illumination of TiO2 by light with an energy higher than 3.2 eV and 3.0 eV for anatase and rutile induces electrons to jump from the valence zone to the conductivity zone, respectively. This transition causes pairs of electrons (e−) and electrical holes (h+) via photocatalysis. When an organic compound falls on the surface of the photocatalyst, it will react with the produced O2 − and OH, transforming into carbon dioxide and water. Thus, the photocatalyst decomposes organic matter in the air, including odor molecules, bacteria, and viruses. The Escherichia coli (*E. coli*) bacterium has been used many times for experimental purposes [54].

Hollow-nanosphere titania were used in one study, and their antibacterial activity was evaluated in *E. coli* [55]. Figure 8 shows the survival curve of *E. coli* cells for various conditions. First, the *E. coli* cell concentration was measured in the presence of TiO2. One observed about a 20% reduction in *E. coli* cells after 79 min of incubation. Furthermore, *E. coli* cells were exposed to illumination for 70 min and reduced close to 20%. The *E. coli* cell concentration went down to 0% quickly in the cases illuminated in TiO2. When the light went out after 30 min, followed by an additional 40 min incubation in the dark, one received the same number of viable cells at 70 min as the sample exposed to light for 70 min continuously.

**Figure 8.** *E. Coli* cell survival in the presence of TiO2 nanocontainers for *E. coli* + TiO2, *E. coli* + hv, *E. coli* + TiO2 + 30 min hν and *E. coli* + hv + TiO2.

The same experiments were conducted to investigate the antibacterial activity of hollow nanocontainers of cerium molybdenum (CeMo). Again, the hollow nanocontainers were exposed to *E. coli* culture. The study established parameters such as irradiation and time on the antibacterial activity of hollow nanospheres. Figure 9 shows the results of these studies [46]. One can perceive from this work that the E. coli cells in the presence of CeMo nanocontainers diminish after 10 min with or without exposure to the light. The CeMo is a "zero-light" antibacterial compound in the form of a nanocontainer, offering applications in the transport industry, etc.

**Figure 9.** Bacterial survival in CeMo hollow nanospheres' presence with or without light illumination.

#### *3.4. Energy*

Thermal energy storage can be carried out in two ways: with latent heat systems (LHS) or thermal energy storage (TES) systems. For LHS, storage is achieved by heat dissipation or by release through a change in the phase of the material. The high energy density and the narrow range of temperature make these materials effective in various applications. Organic phase-change materials include paraffin waxes, fatty acids, and polyethylene glycol. However, they cannot be used freely on devices because of the leakage they sustain that causes severe damage to the device. One solves this problem when LHS materials such as paraffin are trapped in nano- or microcontainers to store the working substance and do not escape into their incorporated material [56].

#### Nanocontainers Encapsulating PCMs

Implementing the material phase change (PCMs) in thermal energy storage gained significant attention due to the increase in energy consumption and the rescue of the environment from pollution. PCMs absorb, store, and release large amounts of latent heat at specified temperature ranges while phase changes improve device energy efficiency. Depending on the application, the size of the PCMs is selected. Typically, PCMs are classified into nanoPCMs, microPCMs, and macroPCMs, depending on the diameter. The size of the microPCMs usually varies from 1 mm to 1 mm, while capsules less than 100 nm are classified as nanoPCMs and capsules greater than 1 mm as macroPCMs. Encapsulated phase-change materials (EPCM) consist of PCMs with polymer cores and inorganic shells. Microcapsules and nanocapsules containing N-Octadecane in the melamine-formaldehyde shell are manufactured from spot polymerization.

The effects of stirring, the emulsifier's content, the cyclohexane's diameters, morphology, phase-change properties, and thermal stability of PCMs are studied using FT-IR, SEM, DSC, and TGA. For mass production, one can use the spray-drying technique. One can

also use the sol–gel method for their production [3]. In this study, the group observed for the latent heat a value of 156 J/g for paraffin and 80% encapsulation into the SiO2 containers. In a recent survey, n-octadecane paraffin wax as PCM was studied theoretically and experimentally in nanocontainers in terms of size and conditions of measurements. They observed a thin layer of melted PCM between the hot container wall and solid PCM. The concrete PCM sank and the liquid rose to the sphere's top half. Then, the natural convection became dominant at the top half of the sphere, where the melting rate was lower than the bottom half, causing a reduction in the heat transfer and melting rate in general. Encapsulation seaed the nanoparticles to prevent paraffin from being eliminated, and the process was repeated for many cycles [57]. This improvement in nanofluids' heat transfer coefficient impacts the size of the absorbent surface, water-heating time in a water heater, etc. An innovative method was described to encapsulate high-temperature PCM (salts and eutectics, NaNO3, KNO3, NaNO3-KNO3, NaNO3-KNO3-LiNO3) melt in the 120–350 ◦C temperature range [58]. The study was started to manufacture encapsulated PCMs that can endure the highly corrosive environment of molten alkali metal nitrate-based salts and their eutectics. The established technique does not need a sacrificial layer to lodge the volumetric expansion of the PCMs on melting and reduces the chance of metal corrosion inside the capsule. The encapsulation consists of coating a nonreactive polymer over the PCM pellet, followed by the deposition of a metal layer by a novel nonvacuum (more practical and economically feasible) metal deposition technique (for large-scale fabrication of capsules utilizing commercially available electroless and electroplating chemistry). The fabricated capsules survived more than 2200 thermal cycles (5133 h, equivalent to about 7 years of power plant service) [59]. The thermal cycling test showed no significant degradation in the thermophysical properties of the capsules and PCM on cycling at any testing stage [59].

#### *3.5. Biomaterials*

Today, there is a significant need for implants due to the large percentage of diseases, the treatment of which is mainly carried out by a surgical procedure. As far as the surgical procedure is concerned, there is excellent evolution due to the advanced antibiotics, new anesthetics, and stable implants for treating bone defects and motor problems. We call biomaterials the implants made by humans. Their use requires biocompatibility with the body, i.e., not causing thrombosis and toxic or allergic inflammations when used as implants in vital tissue. Furthermore, biomaterials must be stable on the surface of contact with the tissues to avoid breakage. Unfortunately, they do not heal themselves like tissues, which determines the time of their life and proper functioning.

Another category of biomaterials, which we call bioactive, react with their surface during contact with their normal body fluids, through which they develop a bond with the bone and tissues, with the result that the organism assimilates them. L. Hench prepared the first bioactive material in 1971 [60–62]. These materials are regenerative because they can suck and regenerate from the bones without leaving residues and are based on silica, calcium, phosphorus, and sodium elements. These materials should be cell-growth drivers facilitated by having a porous size of 100 μm [15,63]. These materials produce links with the tissues and are histogenic. The material produces only extracellular occlusion on its surface, and its surface is flooded by embryonic cells. A great premise is that these materials are prepared easily, repetitively, and economically. In a relatively recent paper, the synthesis of nanocontainers of the SiO2-CaO-P2O5 (SiCaP) system was performed with a relatively high concentration in Ca and P. The outer diameter was 330 nm and the thickness of the shell was 40 nm, leaving a cavity of about 250 nm. These properties, with their composition, make them candidates for bone tissue-regeneration applications. In another work, nanocontainers of systems: SiO2–CaO, SiO2–Na2OSiO2–P2O5–CaO, and SiO2–P2O5–Na2O were produced, and their osteogenic properties were examined [6]. Treatments in body fluid revealed their osteogenic properties due to the development of a surface-induced hydroxyapatite layer that resembled in structure the naturally occurring apatite component of bone, enhancing

bone development. These systems can be candidates for osteogenic applications tackling bone pathologies such as metabolic bone disease, trauma, and bone cancer ablation.

#### *3.6. Cement*

Reinforced concrete is a composite material that results from concrete reinforcement with other materials of greater strength. For example, steel in the form of rods is usually used as a reinforcement, and more rarely, fibers of glass, polymeric materials, and others. The aim is to combine the properties of the above materials into a new one that will meet the needs of the construction. The main disadvantage of concrete is its insufficient tensile strength. Therefore, the reinforcing material must have a high tensile strength to cover the concrete's weakness. In addition, the reinforcing material must have a similar coefficient of thermal expansion. Steel has both of these properties (Figure 10A). On the other hand, a disadvantage of steel is its susceptibility to corrosion (rust) and fire (Figure 10B).

**Figure 10.** Self-healing mechanism in concrete via bacteria and SAP in nanocontainers. (**A**) Concrete; (**B**) Concrete with crack, water induces corrosion on steel; (**C**) Concrete with bacteria, SAP, Nanocontainers filled with SAP or Bacteria; (**D**) Self-healing.

The microstructure of concrete is porous, which can be isolated or interconnected. Interconnected pores allow water and chemicals to penetrate the concrete. One can understand that permeability plays a vital role in the wear mechanism of concrete. Interconnected pores allow water and chemical compounds to penetrate the concrete matrix. Moreover, CO2 penetrates the pores to form the cement's alkaline components, e.g., Ca(OH)2. This makes it clear that the number of pores must be reduced to limit the movement of harmful substances into the uterus, resulting in iron corrosion. The bibliography has recently developed iron protection technology with ORMOSIL coatings reinforced with CeO2 (5-ATDT) nanocontainers. These coatings significantly increase metal protection from corrosion and

the appearance of the self-healing effect. Recently, the biological restoration technique has reduced the occlusion of newly formed cracks by introducing bacteria into the concrete. Figure 10C schematically presents this technology. This technology is based on incorporating a bacterium that metabolizes urea and immerses CaCO3 in the crack environment. Microbial immersion of CaCO3 is certified by several factors, such as the concentration of dissolved inorganic carbonate ions and the concentration of Ca2+ ions. Bacteria are protected from cement by encapsulation in microcontainers that do not show toxicity.

The spherical poly(methacrylic acids) microspheres of ~700 μm diameter were prepared by distillation–precipitation polymerization. The conversion of carboxylic groups followed this into their sodium salts by treatment with an aqueous sodium hydroxide solution. Figure 11 shows that these water-trap spheres can absorb water 70 times their weight. The absorption and drying cycles are repeated countless times.

**Figure 11.** SEM images of water traps capable of absorbing water 70 times their weight.

A recent study expanded previous work and produced P(MAA-co-EGDMA)@SiO2 by copolymerizing methacrylic acid (MAA) with ethylene glycol dimethacrylate (EGDMA) embedded in the cement slurry, which was found to maintain its structure by exhibiting chemical compatibility with it [16]. The production of P(MAANa-co-EGDMA) @CaO-SiO2 was an extension of the initial study. Flexural strength and compressive strength of cement-based composites were measured with concentrations bwoc: 0% SAPs, 0.5% SAPs, και 2% SAPs where it was 1.05 MPa, 1.51 MPa, and 1.83 MPa and 63.68 MPa, 59.67 MPa, and 56.27 MPa, respectively. Cracks of cement composites with 2% SAPs healed after 28 days [64].

#### *3.7. Nanomedicine*

When a person is diagnosed with cancer, doctors suggest three treatments: surgery, chemotherapy, and radiotherapy. All solutions are painful, with visible and invisible results. The visual effect of chemotherapy is hair loss, heart dysfunction, and many other unfortunate consequences for the patient. Chemotherapy causes a problem to the organs because a small part of the drugs ends up in cancer sites, and a significant fraction of the organs cause severe damage to their functionality. The question is: how can nanomedicine help alleviate the chemotherapy problem? To begin the discussion, let us answer the question: Is cancer the same as other healthy cells? The answer is: no! Cancer has different

temperature, pH, and redox values than healthy cells [19,20,65–68]. Can nanocontainers recognize that environment and deliver the chemotherapy drug locally? Another question is: Can nanocontainers target only cancer and provide the drug locally? The answer is yes if we use the nanocontainers of Figure 1. The shell of the Nano4XX platform consists of three polymers sensitive to temperature, pH, and redox. This platform contains magnetic nanoparticles for hyperthermia and targeting groups (folic acid for breast cancer, leuprolide for prostate cancer). The targeting groups can attach cancer-terminating groups, and via endocytosis can help the Nano4XX platform to enter cancer cells. The Nano4XX platform exhibits the same T, pH, and redox as cancer, so they can expand inside cancer and deliver the drug locally.

The realization of this technology involved several individual steps [1,7,19,69–72]. Extensive toxicological studies were conducted on animals [73]. We proved the targeting of cancer cells via positron emission tomography (PET) studies [19]. Figure 12 shows Nano4XX (Dox) functionalized with folic acid (F.A.) to target the cancer cells (HeLa) overexpressed at the surface of the explicit hormone. The nanocontainers enter the cancer cells, illuminating the cells red via Dox. On the contrary, the nanocontainers are not targeted with F.A. on the surface, coloring their site green due to Fitch. DNA replication is canceled by intercalation mode. [74,75] The Nano4XX (Dox) platform enters the cancer cells within 15 min of treatment, contrary to the nonfunctionalized Nano4XX (Dox) platform that agglomerates outside cancer cells.

**Figure 12.** Cell studies for targeting HeLa cells by confocal microscopy [74,76]. (**A**) Agglomeration because the Nano4XX platform is not FA grafted (green color Nano4XX); (**B**) FA grafted Nano4XX color the cancer cell surface green, inside the cancer cells are colored red due to Doxorubicin; (**C**) FA-grafted Nano4Dox enter the cancer cell where they release Doxorubicin inside resulting in a destruction of cancer.

Now that we know that the Nano4XX platform is entering cancer cells, we devised an experiment where the cytotoxicity of the Nano4XX (empty), Nano4Dox platform, and free doxorubicin (0.01, 0.1, 1, 5, 10, and 30 μM) was studied in the cell lines MCF-7 (breast carcinoma) and HeLa. (Cervical carcinoma) [77]. The F.A. receptor recognizes the HeLa cells located on their surface. [24–27] Measurements were made after incubating cells in the presence of Nano4XX with or without F.A. for 72 h. Figure 13 shows that Nano4XX (empty) is not toxic to MCF-7 cells for concentrations from 0.01 to 30 μM. However, once Nano4Dox and doxorubicin are encapsulated in cells, cytotoxicity is practiced in both cases. The same results were obtained in HeLa cells, respectively [76].

**Figure 13.** Cytotoxicity of F.A.-Nano4XX, FA-Nano4(Dox), and free DOX in MCF-7 cells repeated three times [5,18].

The PET measured Nano4 (Dox) biodistribution with and without F. A. in Hela mice bearing tumors. Figure 14 shows the distribution of Nano4 (Dox) with or without PET F.A. target groups across various organs and tumors. The measurement was made after a one-hour accumulation where we see the concentration of Nano4 (Dox) in cancer. The concentration in the volume Nano4 (Dox) with F. A. rises to 3.5% after one hour of accumulation [5,18]. Conversely, the attention in the volume without folic acid is zero [21].

Now that we know the Nano4 (Dox) platform with F. A. enters the cancer cells and acts on them; the question is whether they have a therapeutic effect. For this purpose, SCID mice bearing HeLa cervical tumors were studied and used to monitor cancer volume as a function of time in different groups. The experiments were carried out on two types of drugs: doxorubicin and cisplatin. The results are summarized in Figure 15. When the Nano4 (Dox) platform is not equipped with F. A., then there is an increase in cancer volume with time (Figure 15A). The same happens in administering cisplatin to animals with increased volume over time.

**Figure 14.** In vivo intake in 1 h in different organs and cancer for Nano4 (Dox) with and without F. A.

**Figure 15.** (**A**) The behavior of Nano4Dox. (Black line) increased cancer volume when nanocontainers were delivered with DOX; (green line) decrease in cancer volume when delivering FA-targeted nanocontainers loaded with DOX; (red line) decrease in cancer volume of FA-targeted nanocontainers loaded with DOX with an application of hyperthermia. (**B**) (Blue line) Increase in cancer volume when delivering cisplatin; (red line) decrease in cancer volume when producing cisplatin; (black line) further reduction in cancer volume with disposal of Nano4Cis platforms.

In contrast, the volume decreases with time for the Nano4 (Dox) platform when it incorporates the target molecule. In this case, a decrease in cancer volume by 20% is observed in 25 days (Figure 15A). The result is better when hyperthermia is induced in the treatment. The same effect is obtained in the case of the Nano4Cis platform, which shows better results than even lipoplatin. PET measurements have shown that 3.5% attaches to cancer when the Nano4XX platform (Dox, Cis) contains F.A. Toxicological studies and confocal microscopy measurements have found that the Nano4XX platform (Dox, Cis) enters cancer cells and works therapeutically. All these results suggest that the new system is effective in treating cancer. The Nano4XX platform has the intelligence to recognize cancer and act as a system with "artificial intelligence" because it distinguishes healthy cells from cancer cells. These experiments proved that Nano4XX (Dox, Cis) is significantly safer and more effective in vivo than the current gold standard, Doxil© (doxorubicin liposomal), an absolute nanomedical blockbuster in oncology [20,67,78,79]. This Nano4XX (Dox, Cis, etc.) technology has been patented with European and USA patents (see Patents).

#### **4. Conclusions and Perspectives**

Every nanocontainer technology has reached a specific technology readiness level (TRL = 1–9). For example, organic nanocontainers present artificial intelligence and have been tested in terms of their therapeutic efficacy with various anticancer drugs, a worldwide patent has been written, and a business plan has been drawn up. However, this technology has a TRL 7 where there must be human studies and GMP production of nanocontainers from now on. Such a Phase I and IIa clinical study costs EUR 10 million and lasts one year. With this, finding a pharmaceutical company to continue the development in the following phases will be straightforward.

The antifouling paint technology also has a significant technology readiness level, TRL 7, because the technology was tested on two commercial ships, produced on an industrial scale of the nanocontainers, and supported by a patent, and used ecological antifoulants. After a year of sailing, the vessel partially painted with nanotechnology showed much better results than commercial paints.

The technology of anticorrosion painting metals with CeMo (MBT, 8HQ) nanocontainers was made with the funding of two European projects, MULTIPROTECT and MUST, involving DAIMLER, FIAT, EADS, Chemetal, Mankiewicz, and Sika. Prototypes were made in representative metal parts, where nanotechnology paint technology was demonstrated using parts of automobiles and airplanes with a small mix of nanocontainers. In terms of TRL, this paint technology is very advanced because large companies were involved. It is up to the manufacturers to adopt and promote these technologies.

Other technologies, such as nanocontainers in biomaterials, cement self-healing, energy storage, and antimicrobial technology, are in the run-up but are promising technologies. In addition, discussions with industrial partners and funding agencies are underway to develop these technologies further. However, many questions have not been answered regarding the lifetime of these technologies. For example, a building requires the incorporation of self-healing nanocontainers at a time that has not been convincingly verified until today. Furthermore, as far as SiO2 (paraffin) PCMs are concerned, there are problems with exploiting paraffin by leakage of the nanocontainers that limit their lifetime to applications.

All these achievements, with a research effort of many researchers who have understood the opportunities offered by the nanocontainers, will soon be flooding the commercial world with nanocontainer-based products benefiting human beings. I hope this review will incentivize researchers to engage in this field with many innovations.

#### **5. Patents**

W.O. 2015/074762 A1, US2016263221, "MULTI-RESPONSIVE TARGETING DRUG DELIVERY SYSTEMS FOR CONTROLLED-RELEASE PHARMACEUTICAL FORMULA-TION".

**Funding:** Support by the grant Self-Healing Construction Materials (contract No. 075-15-2021-590 dated 4 June 2021) is greatly appreciated. The Nano4XX platforms were developed under the two IDEAS ERC Grants with the project acronyms Nanotherapy and grant numbers 232959 (AdG) and 620238 (PoC).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The author is thankful for support from the grant Self-Healing Construction Materials (Contract Nos. 075-15-2021-590 dated 4 June 2021).

**Conflicts of Interest:** There are no conflict of interest.

#### **References**


### *Review* **Acoustic-Based Machine Condition Monitoring—Methods and Challenges**

**Gbanaibolou Jombo 1,\* and Yu Zhang <sup>2</sup>**


**Abstract:** The traditional means of monitoring the health of industrial systems involves the use of vibration and performance monitoring techniques amongst others. In these approaches, contact-type sensors, such as accelerometer, proximity probe, pressure transducer and temperature transducer, are installed on the machine to monitor its operational health parameters. However, these methods fall short when additional sensors cannot be installed on the machine due to cost, space constraint or sensor reliability concerns. On the other hand, the use of acoustic-based monitoring technique provides an improved alternative, as acoustic sensors (e.g., microphones) can be implemented quickly and cheaply in various scenarios and do not require physical contact with the machine. The collected acoustic signals contain relevant operating health information about the machine; yet they can be sensitive to background noise and changes in machine operating condition. These challenges are being addressed from the industrial applicability perspective for acoustic-based machine condition monitoring. This paper presents the development in methodology for acoustic-based fault diagnostic techniques and highlights the challenges encountered when analyzing sound for machine condition monitoring.

**Keywords:** machine condition monitoring; anomalous sound detection; industrial sound analysis; detection and classification of acoustic scenes and events

#### **1. Introduction**

Unplanned interruption of industrial processes can result in serious financial losses; as such, it becomes of significant relevance to prevent unplanned shutdowns of machinery. The monitoring and diagnosis of the current health state of the machine is crucial in achieving this.

The conventional approach of machine health monitoring involves the use of vibration and other performance monitoring techniques. In these circumstances, sensors such as accelerometer, proximity probe, pressure transducer and temperature transducer are installed on the machine to monitor its health state. However, these methods are of an intrusive nature, requiring physical modification of the machine for their installation. Alternatively, the use of acoustic-based monitoring provides an improved approach which is non-intrusive to the machine operation. Sound signals from a machine contains substantial relevant health information; however, acoustic signals in an industrial environment can be affected by background noise from neighbouring operating machineries; thus, posing a challenge during industrial condition monitoring.

The analysis of sound has been successful in speech and music recognition, especially for creating smart and interactive technologies. Within this context, there exist several largescale acoustic datasets such as Audio Set [1] and widely available pre-trained deep learning models for audio event detection and classification such as: OpenL3 [2,3], PANNs [4] and VGGish [5]. However, within the context of machine condition monitoring and fault

**Citation:** Jombo, G.; Zhang, Y. Acoustic-Based Machine Condition Monitoring—Methods and Challenges. *Eng* **2023**, *4*, 47–79. https://doi.org/10.3390/ eng4010004

Academic Editor: Antonio Gil Bravo

Received: 26 October 2022 Revised: 26 December 2022 Accepted: 28 December 2022 Published: 1 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

diagnostics, these is a nascent problem for the detection and classification of acoustic scenes and events [6–8].

This paper presents the development in methodology for acoustic-based diagnostic techniques and explores the challenges encountered when analysing sound for machine condition monitoring.

#### **2. Methods—Acoustic-Based Machine Condition Monitoring**

*2.1. Detection of Anomalous Sound*

The goal of anomalous sound detection is to determine if the sound produced by a machine during operation typifies a normal or an abnormal operating state. The ability to detect such automatically is fundamental to machine fault diagnostics using data driven techniques. However, the challenge with this task is that sound produced from anomalous state operation of the machine is rare and varies in nature, hence presenting difficulty in collecting training dataset of such observed abnormal machine operating state. Furthermore, in actual industrial applications, it would be costly and damaging to consider running machines with implanted faults for the sake of data collection. Therefore, the traditional approaches which may be initially apparent such as framing the problem as a two-class classification problem becomes impractical.

In addressing the anomalous sound detection problem, consideration must be given to the fact that only training dataset of the machine running in its normal state would be available. As such, this forms the context within which the problem should be considered. Any such technique would have to learn the normal behaviour of the machine based on this available training dataset.

In furtherance of actualizing anomalous machine sound detection for industrial environment, saw the birth of the Detection and Classification of Acoustic Scenes and Events (DCASE) challenge task "Unsupervised Detection of Anomalous Sounds for Machine Condition Monitoring" in 2020. With the provision of a comprehensive acoustic training dataset combining ToyADMOS [9] dataset and MIMII dataset [10], six categories of machines (i.e., toy and real) of toy car, toy conveyor, valve, pump, fan, and slide rail, operating both in normal and abnormal conditions were considered; researchers were expected to develop and benchmark techniques for detection of anomalous machine sounds. Since the inclusion of this task as part of the DCASE Challenge, over the subsequent years, the task has evolved to account for challenges such as: domain shifted conditions (i.e., accounting for changes in machine operating speed, load, and background noise) [11] and domain generalisation (i.e., invariant to changes in machine operating speed, load, and background noise) [12].

The challenge of machine anomaly detection is to find a boundary between normal and anomalous operating sound. In achieving this, the following methods have emerged.

#### 2.1.1. Autoencoder-Based Anomaly Detection

An autoencoder is a neural network, trained to learn the output as an accurate reconstructed representation of the original input. As an unsupervised learning technique, it has been used by several studies for the detection of anomalous machine operating sound [7–10,13–15].

Autoencoder acts as a multi-layer neural network as shown in Figure 1, consisting of the following segments: encoder network, which accepts a high-dimensional input and transforms to a low-dimensional representation, decoder network, which accepts a latent low-dimensional input to reconstruct the original input, and at least a bottleneck stage within the network architecture. The presence of the bottleneck stage acts to compress the knowledge representation of the original input in order to learn the latent space representation. When the autoencoder is used for anomaly detection the goal during training is to minimize the reconstruction error between the input and the output using the normal machine operating sounds. Herein, the reconstruction error is used as the anomaly score. Anomalies are detected by thresholding the magnitude of the reconstruction error. Based on the application, this threshold could be set. Once an anomalous machine operating sound

is provided to the system, it would yield a higher-than-normal reconstruction error, thereby flagging as a fault mode. Table 1 provides baseline autoencoder architecture parameters as applied for anomaly detection. Purohit et al. [10] implemented AE for anomaly detection based on acoustic dataset of malfunctioning industrial machines consisting of faulty valve, pump, fan, and slide rail. Although the dataset used MIMII [10] has been made publicly available, a key part of their work is the adopted architecture of their AE model. Purohit et al. [10] based the input layer on the log-Mel spectrogram. The Mel spectrogram is a spectrogram where frequencies have been transformed to the Mel scale. The Mel spectrogram provides a good correlation with human perception of sound, due to the Mel scale representing scale of pitches that humans would perceive to be equidistant from each other. As such, it not uncommon to find log-Mel spectrogram as performant input feature representation for acoustic event classification amongst others [16]. In [10], the log Mel spectrogram was determined for a frame size of 1024 acoustic time series data points, with a hop size of 512 and 64 Mel filter banks. This results in a log Mel spectrogram of size equal 64. This process was repeated for five consecutive frame sizes. The final input layer feature is formed by concatenating the log Mel spectrogram of five consecutive frames, resulting in an input feature vector size of 5 × 64 = 320. This is feed into an auto-encoder network with fully connected layers (FC) such as: encoder section—FC (input, 64, ReLU), FC (64, 64, ReLU), and FC (64, 8, ReLU) and decoder section—FC (8, 64, ReLU), FC (64, 64, ReLU) and FC (64, Output, none). Here, FC (x, y, z) translates fully connected layer with x input neurons, b output neuron, and z activation function such as rectified linear units (ReLU). The implemented AE model is trained for 50 epochs using Adam optimization approach. Similar approach can be adopted using the baseline AE topologies in Table 1.

**Figure 1.** Schematic of an autoencoder [17].


#### **Table 1.** Baseline auto encoder system architecture for anomaly detection.

\* STFT: Short-Time Fourier Transform; ReLU: Rectified Linear Unit; MFCC: Mel-Frequency Cepstral Coefficients.

2.1.2. Gaussian Mixture Model-Based Anomaly Detection

Gaussian Mixture Model (GMM) is an unsupervised probabilistic clustering model that assumes each data point belongs to a Gaussian distribution with unknown parameters. As an unsupervised learning technique, it has been used by several studies for the detection of anomalous machine operating sound [19–21].

GMM approach finds a mixture of multi-dimensional Gaussian probability distributions that most likely model the dataset. To achieve this, expectation-maximisation algorithm is used to estimate the parameters of the Gaussian distributions: mean, covariance matrix and mixing coefficients. Expectation-maximisation method is a two-step iterative process which aims to find the maximum likelihood estimates of the Gaussian mixture parameters. It alternates between the expectation step and the maximisation step. Within the expectation step, the responsibilities (which data point belongs to which cluster) are determined using the current estimate of the model parameters, while the maximisation step estimates the model parameters for maximizing the expected log-likelihood function. GMM for anomaly detection uses trained GMM model based on acoustic features as shown in Table 2 to predict the probability of each datapoint being part of one of the k Gaussian

distribution clusters. An anomaly is detected by a data point having a probability lower than a threshold which could be either a percentage or a value threshold.

**Table 2.** Baseline GMM acoustic features.


#### 2.1.3. Outlier Exposure-Based Anomaly Detection

Outlier Exposure (OE) is an approach for improved anomaly detection in deep learning models [22]. Key in this method is the use of an out-of-distribution dataset, to fine tune a classifier model that enables it to learn heuristics that discriminate in-distribution data points from anomalies. The learned heuristics then has the capability to generalize to new distributions. The OE methodology, first proposed by [22], is achieved by adding a secondary loss to the regular loss for in-distribution training data, which is usually a cross-entropy loss or an error loss term. For classification models, the secondary loss is also a cross-entropy loss computed between the outlier logits and a uniform distribution.

The OE approach has already been applied in the domain of detecting anomalous machine operating sound using classifier models such as MobileNetV2 [11,12]. Herewith, MobileNetV2 [23] is trained to identify from which data segment within both in-distribution and out-of-distribution datasets the observed signal was generated (machine anomaly identification). The trained classifier then outputs the SoftMax value that is the predicted probability for each data segment. The anomaly score becomes the averaged negative logit of the predicted probabilities of the correct data segment. Table 3 shows baseline parameters for an OE approach using MobileNetV2 classifier model.

**Table 3.** Baseline OE architecture based on MobileNetV2.


#### 2.1.4. Signal Processing Methods

Acoustic signal processing methods are an adaptation from existing vibration-based approaches reliant on time, frequency, and time-frequency domain analysis of the signal.

Time domain analysis is performed on the acoustic signal time series representation through statistical analysis for calculating feature parameters such as mean, standard deviation, skewness, kurtosis, decibel, crest factor, beta distribution parameters, root mean square, maximum value, etc. These calculated statistical feature parameters from the acoustic signal are used to provide an overall indication of the current health condition of the machine. This approach, although simplistic, has been explored by various investigations for acoustic-based machine fault detection: e.g., Heng and Nor [24] evaluated the applicability of the statistical parameters such as crest factor, kurtosis, skewness, and beta distribution as fault indicators from acoustic signals for monitoring rolling element bearing defect.

For a machine operation under steady state conditions, frequency domain analysis techniques are commonly applied to examine the acoustic signals. Fast Fourier Transform (FFT), a computationally cheap technique to transform time-domain signals to the frequency domain, has been applied in acoustic-based condition monitoring of electric induction motors [25,26], engine intake air leak [27], among others. To capture nonlinear and nonstationary processes in machine operations, Ensemble Empirical Mode Decomposition (EEMD) method has been used [28]. EEMD simulates an adaptive filter, extracting underlying modes in the signal to decompose into a series of intrinsic mode functions (IMF) from high to low frequency content. Spectrum of IMFs has been adopted as a fault indicator for detecting incipient faults in wind turbine blades from acoustic signals [29].

Furthermore, time-frequency domain analysis, such as, short time Fourier transform and wavelet transform, are also powerful approaches for capturing nonstationary processes within machinery acoustic signals. Grebenik et al. [30] used consumer grade microphones and applied EMD and wavelet transform as diagnostic criteria for the acoustic fault diagnostics of transient current instability fault in DC electric motor. Spectral autocorrelation map of acoustic signals has been applied for detection of fault in belt conveyor idler [31]. EMD and wavelet analysis has been applied to extract features from acoustic signals produced by a diesel internal combustion engine for monitoring its combustion dynamics [32,33]. Anami and Pagi [34] used the chaincode of the pseudospectrum to analyse acoustic fault signals from a motorcycle for fault detection.

#### *2.2. Classification of Anomalous Sound*

The goal of classification of anomalous sound is to categorise a machine sound recording into one of the predefined fault classes that characterises the machine fault state.

Two main approaches have emerged for machine fault diagnostics based on acoustic signal. The first based on feature-based machine learning techniques and the second based on 2D acoustic representation deep learning approaches.

#### 2.2.1. Feature-Based Machine Learning Methods

Feature-based machine learning methods can be broken into three stages. The first stage involves, extracting features from the machine condition acoustic signals. Features are important as fault descriptors are determined using statistical methods, fast Fourier transform, EEMD, or wavelet transform, etc. Extracted features are used to train a machine learning classifier such as Support Vector Machine (SVM), k-Nearest Neighbor (kNN), Random Forest (RF), logistic regression, naïve Bayes, Deep Neural Network (DNN), etc. The trained ML model is then used as a predictor for machine health state based on unknown machine condition acoustic signals.

This approach for machine fault detection based on acoustic inputs is presented in Figure 2. Although the system consists of several steps, the focus here would be in addressing the challenges in engineering feature extraction and for selecting appropriate classifier learning algorithm.

**Figure 2.** Schematic of feature extraction-based technique for machine fault detection based on acoustic inputs.

(1) Feature Extraction

An approach for acoustic signal representation is required, which is capable to differentiate normal and abnormal operating sound from machinery, utilising low-level features derived from the time domain, frequency domain and time-frequency domain of the acoustic signal. This is achieved as follows and summarized in Table 4:

(a) Time domain-based feature extraction

Time domain features find their basis from descriptive statistical parameters derived from the acoustic signal time-series for representation of both healthy and faulty machine states and training various machine learning models. This approach has been adopted by several investigators [35] and relevant time-domain parameters summarized in Table 4.

(b) Frequency domain-based feature extraction

Frequency domain features take their basis from the Fourier transform spectral transformation of the acoustic signal. Pasha et al. [36] used a band-power ratio as discriminant feature from acoustic signals to monitor air leaks in a sintering plant associated with pallet fault. Here, band-power ratio refers to the ratio of the spectral power within the fault frequency band to the spectral power of the entire signal spectrum. In [36], the feature extraction from a sound recording consisted of the band-power ratio performed repeatedly at fixed sampling window length (i.e., 1024 samples) within the fixed time duration/recording. Other potential parameters can be extracted from the frequency spectrum as demonstrated by [37] and listed in Table 4.

(c) Time-frequency domain-based feature extraction

Time-frequency signal analysis refer to approaches that enable the simultaneous study of signals in both time and frequency domain. The time-frequency representations, such as STFT, wavelet transform, Hilbert-Huang transform, amongst others, provide useful parameters to characterise acoustic signals. Based on the work of [37], relevant timefrequency parameters are provided in Table 4.




#### **Table 4.** *Cont.*

#### (2) Classifier Learning Algorithms

Classifier learning algorithms provide an automated intelligent approach for the detection and classification of machine faults. The generally adopted approach for the development of these machine fault inference systems are based on machine learning classifiers. The machine learning classifier is a supervised learning model that can learn a function that maps an input to a categorical output based on the example input-output pairs [38]. The input for the machine learning classifier model includes the extracted features from the acoustic signal, while the output is the class labels which represent different operational or health state of the machine. To further estimate the optimal classifier model, a cross validation technique can be applied to tune the hyper-parameters of each model.

There are several types of supervised machine learning classifier models, such as: logistic regression, naïve Bayes, decision trees, RF, k-nearest neighbor (kNN), SVM, discriminant analysis, DNN, etc. [39,40]. Each machine learning classifier model has its strengths and weaknesses; for an application, choosing the most appropriate is mostly based on comparing the accuracy and other performance metrics, such as recall rate, F-score, true positive rate, false positive rate, etc. Table 5 highlights exemplar applications of machine learning classifiers for the classification of machine operating sounds.


plane. Sometimes, the data are not linearly separable, SVM circumvents this by adopting either a soft margin parameter in the optimisation loss or using kernel tricks to transform the feature set into a higher dimensional space.


$$P(Y|features) = \left(P(features|Y) \times P(Y)\right) / P(features) \tag{1}$$

where *<sup>P</sup>*(*f eatures*|*Y*) represent probabilities or likelihood of the features given the class label determined from a naïve assumption of a generative model underlying the dataset such as Gaussian distribution, multinomial distribution, or Bernoulli distribution; *P*(*Y*) is the prior probability or initial guess for the occurrence of the class label based on the underlying dataset.

(f) Artificial Neural Network (ANN)/Multi-Layer Perceptron (MLP): ANN or MLP is inspired by the brain biological neural system. It uses the means of simulating the electrical activity of the brain and nervous system interaction to learn a data-driven model. The structure of an ANN comprises of an input layer, one or more hidden layers and an output layer as shown in Figure 3 [39]. Each layer is made up of nodes or neurons and is fully connected to every node in the subsequent layers through weights (w), biases (b), and threshold/activation function. Information in the ANN move in two directions: feed forward propagation (i.e., operating normally) and backward propagation (i.e., during training). In the feedforward propagation, information arrives at the input layer neurons to trigger the connected hidden neurons in subsequent layer. All the neurons in the subsequent layer do not fire at the same time. The node would receive the input from previous node, this is multiplied by the weight of the connection between the neurons; all such inputs from connected previous neurons are summed at each neuron in the next layer. If these values at each neuron is above a threshold value based on chosen activation function, e.g., sigmoid function, hyperbolic tangent (tanh), rectified linear unit (ReLU), etc. the node would fire and pass on the output, or if less than the threshold value, it would not fire. This process is continued for all the layers and nodes in the ANN operating in the feedforward mode from the input layer to the output layer. The backward propagation is used to train the ANN network. Starting from the output layer, this process

compares the predicted output with actual output per layer and updates the weights of each neuron connection in the layer by minimize the error using a technique such as gradient descent amongst others as shown in Figure 3. This way, the ANN model learns the relationship between the input and output.

**Figure 3.** Structure of an artificial neural network (ANN) (**a**) ANN (**b**) single neuron or node (**c**) optimizing weights using gradient descent.


**Table 5.** Exemplar classifier learning algorithm for classification of machine operating sounds.

#### 2.2.2. Acoustic Image-Based Deep Learning Methods

This approach leverages techniques from the field of machine hearing [45]. Machine hearing involves sound processing considering inherent sound sensing system structures as humans and sound mixtures in realistic context [45].

In emulating human hearing, machine hearing adopts a four-layer architecture within which each layer represents a distinct area of research. The first layer, auditory periphery layer (cochlea model), mimics the representation of the nonlinear sound wave propagation mechanism in the cochlea as cascading filter systems; the second layer, auditory image computation, provides a projection of one or more forms of auditory images to the auditory cortex mimicking the auditory brain stem operation; the third layer abstracts the operation within the auditory cortex via extraction of application-dependent features from the auditory images; the final and forth layer addresses the application specific problem using appropriate machine learning system [46].

For application in classifying anomalous machine operating sound, variations are made in the auditory image computation representation; as such, best referred to as acoustic image representation. From the literature, there have been several possibilities for the 2D acoustic image representation such as: spectrogram (from STFT), Mel-spectrogram, cochleagram, amongst others [47,48]. Table 6 provides a summary of acoustic image representation in combination with deep learning models for classifying anomalous machine operating sounds and Figure 4 shows examples of acoustic image representations.

**Figure 4.** Acoustic image representation (**a**) acoustic input (**b**) spectrogram of acoustic input (**c**) cochleagram of acoustic input (**d**) Mel spectrogram of acoustic input [16].


first divided into smaller segments of equal length with some overlap; then, fast Fourier transform (FFT) is applied to each segment to determine its frequency spectrum; the resulting spectrogram becomes a side-by-side overlay of the frequency spectrum of each segment over time. FFT represents an algorithm to compute the discrete Fourier transform (DFT) of the windowed time-domain signal, represented as [16]:

$$F\_n = \sum\_{k=0}^{N-1} \mathbf{x}\_n w\_n e^{-2\pi i nk/N}, \ n = 0, \cdots, N-1 \tag{2}$$

where *Fn* is discrete Fourier transform, *N* is number of sample points within the window, *fk* is the discrete time-domain signal, and *wn* is the window function. The spectrogram is obtained as the logarithm of the DFT, as such [16]:

$$S\_n = \log |F\_n|^2 \tag{3}$$

where *Sn* is spectrogram, and *Fn* is discrete Fourier transform.

(b) Mel Spectrogram: This is a spectrogram where frequencies have been transformed to the Mel scale as shown in Figure 5. The Mel scale is a linear scale model of the human auditory system, represented as [49,50]:

$$f\_{\rm mel} = 2595 \times \log\_{10}(1 + f/700) \tag{4}$$

where *fmel* is frequency on the Mel scale, and *f* is frequency from the spectrum.

As shown in Figure 5, Mel spectrogram is computed by passing the result of windowed times-series signal FFT for each smaller segment of the divided signal through a set of half-overlapped triangular band-pass filter bank equally spaced on the Mel scale. The spectral values outputted from the Mel band-pass filter bank are summed and concatenated into a vector of size dependent on the number of Mel filters, e.g., 128, 512, etc. The resulting Mel spectrogram becomes a side-by-side overlay of the resulting vector representation from each consecutive time-series signal segment over time.

**Figure 5.** Mel spectrogram operation.

(c) Cochleagram: A cochleagram is a time-frequency representation of the frequency filtering response of the cochlea (in the inner ear) as simulated by a bank of Gammatone filters [48]. The Gammatone filter represents a pure sinusoidal tone that is modulated by a Gamma distribution function; the impulse response of the Gammatone filter is expressed as [16]:

$$h(t) = At^{n-1}e^{-2\pi bt}\cos(2\pi f\_{cm}t + \phi) \tag{5}$$

where *A* is amplitude, *n* is filter order, *b* is filter bandwidth, *fcm* is filter centre frequency, *φ* is phase shift between filters, and t is time.

As shown in Figure 6, cochleagram is computed by passing the result of windowed times-series signal FFT for each smaller segment of the divided signal through a series of overlapping band-pass Gammatone filter bank. The spectral values outputted from the Gammatone filter bank are further transformed by logarithmic and discrete cosine transform operations before been summed and concatenated into a vector of size dependent on the number of Gammatone filters, e.g., 128, etc. The resulting cochleagram becomes a side-by-side overlay of the resulting vector representation from each consecutive time-series signal segment over time.

**Figure 6.** Cochleagram operation.


= 32 × 32, ReLU, max. pooling = 2 × 2), and fully connected layer (shape = 64 × 64, ReLU, max. pooling = 2 × 2) and a final classification stage based on multi-layer perception with 512 hidden nodes, ReLU and sigmoid activation function. Dataset was very sparse, and model was not optimized; therefore, impacting model performance on training accuracy. Table 6 highlights other applications of acoustic image-based classifiers of anomalous machine operating sounds.

**Figure 7.** CNN basic architecture [51].

(b) Recurrent Neural Network (RNN): RNN is a type of neural network which uses sequential data or time series data to learn. Unlike CNN, RNN have internal memory state (i.e., can be trained to hold knowledge about the past); this is possible as inputs and outputs are not independent of each other, prior inputs influence the current input and output; simply put, output from previous layer state are feed back to the input of the next layer state. As shown in Figure 8, x is input layer, h is middle layer (i.e., consist of multiple hidden layers) and y is output layer. W, V and U are the parameters of the network such as weights and biases. At any given time (t), the current input is constituted from the input x(t) and previous x(t − 1); as such the output from x(t − 1) is feedback into the input x(t) to improve the network output. This way, information cycles through a loop within the hidden layers in the middle layer. RNN uses the same network parameters for every hidden layer, such as: activation function, weights, and biases (W, V, U). Despite the flexibility of the basic RNN model to learning sequential data, they suffer from the vanishing gradient problem (i.e., difficulty training the model when the weights get too small, and the model stops learning) and exploding gradient problem (i.e., difficulty training the model due to very high weight assignment). To overcome these challenges, the long short-term memory (LSTM) network variant of RNN is normally used. LSTM has the capability to learn long-term dependencies between time steps of sequential data. LSTM can read, write and delete information from its memory. It achieves this via a gating process made up of three stages: forget gate, update/input gate and output gate which interacts with is long-term memory and short-term memory pathways used to feedback its memory states amongst hidden layers. As shown in Figure 9, "c" represents the cell state and long-term memory, "h" represents the hidden state and short-term memory, and "x" represent the sequential data input. The forget gate determines how much of the cell state "c" is thrown away or forgotten. The update gate determines how much of new information is going to be stored in the cell state, and output gate determines what is going to be outputted. [52] has applied LSTM RNN with cochleagram features to classify varying rolling-element bearing faults based on 60 s acoustics signals. Implemented model consisted of an input feature set based on 128 gammatone filter bank cochleagram; Considering a 1 s. duration as a frame, the 60 s dataset generated 60-time frames. Each frame is represented as a cochleagram. 67% of the dataset was used to train the LSTM RNN model and 33% for testing. Model accuracy

on fault classification task was 94.7%. Table 6 highlights other applications of acoustic image-based classifiers of anomalous machine operating sounds.

**Figure 8.** RNN basic architecture.

**Figure 9.** LSTM RNN architecture [52].

(c) Spiking Neural Network (SNN): SNN is a brain-inspired neural network where information is represented as binary events (spikes). It shares similarity with concepts such as event potentials in the brain. SNN incorporates time into its propagation model for information; SNN only transmit information when neuronal potential exceeds a threshold value. Working only with discrete timed events, SNS accepts as input spike train and outputs spike train. As such, information is required to be encoded into the spikes which is achieved via different encoding means: binary coding (i.e., all-or-nothing encoding with neurons active or inactive per time, rate coding, fully temporal codes (i.e., precise timing of spikes), latency coding, amongst others [53]. As shown in Figure 10, SNN is trained with the margin maximization technique, described in [54]. During first epoch, SNN hidden layer is developed based on neuron addition scheme. In subsequent epochs, the weights and biases of the hidden layer neurons are updated further using the margin maximization technique. Here, weights of the winner neuron are strengthened, while those of the others are inhibited; this reflects the Hebbian learning rule of the natural neurons; as a result, neurons are only connected to their local neurons, so they process the relevant input patterns together. This approach maximizes the margin among the classes which lends itself to training the spike patterns. Ref. [48] has applied SNN with cochleagram features to classify varying rolling-element bearing faults based on 10 s acoustics signals. Implemented model consisted of an input feature set based on 128 gammatone filter bank cochleagram; later reduced to 50 using principal component analysis (PCA). Considering a 10 ms duration as a frame, the 10 s dataset generated 1000-time frames. Each frame was encoded into a spike train using the population coding method. 90% of the dataset was used to train the SNN model and 10% for testing. Model accuracy was above 85%. Table 6 highlights other applications of acoustic image-based classifiers of anomalous machine operating sounds.

**Figure 10.** SNN architecture [48].



\* CNN: Convolutional Neural Network, RNN: Recurrent Neural Network, SNN: Spiking Neural Network.

#### **3. Datasets for Detection and Classification of Anomalous Machine Sound (DCAMS)**

Openly available datasets are vital for progress in the data-driven machine condition monitoring approaches. In recent time, there have been significant progress in the corollary area of acoustic scene classification mainly due to opensource dataset such as: AudioSet dataset [1], which provides a collection over 2 million manually labelled 10 s sound segments from YouTube within 632 audio event classes. However, nothing of such large scale is available for Detection and Classification of Anomalous Machine Sounds (DCAMS). Within limited scale, several research projects are beginning to lay the foundation as they were bridging the dataset gap for DCAMS.

#### *3.1. ToyADMOS Dataset*

This dataset provided by [9], is a collection of anomalous machine sounds produced by miniaturised machines (i.e., toy car, toy conveyor, and toy train) as shown in Figure 11. It is designed to provide scenarios such as: inspecting machine condition (toy car), fault diagnostics for a static machine (toy conveyor) and fault diagnostics for a dynamic machine (toy train). The data acquisition setup for each scenario is performed using four microphones sampled at 48 kHz and measurement locations are shown in Figure 12. To provide anomalous operating conditions for the miniaturised machines, systematic fault modes as shown in Table 7 are imbedded in the various toy machines.

**Figure 11.** Schematic of ToyADMOS miniaturised machines (**a**) toy car (**b**) toy conveyor (**c**) toy train [9].

**Figure 12.** Schematic of microphone installation setup for ToyADMOS miniaturised machines (**a**) toy car (**b**) toy conveyor (**c**) toy train [9].



#### *3.2. MIMII Dataset*

The MIMII (Malfunctioning Industrial Machine Investigation and Inspection) dataset comprises normal and anomalous machine operating sounds of four types of real machines such as valves, pumps, fans, and slide rails [10]. The dataset was captured using an 8-microphone circular array with machine configuration in Figure 13 and sampled at 16 kHz. Each recording consists of 10 s. segments recordings of the machines with various faults as shown in Table 8.

**Table 8.** Imbedded faults in MIMII real machines [10].


**Figure 13.** Schematic of microphone installation setup for MIMII [10].

#### *3.3. DCASE Dataset*

The DCASE dataset [13] is a merge of subset of ToyADMOS and MIMII dataset comprising both normal and anomalous machine operating sounds. To harmonise both datasets, each audio file includes a single channel and 10 s in duration. All the audio files are resampled at 16 kHz. The dataset relates to the following machine operating sounds: toy car (ToyADMOS), toy conveyor (ToyADMOS), valve (MIMII), pump (MIMII), fan (MIMII) and slide rail (MIMII).

#### *3.4. IDMT-ISA-ELECTRIC-ENGINE Dataset*

The IDMT-ISA-ELECTRIC-ENGINE dataset [14] consists of anomalous operating sounds of three brushless electric motors. Different operational states such as good, heavy load and broken are simulated within the electric motors by changing the supply voltage and loads. The dataset provides mono audio for each sound file sampled at 44.1 kHz. For each of the operational states, IDMT-ISA-ELECTRIC-ENGINE dataset provides 774 sound files for "good" state, 789 for "broken" state and 815 for "heavy load". Figure 14 shows the setup for acoustic data acquisition in the electric motor machines.

**Figure 14.** Three electric motor setups for IDMT-ISA-ELECTRIC-ENGINE dataset [14].

#### *3.5. MIMII DUE Dataset*

The MIMII DUE (Malfunctioning Industrial Machine Investigation and Inspection with domain shifts due to changes in operational and environmental conditions) provides a sound dataset for training and testing anomalous sound detection techniques and their invariance to domain shifts [56]. This builds on the authors' previous released MIMII dataset [10] which had the limitation of not representing industrial scenarios with changes in machine operational speed and background noises.

MIMII DUE provides normal and anomalous sounds for five industrial machines: fan, gearbox, pump, slide rail and valve. For each of the machines, six sub-division is provided referred to as sections. Each section refers to a unique instance of machine product; this provides for manufacturing variability within machine type. Furthermore, each section has its dataset is split into source domain and target domain. The source domain contains machine operating sound running at design point while target domain contains machine operating sound running at off-design point.

#### *3.6. ToyADMOS2 Dataset*

ToyADMOS2 dataset also provides for training and testing anomalous machine sound detection techniques for their performance in domain shifted conditions [57]. As opposed to ToyADMOS its predecessor, it only carters for two types of miniature machines: toy car and toy trains. The recording and system setup is same for ToyADMOS [9]; however, a key difference, ToyADMOS2 has the normal and anomalous machine operating sounds recorded with machines operating under different speeds. This provides for a source domain consisting of machines with specified operating conditions and the target domain with machines having different operating conditions. Suitable for training and testing with the different domains.

#### *3.7. MIMII DG Dataset*

MIMII DG dataset provides normal and anomalous machine operating sounds for benchmark Domain Generalisation techniques [58]. It comprises five groups of machines including

valve, gearbox, fan, slide rail and bearing. The audio recording for each machine consists of three sections representing different types of domain shift conditions, which for each machine could be operating condition change and environmental background noise change.

#### **4. Challenges**

#### *4.1. Sound Mixtures with Background Noise*

The presence of background noise interfering with machine fault signature during acquisition of acoustic data poses a challenge in terms of accuracy and repeatability of machine fault diagnostics. Background noise in this context refers to sound from other operating machines that are different from the target machine. Additionally, it includes the sounds from other activities in the industrial environment.

Approaches are therefore required to eliminate background noise from the collected acoustic data. The challenge lies in the fact that the background noise sources are uncorrelated, as such, filtering techniques are not applicable. Techniques, such as Blind Signal Separation (BSS) and Independent Component Analysis (ICA), have the potential to address this challenge by recovering the signal of interest out of the observed sound mixtures. BSS has been applied in [59] for extracting the unobserved fault acoustic signal during metal stamping with a mechanical press. Wang et al. [60] also applied BSS using sparse component analysis for separating sound mixtures of power transformer origin. In [48], ICA was applied together with variational mode decomposition, to separate the independent components hidden in the observation low signal-to-noise ratio signals, for an intelligent diagnosis application.

In practice, the mixture of acoustic signals is formed by the random mixing of multiple sound sources resulting in non-linear mixture models, which is an area requiring further attention for acoustic-based machine condition monitoring.

#### *4.2. Domain Shift with Changes in Machine Operation and Background Noise*

Domain shift represents the change in machine operating and environmental conditions. This is common in industrial settings as machines would not always operate in their design point conditions. There is always a need for the machine to run at an off-design point, indicating changes to both speed and loading as well as changes in the background noise from auxiliaries during operation. Tackling the domain shift problem is important for effective anomaly detectors applicable to machine operating sound.

The concept of domain adaptation is gaining prominence as an approach for anomaly detection in domain shifted conditions [11,61]. Domain adaptation addresses the problem as: when provided with a set of normal data from a source domain and a limited set of normal data from a target domain, how do you develop a performant anomaly detector in the target domain. From the literature, the following approaches for domain adaptation have emerged: learning the transformation from the source domain to the target domain [62,63], learning invariant representations between the source and the target domains [64–67] and few-shot domain adaptation [68,69]. With the option of domain adaptation, it opens opportunities for application to acoustic-based machine condition monitoring and fault diagnostics.

#### *4.3. Domain Generalisation Invariant to Changes in Machine Operation and Background Noise*

Domain generalisation is an attempt to provide an alternative to the domain adaptation techniques when dealing with domain shift due to the computational cost of the domain adaptation techniques. Domain generalisation poses the problem of learning commonalities across various domains (i.e., source and target) to enable the model to generalize across the domains. Such generalisation would need to account for domain shift caused by differences in environmental conditions, machine physical conditions, changes due to maintenance, and differences in recording devices for instance.

Fundamentally, domain generalisation attempts the out-of-distribution generalisation by using only the source domain data. In the literature, several techniques have emerged such as [70]: domain alignment, meta-learning, ensemble learning, data augmentation, selfsupervised learning, learning disentangled representations, regularisation strategies, and reinforcement learning. With the development and application of domain generalisation techniques for machine fault diagnostics problem, it would open compelling opportunities for the applicability of the acoustic-based approaches.

#### *4.4. Effect of Measurement Distance, Measurement Device and Sampling Parameters* 4.4.1. Measurement Distance (Microphones Positions)

Sound propagates through air as a longitudinal wave; as it moves through the air medium, from the source to the listener or observer, sound as characterised by sound intensity, experiences attenuation, i.e., loss in energy. For a point source (i.e., uniformly radiating sound in all directions), this attenuation follows the inverse square law as shown in Figure 15, which is dependent on the measurement distance. In practice, for every doubling of measurement distance, the sound intensity reduces by a factor of 4; alternatively, the sound pressure level reduces by 6 dB. From sound propagation theory, it is evident that, the measurement distance of anomalous machine operating sound is important [71]. However, very little consideration has been given to this effect during experimental setup for anomalous machine sound data acquisition as corroborated by the benchmarking opensource datasets such as ToyADMOS, MIMII, IDMT-ISA-ELECTRIC ENGINE, MIMII DUE, ToyADMOS2, and MIMII DG. One can argue, the measurement distance effect can be accounted for within domain adaptation or domain generalisation challenges. Yet, the various datasets do not provide a systematic grouping of the dataset based on the measurement distance for this to be considered. The parameters often considered are changes in machine operating parameters (i.e., rotating speed and load) and environmental/background noise.

An important question is then raised; how far should the microphones be from the sound source considering the measurement distance effect?

In acoustics, two physical regions exist that shed light to the above question: the acoustics near field and acoustics far field as shown in Figure 16. The transition from near field to far field occur in at least 1 wavelength of the sound source [72]. It is important, to note, as wavelength is a function of frequency, this transition distance would change as the frequency content of the sound source changes. The near field exist very close to the sound source with no fixed relationship between sound intensity and distance. Within the far field, the inverse square law of sound propagation holds true. In practice, this is the region where the measuring microphone should ideally be located. As a minimum, a single microphone can suffice for accurate and repeatable measurement of sound. Although fundamental acoustics theory would place the far field at least 1 wavelength of the sound source [72]; ISO 3745, provides several guidelines or criteria for microphone placement within the far field for sound power measurement [73]:

$$(\mathbf{a}) \; r \ge 2d\_o \tag{6}$$

$$(\mathbf{b}) \; r \ge \lambda / 4 \tag{7}$$

$$(\mathbf{c}) \; r \ge 1 \; metre \tag{8}$$

where *r* is measurement distance, *do* is characteristic dimension or largest dimension of the sound source, and *λ* is the lowest wavelength of the sound source.

For small, low-noise sound sources with measurement over a limited frequency range, the measurement distance can be less than 1 m, but not less than 0.5 m, provided consideration for criteria (a) and (b) above are adhered to [73].

Within the near field, measurement is feasible; but would require multi-microphone array. For the measurement of anomalous machine operating sound, guidelines are lacking in the literature and further research is required.

**Figure 15.** Distance effect on sound intensity propagation and attenuation [74].

**Figure 16.** Acoustic sound field consideration [72].

4.4.2. Single Microphone Measurement Device and Sampling Parameters

Acoustic measuring device mismatch between development data acquisition and testing can occur in practice. As every microphone have its unique transfer function which dictates its frequency response and perception of sound, measuring device mismatch needs to be considered. Very little has been done in considering this challenge in the detection and classification of anomalous machine operating sound. However, such consideration is already attracting attention in the corollary field of acoustic scene classification [75]. Key to this consideration in acoustic scene classification field, is the realization of the TUT Urban Acoustic Scenes dataset which consists of ten different acoustic scenes, recorded in six large European cities with four different microphone devices: highlighting the importance of considering the acoustic measuring device for robust pattern learning algorithm [75].

As very little work has been explored on the effect of recording device mismatch in anomalous machine operating sound detection and classification to inform device choice; still, some learning can be gleaned from the choice of microphones, sampling frequency and sample duration as shown in Table 9 from the opensource dataset projects on DCAMS.


**Table 9.** Exemplar acoustic measurement devices and sampling parameters.

#### 4.4.3. Microphone Array Measurement (Acoustic Camera)

Acoustic camera measurement provides the capability for sound source localisation, quantification and visualization using multi-dimensional acoustic signals processed from a microphone array unit and overlaid on either image or video of the sound source as shown in Figure 17 [76]. An acoustic camera, is a collection of several microphones, acting as a microphone array unit, where the microphones within the array can be arranged either as uniform circular configuration, uniform linear configuration, uniform square configuration or customized array configuration for specific application. Acoustic camera can provide acoustic scene measurement both in the near and far acoustic fields.

For localizing anomalous machine operating sound in application, acoustic camera has been used to map the variation in machine emitted sound for fault detection as follows: localizing sources of aircraft fly by noise [77], characterising emitted sound from internal combustion engine running idle in a vehicle [78], fault detection in a gearbox unit [79], fault localisation in rolling-element bearing [80], etc.

**Figure 17.** Acoustic camera for fault detection based on variation in emitted sound (**a**) Acoustic camera setup (**b**) test object without a fault (**c**) test object with a fault [81].

Central to the analysis and interpretation of the multi-dimensional acoustic signals is acoustic beamforming technique [76,82]. Ref. [82] provides an extensive review on acoustic beamforming theory including consideration for acoustic beamforming test design criteria.

Acoustic beamforming is a spatial filtering technique used in far field acoustic domain, for localisation and quantification of the sound source; where it amplifies the acoustic signal of interest while suppressing interfering sound sources (e.g., background noise) [82]. In principle, the beamforming algorithm works by summing individual acoustic signals based on their arrival times from the sound source to the microphone array. This summation process suppresses the interfering signals while enhancing the acoustic signal of interest. The technique can be performed both in the time-domain and frequency domain [82].

(1) Delay and Sum Beamforming in the Time-Domain: This is demonstrated in Figure 18 as follows, considering only two sound sources as an example (i.e., source 1 and source 2). For each sound source, the travel path of emitted sound to the microphone array would be different; as such, captured signals by the microphone array would show different delays and phases for the measured signals from both sources. As both parameters, delay, and phase, are proportional to the travelled distance between microphone array and source; with the knowledge of the speed of sound in the medium (e.g., air), the runtime delay is estimated for the signal of interest (source 1) reaching all the microphone locations. The measured signal for every microphone in the array is then shifted by the calculated runtime delay for that channel, creating an alignment in phase in the time-domain for the signal of interest (source 1). The resulting signals from every microphone channel are summed and normalised by the number of microphones in the array; As shown in Figure 18, the signal of interest (source 1) is amplified due to constructive interference while source 2 is minimized due to destructive interference. To create the final acoustic scene representation, for each microphone channel, the root mean square (RMS) amplitude value or the maximum amplitude value of the time-domain acoustic signal can be evaluated for visualization as an acoustic map.

**Figure 18.** Schematic of delay and sum beamforming in the time domain for acoustic sources [83].

(2) Delay and Sum Beamforming in the Frequency Domain: This is demonstrated in Figure 19 as follows, considering only two sound sources as an example (i.e., source 1 and source 2). For each sound source, the travel path of emitted sound to the microphone array would be different; as such, captured signals by the microphone array would show different delays and phases for the measured signals from both sources. The delay for the signal of interest can be determined using information such as, distance between source and microphone and the speed of sound in the medium. Fourier transform is performed at all microphone channel resulting in a complex spectrum for amplitude and phase. To eliminate the delay in phase for the signal of interest at all microphone location, the complex spectra is multiplied by a complex phase term as shown in Figure 19, bringing the interested acoustic source in phase without impacting the amplitude of the spectra. The resulting complex spectra from all the microphone channels are summed and normalised by the number of microphone channels. The interest sound source signal (source 1) is enhanced due to constructive interference, while source 2 is diminished due to destructive interference.

**Figure 19.** Schematic of delay and sum beamforming in the frequency domain for acoustic sources [84].

Application of acoustic camera to machine diagnostics have been attracting increasing interest [77–80,85,86]. Of note, is the approach proposed by [85,86] to localise faults in rotating machinery using acoustic beamforming and spectral kurtosis (i.e., spectral kurtosis is an effective indicator of machine fault [87,88]). As shown in Figure 20, spectral kurtosis is used as a post-processor of the multi-dimensional acoustic time-domain signals from the microphone array to identify and localise fault-related frequency bands (i.e., frequency bands that are impulsive); the resulting kurtogram having a spatial dimension provides the capability to localise the high kurtosis region providing indication of machine fault.

**Figure 20.** Application of spectral kurtosis to acoustic beamforming for machine fault diagnosis [85,86].

#### **5. Outlook**

Anomalous machine operating sound provides a rich set of information about a machine's current health state upon which to automate the detection and classification of machinery faults. Despite advances in data-driven machine learning and deep learning approaches as currently applied for acoustic-based machine condition monitoring, there still exist areas for further research for this technique to be industrially applicable.

#### *5.1. Addressing Pitfalls in Acoustic Data Collection*

The performance of data-driven models and their ability to generalize during training and testing depends on the available datasets being a representative of the actual fault scenario. However, generating machine fault dataset for actual machines is a costly endeavor. If the training dataset is too small, the model learns sampling noise. As a work around, most of the opensource dataset for the detection and classification of anomalous machine operating sounds have focused on either toy machines or scaled down machine models. This approach has provided initial seeding to be able to benchmark currently developed techniques. Generally, available datasets account for steady-state changes in machine operational parameters such as speed and load, consideration of varying degree of background noise during acoustic signal measurement, and different models of similar machine class. These datasets are lacking in the following areas: consideration of the distance effect during grouping of the dataset (i.e., it would be relevant to have measurements at different distances from the source to test the robustness of developed approaches working in the field where it would be difficult to maintain repeatable measurement distance), consideration of transient operation regime of machines during dataset grouping (i.e., steady-state dataset alone is a non-representative training data; developed approach need to be able to differentiate transient operation from anomalous operation), and consideration of device mismatch during data acquisition (i.e., recording for same machine fault with different types of microphones, such as omni-directional microphone, pressure-free field microphone, condenser microphone, etc.; Furthermore, it would be relevant to specify a standard reference microphone such as the omni-directional microphone, in other for spectrum correction coefficients for various microphones to be provided with respect to this [89]; using spectrum correction coefficients opens up the possibility of data transformation to account for device mismatch).

#### *5.2. Addressing Measurement Artifacts (i.e., Background Noise, and Distance Effect)*

In the industrial environment, acoustic-based machine condition monitoring is often plagued with the problem of having multiple signals mixing such as acoustic signal of interest indicative of anomalous machine operation and the background noise, i.e., neighboring machinery, factory noise, etc. It is required for the sound mixture to be separable, i.e., separating the acoustic signal of interest from the background noise. Conventional approaches such as spectral subtraction methods which rely on the background noise having a constant magnitude spectrum and acoustic signal of interest been short-time stationary would not be applicable as there is the possibility of removing fault frequencies from the spectrum of the acoustic signal of interest [90]. Blind signal separation can be useful as it offers sound mixture separation without prior knowledge of either of the signals or the way in which they are mixed [91]. Application and optimisation of blind signal separation for acoustic-based machine condition monitoring provides an area for further research.

The effect of distance between the acoustic source and microphone leads to attenuation of the measured sound intensity. Furthermore, it places a burden of repeatability between laboratory conditions and industrial conditions, impacting data-driven model accuracy for application. Eliminating or minimizing the distance effect on the acquired acoustic signal is an area requiring further research. [71] proposed a normalisation scheme (i.e., d-normalization) in the frequency domain using the spectrum representation of the acoustic signal which minimized the distance effect as shown in Figure 21 and expressed as:

$$I(f) = \exists (f) / \mu\_I \tag{9}$$

where *I*(*f*) is the normalised spectrum of the measured sound intensity, *I*(*f*) is the unnormalised spectrum of the measured sound intensity (i.e., determined from fast Fourier transform of the time-domain acoustic signal), and *μ<sup>I</sup>* is the mean of the rectified timedomain acoustic signal intensity, given as:

$$
\mu\_I = (1/N) \times \sum\_{i=1}^{N} |X\_i| \tag{10}
$$

where *N* is number of sample points in the acoustic time-domain signal, |*Xi*| is the absolute amplitude value of the acoustic time-domain signal.

Although the result is promising, it is applicable to the spectral representation of the acoustic signal. Alternative normalisation scheme be required for other acoustic image representation such as cochleagram, Mel-spectrogram, amongst others? Furthermore, what would be the impact on the data-driven model accuracy due to normalisation of the input acoustic representation? These are open questions for further research.

#### *5.3. Improving Data-Driven Model Accuracy for Application: Domain Adaptation versus Domain Generalisation*

Domain shift (i.e., changes in machinery operating speed and load) is inevitable in industrial processes due to machines operating in off-design conditions and harsh environment. As such, training data-driven models for the DCAMS problem to account for this system dynamics is a must have. However, learning robust model representation by using data from multiple domains to identify invariant relationships between the various domains is still a challenging problem. Two schools of thought have emerged to address the domain shift problem in acoustic-based machine condition monitoring: domain adaptation [92,93] and domain generalisation [94]. Both approaches tackle the same problem based on the available dataset. Domain adaptation assumes you have dataset from the source domain (i.e., machine operating at design point) and some set of data in the target domain (i.e., machine operating at off-design point), it attempts to learn the mapping between the source and target domain based on these criteria. Alternatively, domain generalisation assumes you have dataset from two different source domains, it attempts to learn the mapping to an unseen domain. Although several domain adaptation and generalization techniques have been proposed in the literature, the model performance for

both approaches is yet to reach satisfactory level in applications as evident from DCASE2021 and DCASE2022 Task 2 challenges [11,12].

**Figure 21.** Minimizing distance effect on measured acoustic signal using d-normalisation [71].

#### *5.4. Addressing Multi-Fault Diagnosis*

In industrial environment, machinery may need to operate in both off-design conditions and harsh conditions continuously for extended periods of time. As such, machine components are liable to the occurrence of multiple faults at the same time. When these multi-faults occur, their impact to machine performance and lifespan is more severe as compared to the presence of a single fault due to fault interactions [95]. Fault diagnosis approaches needs to be able to accommodate both single fault and multi-faults detection scenarios. From the literature, within acoustic-based condition monitoring methodology, the focus has been on addressing the single-fault diagnosis problem; multi-fault diagnosis of machinery is still lacking. This area of research needs consideration for viable industrial applications, e.g., fault diagnosis in gearbox, electric motor, compressor, pump, amongst others.

#### *5.5. Improving Acoustic Camera Spatial Detection of Machine Faults*

Acoustic camera for machine fault diagnosis provides spatial information not possible with conventional condition monitoring approaches such vibration analysis. However, interpreting the visualization of the emitted sound field from the machine from acoustic beamforming is very limited; It is important to note that regions of high sound pressure level does not necessarily correlate with the presence of a fault. Further research is required to analyse the multi-dimensional acoustic time-domain signals as a function of space from the acoustic beamforming analysis using either signal processing methods or data-driven machine learning/deep learning approaches. Pioneering in this regard, [85,86] have proposed spectral kurtosis as means to filter the multi-dimensional acoustic time-domain signals from acoustic beamforming to localise impulsive-related machine faults, e.g., gearbox faults, rolling-element bearing faults, etc., as well as extract the time-domain acoustic signals from the region of high spectral kurtosis. This area of research is still limited in correlating regions of high spectral kurtosis to a fault. The extract time-domain signal provides an opportunity to be explored for evaluation using data-driven approaches. Furthermore, beyond spectral kurtosis, what other signal processing approaches are relevant with improved sensitivity to localizing machine faults from the multi-domain acoustic signals provided by the acoustic camera?

#### **6. Conclusions**

Acoustic-based machine condition monitoring has been attracting increasing attention, especially with the annual DCASE challenge task on unsupervised anomalous sound detection for identifying machine conditions. Given the industrial relevance and significance of this research area, it becomes important in this paper to address the following questions: (i) are there commonalities or differences amongst the developed methodologies for detecting and classifying anomalous machine operating sounds, (ii) what open datasets are available for benchmarking the developed techniques, and (iii) what challenges are still there for the applicability of acoustic-based machine condition monitoring. Hopefully, this review of the state-of-the-arts can inspire more advancement in the acoustic-based machine condition monitoring research area.

**Author Contributions:** Conceptualization, G.J. and Y.Z.; writing—original draft preparation, G.J.; writing review and editing, Y.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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### *Article* **Analysis of Grid Disturbances Caused by Massive Integration of Utility Level Solar Power Systems**

**Esteban A. Soto 1, Lisa B. Bosman 1,\*, Ebisa Wollega <sup>2</sup> and Walter D. Leon-Salas <sup>1</sup>**

<sup>2</sup> Department of Engineering, Colorado State University–Pueblo, Pueblo, CO 81001, USA; ebisa.wollega@csupueblo.edu

**\*** Correspondence: lbosman@purdue.edu

**Abstract:** Solar generation has increased rapidly worldwide in recent years and it is projected to continue to grow exponentially. A problem exists in that the increase in solar energy generation will increase the probability of grid disturbances. This study focuses on analyzing the grid disturbances caused by the massive integration to the transmission line of utility-scale solar energy loaded to the balancing authority high-voltage transmission lines in four regions of the United States electrical system: (1) California, (2) Southwest, (3) New England, and (4) New York. Statistical analysis of equality of means was carried out to detect changes in the energy balance and peak power. Results show that when comparing the difference between hourly net generation and demand, energy imbalance occurs in the regions with the highest solar generation: California and Southwest. No significant difference was found in any of the four regions in relation to the energy peaks. The results imply that regions with greater utility-level solar energy adoption must conduct greater energy exchanges with other regions to reduce potential disturbances to the grid. It is essential to bear in mind that as the installed solar generation capacity increases, the potential energy imbalances created in the grid increase.

**Keywords:** photovoltaic systems; grid disturbances; energy market; renewable energy systems

#### **1. Introduction**

#### *1.1. Proposed Solution*

In the last decade, solar energy generation has grown enormously around the world. At the end of 2019, the installed capacity in the world of photovoltaic systems was more than 635 GW [1]. By 2050, it is predicted that solar energy will become the second-largest renewable generation source in the world after wind. In 2050, it is also predicted that the installed capacity in the world will exceed 8000 GW [2]. The increase in renewable generation, particularly solar energy, increases the probability of grid disturbances. Due to the above issues, it is necessary to quantify the potential impact of grid disturbances produced by the integration to the transmission line utility-scale solar energy loaded to the balancing authority high-voltage transmission lines (not utility-scale solar powering low voltage local distribution). In this way, electric power companies can size the problem and justify implementing solutions. This study proposes an analysis of the impact on the grid considering integrating solar energy plants to the grid in four regions of the United States electrical system: (1) California (high solar generation), (2) Southwest (moderate solar generation), (3) New England (low solar generation), and (4) New York (null solar generation). These four regions were selected because there is variation between them, ranging from the region with the most solar generation, California, to one with no utilitylevel solar generation (according to the Energy Information Administration [3]), New York. The impact analysis of the grid was completed using hourly increments, considering net

**Citation:** Soto, E.A.; Bosman, L.B.; Wollega, E.; Leon-Salas, W.D. Analysis of Grid Disturbances Caused by Massive Integration of Utility Level Solar Power Systems. *Eng* **2022**, *3*, 236–253. https:// doi.org/10.3390/eng3020018

Academic Editor: Antonio Gil Bravo

Received: 7 March 2022 Accepted: 18 April 2022 Published: 29 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> Purdue Polytechnic Institute, Purdue University, West Lafayette, IN 47907, USA; soto34@purdue.edu (E.A.S.); wleonsal@purdue.edu (W.D.L.-S.)

generation changes, net generation error with demand, and energy power peaks. The findings contribute to solving the problem by quantifying the impact on the energy balance and the power peaks caused by the massive integration of solar power plants. This study seeks to answer the following research question.

Research Question: How does the penetration of solar energy utility level affect energy imbalances and the peak of power in the grid?

#### *1.2. Current Approaches to the Problem and Gaps in Current Approaches*

Among the current approaches, several technologies support the integration of solar energy into the grid to reduce potential disturbances, including technological advancements of inverters, solar grid protection plants, better forecasts of solar energy generation, net metering policies, and peer-to-peer energy trading [4].

The function of the inverters is to convert the direct current (DC) produced by the solar panels into alternating current (AC) and control its output voltage [5]. These inverter features are validated at the manufacturing stage, where the devices are subjected to loads that simulate their operation and interaction with the network [4]. However, a gap exists in that implementing inverters that allow voltage control to maintain a more stable grid can only be applicable to small-scale and small-sized photovoltaic installations, generally used in solar plants of less than 30 MW. In larger plants, grid and plant protection is required.

Other technologies include grid and plant protections, which are devices that monitor all the critical parameters of the grid and disconnect the plant from the network in the event of a disturbance [4]. Grid plant protection is a solution for today's grid. However, a gap exists in moving to a smart grid and increasing solar energy penetration, and this technology will need to be adapted for future solutions [6].

Solar forecasting is another technology used to reduce disturbances on the grid; it consists of predicting the behavior of solar generation to react quickly to any problem on the grid. Generally, solar forecasting uses historical data of generation and weather conditions [7]. However, a gap exists in that a few countries have established standards on performing solar forecasting, whereby the methodologies vary from one electrical system to another. Additionally, there are unique local factors in each region that can impact the prediction of solar generation. Also, there is still a gap in the analysis of the integration of solar energy considering the hourly operation of the electricity market at the transmission level.

Another approach is net metering policies which allow users to load excess energy production into the local grid. Some studies have shown that net metering can improve the quality of the power, which would help reduce disturbances in the grid [8,9]. However, a gap exists in that the penetration of solar energy at the residential level is still shallow in the world and most of the states of the United States. As a result of an imminent massive increase in solar generation at the utility level, net metering will not be enough to reduce disturbances in the grid. In addition, it has been reported that net metering is being phased-out [10].

Finally, Peer-to-Peer (P2P) energy trading is another approach that refers to the fact that energy prosumers can sell their electricity surplus to other users in the same grid. P2P has some benefits for the grid, reducing peak demand and improving the grid's reliability [11,12]. However, a gap exists in that P2P still does not have the technical validation, security levels, and regulations necessary to be implemented on a large scale [11]. Furthermore, there are only a few pilot projects worldwide that have not been fully validated [13,14].

The rest of this paper is organized as follows: the next section (Section 2, Background) presents the concepts relevant to the study: grid disturbances, solar energy integration, and power grid in the US, followed by Section 3, Methods, in which the data collection and data analysis are presented. Section 4, Results, presents the main findings of the study. Subsequently, in Section 5, the results are discussed and compared to other studies. Finally, Section 6, Conclusions, summarizes the article.

#### **2. Background**

#### *2.1. Problem Indentification*

It is essential to resolve connectivity issues in the grid for a smooth transition to renewable energy [15]. It is also vital to analyze new methods to correctly integrate renewable energies into the grid [16]. Here, a grid disturbance means tripping one or more elements of the grid energy system such as a generator, transmission line, or transformer, ultimately shutting down electricity access from the grid. As an example, in early 2021, Europe suffered a massive disruption on the grid, which caused concern in the energyintensive industry in Germany [17,18]. The event occurred after a sudden drop in frequency (from 50 Hz to 0.25 Hz), which caused the European interconnected system to split in two. In some regions, sensitive machines automatically stopped working. In addition, the network operators in Italy and France had to disconnect some power plants in an effort to maintain grid stability [17]. While this event has not been linked to an increase in renewable energy, as generation from wind and solar units increases, incidents like this will become more frequent [18,19]. Experts who delivered the report on the incident mentioned that in terms of the transition to renewable energy, a more robust electrical system is required to guarantee a stable supply of power to citizens [18]. Events like this are not limited to Europe. In Australia, there have been problems with integrating renewable energies into the power grid. For example, in 2016, there was a massive blackout because of a wind energy disruption [19]. On the day of the event, Australia experienced an abnormally violent storm, which caused a decrease in the outage of a number of wind farms and the disconnection of several wind towers due to the high wind speed [19]. The increase in the generation of solar energy and its participation in the generation of electricity in the world and the United States is inevitable. With this massive increase in solar generation, it is expected that large amounts of intermittent electricity produced by renewable energies will create huge oscillations in the grid supply. Because of this, when planning the distribution of energy in the energy market, the changes in the supply and demand for energy and the different sources of energy used to meet the users' needs must be considered. However, little is known about the rate (i.e., quantity of solar energy adoption) or tipping point where the greatest potential impact could occur and its implications for the grid, particularly the potential disruptions created by increased solar power generation at the utility level. The following sections will focus on three relevant areas: First, an explanation of the United States power grid. Second a review of grid disturbances. Finally, the last subsection is dedicated to integrating solar energy into the grid.

#### *2.2. The United States Power Grid*

The United States electrical system includes power plants, transmission and distribution lines, sub-stations, and end-users. The system uses a wide variety of energy sources to produce electricity, including coal, natural gas, nuclear power, and renewable energy sources. These components form a complex electrical power grid [20]. The US electricity grid is one of the most complex and technologically demanding systems due to its interconnectivity that requires long-distance power transmission. This long-distance energy transmission has the potential for associated disturbances in the network [21]. In the lower 48 states, the US power system comprises three primary interconnected systems, operating largely independently of each other with a limited interchange of energy between them [22]. The Eastern Interconnection ranges from the east coast to the Rocky Mountains. The Western Interconnection ranges from the Rocky Mountains to the west coast. The third interconnection covers most of the state of Texas, the largest state in the United States [23].

The power grid in the United States has several challenges that are anticipated to arise in the future: first, increase in user demand; second, infrastructure renewal; third, greater risk of a cyberattack; and fourth, greater frequency of grid interruptions [24]. In recent years, the electrical grid has become more fragile and vulnerable to interruptions [25]. Although the US has developed a capacity to protect electrical infrastructure from cyberattacks, it has been impossible to eliminate risks due to its complexity. Distributed energy

resources and more micro-resources are essential to decentralize the electricity grid and thus increase supply security and supply capacity during cyber-attacks [26], yet they can also be problematic when considering grid disturbances. Also, increased solar power generation increases the likelihood of grid disturbances at balancing authority levels in the US electrical systems [27]. Finally, the massive increase in renewable energy generation will also cause interruptions due to intermittent power generation. One of the biggest problems of the massive incorporation of photovoltaic energy is the disturbances that can be created in the grid.

#### *2.3. Grid Disturbances*

The variation in the quality of power in the grid due to the presence of disturbances in the voltage wave of the network is an issue that has increased its intensity due to the energy transition. In technical terms, to maintain a stable grid, the voltage waves must be pure sine waves with a constant frequency [28]. However, the grid is generally unstable since the voltage wave exhibits disturbances, such as noise in the differential, electrical impulses, fast or slow voltage variations, flickering, harmonic distortion, and frequency variations [29]. When a massive number of distributed energy sources are connected to the grid, the grid is subjected to various electrical loads, altering the voltage. This phenomenon increases with the intermittent and often unpredictable generation produced by renewable energy, such as solar or wind [30]. The increase in renewable energy can cause severe problems to the grid, such as power fluctuations; imbalances in the grid that can increase overcurrent, thereby affecting energy efficiency; and efficiency decreases in photovoltaic systems [31]. Although solar generation is currently the third most significant renewable energy source, only after hydro and wind, few countries have implemented technical standards or contingency plans to prevent and reduce disturbances in the grid. Yet, grid disturbances are increasingly becoming a problem due to the growth in solar plants around the world [32]. One of the biggest problems resulting from the addition of photovoltaic-generated electricity into electrical systems is the disturbances caused by voltage variations [33]. Mahela et al. analyzed the behavior in common coupling points of the voltage, the current, and the power and the relationship of these variables with the disturbances in the grid [34]. The authors found that the resistive–inductive load disconnection affects the current, the voltage, and the voltage in photovoltaic systems [34]. Purnamaputra and colleagues analyzed the total distortion of solar systems connected to the grid, considering the frequency of disturbances as the primary variable [35]. They found that the disturbances in the voltage are constant at frequencies of 10 kHz and 30 kHz [35]. Most studies have focused on technical aspects and solar plant disturbances on the local grid. Yet, there is a lack of literature that analyzes the integration of photovoltaic installations considering electrical systems or subsystems as a whole.

#### *2.4. Solar Energy Integration*

In recent years, the decarbonization of the electrical system in the United States has been promoted to lead a transition to a cleaner energy matrix and reduce polluting emissions [36]. In conjunction with decarbonization, it is necessary to expand renewable resources to meet the increased demand for electricity [37]. Also, renewable energy will significantly reduce carbon emissions and greenhouse gases [38]. There is a broad technical consensus that renewable energy resources need the support of multiple critical actors (generation, transmission, and distribution) in the electrical system to be effectively integrated into the grid [39]. A series of profound changes are necessary for the electrical network architecture, including energy distribution and storage [40]. In addition, it is considered that renewable energy technologies for the production of electricity, such as solar energy, wind energy, geothermal energy, and hydroelectric energy, among others, have great potential to satisfy the demand for electric energy when implemented on a large scale [41]. The integration of wind and solar energy has a negative marginal impact on the reliability of an electrical system at low levels of electricity generation [42]. As the

penetration of renewables into the grid increases, the integration challenges will increase. Following an analysis, a mismatch between supply and demand was predicted due to the overproduction of energy at certain times of the day [43]. Solar energy would be a fundamental source when integrating renewable energies into the grid. The supreme competitiveness of solar energy is reflected in the long-term forecast high-penetration levels of solar energy above that of wind and hydro [44]. The increase in solar energy generation is not without its problems. By having greater penetration of solar energy in the grid, higher peaks of generation of gas plants will occur at sunset, which is when solar generation decreases [45]. In this way, the massive integration of solar energy will cause potential disturbances in the electrical system of the United States. Thus, it is necessary to study the potential impacts of the massive integration of solar generation in the US electrical grid.

#### **3. Methods**

#### *3.1. Study Design*

This study includes a comparison of four regions of the United States electrical system (California, Southwest, New England, and New York) before and after the massive incorporation to the transmission line of utility-scale solar energy loaded to the balancing authority high voltage transmission lines (not utility-scale solar powering low voltage local distribution). Data from the Energy Information Administration (EIA) and the National Renewable Energy Laboratory (NREL) were used for the comparative analysis. The EIA data include hourly data from energy generation by source and energy demand; the NREL data include hourly generation from hypothetical solar plants. Statistical analysis was performed to compare the mean at different levels of solar energy penetration. Table 1 shows the list of the 13 regions in which the EIA data were divided and their respective codes; additionally, the percentage of solar generation of each region is shown. Four representative regions were selected for this study, the two regions with the highest utility level solar generation (California and Southwest) and the two regions with low solar generation utility levels (New England and New York). Statistical analysis compared net generation, the difference between net generation and demand, and the power peaks before and after incorporating hypothetical solar plants in the four analyzed regions.


**Table 1.** List of regions in the US electric power system.

#### *3.2. Data Collection*

The EIA is the Department of Energy's statistical and analytical agency in the United States. The EIA provides centralized and complete hourly information on the high voltage electrical power grid in 48 of the contiguous United States (Hawaii and Alaska are excluded). The data (EIA-930) are compiled by the electricity balance authorities and include forecast demand, actual demand, net generation, net interchange, and net generation from the following: coal, natural gas, nuclear energy, all petroleum derivatives, hydroelectric, solar, wind, and other energy sources [3].

For this study, hourly data from actual demand, net generation, and net generation from the following were used between 1 January 2019, and 31 December 2019 [3,46]: coal, natural gas, nuclear, hydropower, solar, wind, and other energy sources. For this study, four regions of the United States electrical system were used: (1) California, (2) New England, (3) New York, and (4) Southwest. These regions were considered to have a broad spectrum of solar generation percentages. According to the EIA data [3], California is the region that generates the most solar energy (16.2%), and New York does not have solar utility generation. Southwest and New England have 3.2% and 0.2% of solar generation between the two extremes.

NREL has decades of leadership focused on clean energy research, development, and implementation. The expertise of NREL is essential for the transition to clean energy [47]. NREL has a hypothetical photovoltaic solar plant database for renewable energy integration studies [48]. The database consists of 1 year (2006) of solar energy generation every 5 min and daily hourly forecasts of about 6000 hypothetical PV plants. For the purpose of this study, the data were aligned by hour. Solar power plant locations were determined based on the capacity expansion plan for renewable energy. The database has three data types: real power output, day-ahead forecast, and 4 h-ahead forecast. For this study, the real data power output and the day-ahead forecast were considered. The number of hypothetical solar plants considered for each analyzed region in the study is shown in Table 2.

**Table 2.** Number of hypothetical utility level solar plants per region included in the study [48].


#### *3.3. Data Analysis*

The EIA-930 data were used as input of a new hourly energy balance (see Equation (1)) [3,46]. For this new energy balance, the new solar energy plants had preference over the existing plants that use fossil fuels to cover the real total net generation. According to the EIA, each fossil fuel produces a different amount of carbon emissions. In decreasing order, the fuels that produce the most carbon dioxide are coal, diesel, gasoline, propane, and natural gas [49]. The selection criteria to replace the fossil fuels with the new solar generation were based on the amount of carbon emissions generated by each fuel. Coal plants are the first to be replaced, followed by petroleum products and natural gas plants. After fossil fuels, nuclear energy was considered along with hydropower and other sources. Solar energy was not selected to replace wind energy. Additionally, different levels of presentation of solar energy, 100%, 75%, 50%, and 25%, were considered when performing the analysis. Data analysis in this study was carried out using the statistical software RStudio Desktop version 1.3.1093 (open-source edition, RStudio, Boston, MA, USA).

Equation (1) represents the energy balance according to the EIA-930 data [3,46].

$$NG = COL + NGA + NLC + PET + WAT + SIN + WND + OTH \tag{1}$$

where

*NG* = *Net generation COL* = *Net generation from Coal in* MWh *NGA = Net generation from Natural Gas in* MWh *NUC* = *Net generation from Nuclear Energy in* MWh *PET* = *Net generation from Petroleum products in* MWh *WAT* = *Net generation from Hydro in* MWh *SUN* = *Net generation from Solar Energy in* MWh *WND* = *Net generation from Wind in* MWh

*OTH* = *Net generation from others energy sources in* MWh.

Equation (2) describes net generation, including the forecast solar generation of the hypothetical solar plants minus the difference (delta) in generation from the other sources. The delta in coal generation (Δ*COLFH*), natural gas generation (Δ*NGAFH*), petroleum generation (Δ*PETFH*), nuclear generation (Δ*NUCFH*), other energy sources (Δ*OTHFH*), and hydro (Δ*WATFH*) are functions of the forecast generation of the hypothetical solar power plants (note that the FH subscript represents forecast hypothetical). The percentage decrease in coal and natural gas, petroleum, nuclear, and other energy sources is offset by the same percentage increase in solar energy.

*NG*(*SUNFH*) = Δ*COLFH* + Δ*NGAFH* + Δ*NUCFH* + Δ*PETFH* + Δ*WATFH* + *SUN* + *WND* + Δ*OTHFH* + *SUNFH* (2)

where *SUNFH* = *Forecast net generation f rom hypothetical solar plants in* MWh.

The following net-generation balance Equation (3) is a function of the forecast generation of the hypothetical solar plants and the actual generation. The forecast generation of hypothetical solar plants (*SUNFH*) is replaced by the actual generation of the hypothetical solar plants (*SUNH*).

*NG*(*SUNFH*, *SUNH* ) = Δ*COLFH* + Δ*NGAFH* + Δ*NUC* + Δ*PET* + Δ*WAT* + *SUN* + *WND* + Δ*OTH* + *SUNH* (3)

After establishing the new energy balances Equations (1)–(3), statistical *t*-tests of two samples means, assuming equal variances, were carried out. The two-sample *t*-test is a method used to test whether the unknown population means of two groups are equal or not.

The hypotheses tested were the following:

#### **Hypothesis 1.**

$$H\_0: \mu\_{NG} - \mu\_{FH,H} = 0\\H\_1: \mu\_{FH} - \mu\_{FH,H} \neq 0\tag{4}$$

where *μNG* = *mean o f NG*; *μFH*,*<sup>H</sup>* = *mean o f NG*(*SUNFH*, *SUNH*).

The null hypothesis is that the mean of the net generation according to the EIA-930 data (denoted by *μNG*) is the same as the mean of the net forecast generation of the hypothetical solar plant and the current generation (represented by *μFH*,*H*), and the alternative is that they are not equal.

#### **Hypothesis 2.**

$$H\_0: \mu\_{NG-D} - \mu\_{(FH,H)-D} = 0\\H\_1: \mu\_{FH-D} - \mu\_{(FH,H)-D} \neq 0\tag{5}$$

where *<sup>μ</sup>NG*−*<sup>D</sup>* = *mean o f* (*NG* − *Demand*); *<sup>μ</sup>*(*FH*,*H*) −*D* = *mean o f* (*NG*(*SUNFH*, *SUNH* ) − *Demand*).

#### **Hypothesis 3.**

$$H\_0: \mu\_{|NG - D|} - \mu\_{|(FH, H) - D|} = 0 \\ H\_1: \mu\_{|NG - D|} - \mu\_{|(FH, H) - D|} > 0 \tag{6}$$

where *<sup>μ</sup>*|*NG*−*D*<sup>|</sup> <sup>=</sup> *mean o f* (*NG* <sup>−</sup> *Demand*) *in absolute value*; *<sup>μ</sup>*|(*FH*,*H*)−*D*<sup>|</sup> <sup>=</sup> *mean o f* (*NG*(*SUNFH*, *SUNH* ) − *Demand*) *in absolute value*.

Hypotheses 1–3 were tested using one year-long hourly data.

#### **Hypothesis 4.**

$$H\_0: \mu\_{\text{Peak}, \text{NG}} - \mu\_{\text{Peak}, \text{FM}, \text{H}} = 0\\H\_1: \mu\_{\text{Peak}, \text{NG}} - \mu\_{\text{Peak}, \text{FM}, \text{H}} > 0\tag{7}$$

where *μPeak*,*NG* = *mean o f daily peak o f energy f rom NG*; *μPeak*,*FH*,*<sup>H</sup>* = *mean o f daily peak o f energy f rom NG*(*SUNFH*, *SUNH* ).

#### **Hypothesis 5.**

*<sup>H</sup>*<sup>0</sup> : *<sup>μ</sup>Peak*, *NG*−*<sup>D</sup>* <sup>−</sup> *<sup>μ</sup>Peak*,(*FH*,*H*)−*<sup>D</sup>* <sup>=</sup> <sup>0</sup>*H*<sup>1</sup> : *<sup>μ</sup>Peak*, *NG*−*<sup>D</sup>* <sup>−</sup> *<sup>μ</sup>Peak*,(*FH*,*H*)−*<sup>D</sup>* <sup>&</sup>gt; 0 (8)

where *<sup>μ</sup>Peak*,*NG*−*<sup>D</sup>* <sup>=</sup> *mean o f daily peak o f energy f rom*(*NG* <sup>−</sup> *Demand*); *<sup>μ</sup>Peak*,(*FH*,*H*−*D*) <sup>=</sup> *mean o f daily peak o f energy f rom* (*NG*(*SUNFH*, *SUNH* ) − *Demand*).

Hypotheses 4 and 5 were tested using a one-year horizon with daily data.

#### **4. Results**

#### *4.1. Results at Different Levels of Solar Energy Penetration*

Table 3 shows the before and after of adding hypothetical solar plants, considering a solar energy penetration of 100%. In Table 3, it is observed that the California region generates the highest percentage of solar energy with 16.2%, followed by the Southwest region with 3.4%. On the other hand, New England only generates 0.2% of solar energy, and the New York region does not have solar generation. This reflects the different levels of solar generation considered in the study. Also, Table 3 shows that the primary energy source in California, New England, and New York is natural gas, with 42.4%, 49.8%, and 34.7%, respectively. In the Southwest region, the main energy-generation resources are nuclear (39.3%) and natural gas (37.5%). The generation from coal and petroleum products, the largest carbon emitters, are less than 4% in California, less than 1% in New England, and less than 3% in New York. However, in the Southwest, the generation from coal reaches almost 15%, being the third most used source, and the generation from petroleum products is zero. This demonstrates that each region has a different energy matrix, with various levels of fossil fuel use.

**Table 3.** 100% Solar Penetration—Generation by region and sources before and after adding the hypothetical solar plants.


Table 3 also shows the results with 100% hypothetical penetration of solar energy. Solar generation almost doubled from 16.2% to more than 30% in the California region. With this increase, solar generation becomes the second source of energy. In the case of New England, where solar generation was only 0.2%, it increased to 4%. This implies that the increase in solar generation helped reduce the consumption of fossil fuels in the New England area. The New York region had no solar generation. However, after the incorporation of 100% of the hypothetical solar plants, it reached a solar generation of 3.7%. The second area with the highest solar generation, the Southwest region, increased from 3.2% to 21%. This implies that Southwest has tremendous potential for solar generation (Arizona, New Mexico, and Southern Nevada).

Table 4 shows the solar generation in each region, and by source, with a penetration of 75%. Even with a 75% penetration of solar energy in the California area, solar energy is the second most used source. Solar energy remains the third most widely used source in the Southwest region. It is essential to mention that even with a 75% penetration, it is still possible to reduce use of fossil fuels significantly. For example, the use of coal in the Southwest decreased from 14.7% to 8.3%. In New England, coal and oil products were cut by almost half. Solar generation becomes the third renewable energy source in the New York region, below hydropower and wind. This implies that even with a 75% penetration of solar energy, a significant reduction in the use of fossil fuels can be achieved in the analyzed regions.

**Table 4.** 75% solar penetration—Generation by region and sources before and after adding the hypothetical solar plants.


Table 5 shows the results in the energy balances before and after the incorporation of hypothetical solar plants, with a 50% penetration of solar energy. While in California and the Southwest solar power generation remains the leading renewable source, in the New England and New York regions, it is the third-largest renewable source behind hydro and wind power. With 50% solar energy penetration, the New England and New York regions only have 2.1% and 1.8% solar generation, respectively. In the Southwest region, there is still a significant decrease in the generation of coal, from 14.7% to 8.7%. This implies that by reducing the penetration of solar generation to 50%, the impacts on the grid are less significant, particularly in New York and New England.

**Table 5.** 50% solar penetration—Generation by region and sources before and after adding the hypothetical solar plants.


Table 6 shows the generation by region and source considering a 25% penetration of integration of photovoltaic generation plants. Solar generation in the California area reaches 19.9%, more than 10% less when compared with 100% penetration of solar energy. After hypothetical solar plant integration, solar generation in the New England and New York regions is about 1% higher than baseline. In the Southwest region, solar generation remains the main source of renewable energy, being 7.7% higher than hydropower (3.2%), and wind (1.9%). This implies that the reduction in fossil fuel use is noticeably less than the other scenarios (higher percentage of solar power generation), particularly in New York and New England, which have the smallest percentage increases in solar power generation.


**Table 6.** 25% solar penetration—Generation by region and sources before and after adding the hypothetical solar plants.

#### *4.2. Results of t-Test for Each Hypothesis*

Table 7 shows the results of the equal means *t*-tests when comparing net generation before and after incorporating the solar plants. Table 7 details the results of Hypothesis 1 by region and solar energy penetration level. Only one *p*-value in the Southwest region with 100% solar energy penetration is significant (*p* < 0.05). The rest of the *p*-values are not significant (using *p* < 0.05), which means that the null hypothesis is not rejected and that there is no evidence to establish that the means are different. The Southwest region had the most significant increase in solar power generation, from 3.2% to 21.0%. The substantial increase in solar generation resulted in a difference in means when considering 100% penetration of solar energy. However, when reducing the percentage of solar energy penetration, there is not enough evidence to reject the null hypothesis that the means are equal. On the other hand, it is observed that in the four regions, California, New England, New York, and Southwest, as the penetration of solar energy decreases, the *p*-value of the statistical test increases. This implies that the equality of the means fails to be rejected as the percentage of the solar penetration decreases. Another important insight from the table is that of the regions analyzed, California produces the most energy on average, followed by Southwest, New York, and New England.


**Table 7.** Hypothesis 1—*t*-test results by region and level of solar penetration.

\* <0.1 and \*\* <0.05.

Table 8 shows the results of Hypothesis 2 by region and level of solar penetration. This part of the analysis shows that when comparing the difference between net generation

and demand before and after incorporating the hypothetical solar plants, there is evidence to reject the null hypothesis in the California and Southwest regions. Particularly in the California area, when considering 100% and 75% solar energy penetration, the *p*-value is less than 0.05, so there is evidence to establish a significant difference between the means (net generation—demand) when comparing before and after incorporating the hypothetical solar plants. In the Southwest area, when solar penetration levels of 100%, 75%, and 50% are considered, there is evidence to reject the null hypothesis (*p* < 0.05). This implies that the means of the difference between net generation and demand before and after incorporating solar plants are different. On the other hand, in the New England and New York regions, at all levels of solar energy penetration, none of the *p*-values is significant (*p* < 0.05), which means that the null hypothesis is not rejected and that there is no evidence to establish that there is a difference between the means (difference between net generation and demand).


**Table 8.** Hypothesis 2—*t*-test results by region and level of solar penetration.

\*\* <0.05.

Table 9 shows the results when comparing the absolute error of the difference between net generation and demand before and after incorporating the solar plants into the system. The *p*-values of the analyses carried out to test Hypothesis 3 of the study indicate a significant difference (using *p* < 0.05) between the means in the California and Southwest regions. In the California region, for penetration levels of 100% and 75%, a *p*-value of less than 0.05 was found. This means that the absolute value of the difference between net generation and demand is different when comparing before and after the massive integration of solar plants. In the case of the Southwest area, a significant difference was found in the means (*p* < 0.05) for penetration levels of 100%, 75%, and 50% of solar energy. In the New England and New York regions, the *p*-values are greater than 0.05, so the null hypothesis cannot be rejected. This implies that based on the given data, there is no strong evidence to suggest that the absolute value of the difference between the net generation and demand is not different.

Additionally, it is observed that the *p*-values in each of the regions increase with increasing levels of solar energy penetration. This means that the massive integration of solar energy impacts the absolute value of the difference between net generation and demand. In other words, solar energy affects the energy interexchange between balancing authorities in absolute value.


**Table 9.** Hypothesis 3—*t*-test results by region and level of solar penetration.

\* <0.1 and \*\* <0.05.

Table 10 shows the results associated with Hypothesis 4 by region and level of solar energy penetration. Hypothesis 4 analyzes the peak energy, considering net generation as a variable before and after integrating solar plants into the system. As a result, it is recognized that the daily peak of energy does not have a statistically significant difference (at *p* < 0.05) when analyzing the net generation. However, it can be observed in the table that as the penetration of solar energy decreases, the *p*-value increases. This implies that the greater the penetration of solar energy, the greater the probability of increasing the power peaks in the balancing authorities.


**Table 10.** Hypothesis 4—*t*-test results by region and level of solar penetration.

Finally, Table 11 shows the results when the energy peaks of the difference between net generation and demand are analyzed before and after the integration of solar plants. As a result, the null hypothesis is not rejected in the four analyzed regions, California, New England, New York, and Southwest. This means that the difference between net generation

and demand before and after the massive integration of solar plants is not different. These results are explained due to the high mean value in the baseline of the difference between net generation and demand (the exchange of energy between balancing authorities). From Table 8, it can be seen that, for example, in California, there are exchanges of almost 8000 MW, in New England and New York of more than 2500 MW, and in Southwest of nearly 6000 MW on average. This implies, as the difference between net generation and demand is significantly high, the impact of solar energy generation is much smaller.


**Table 11.** Hypothesis 5—*t*-test results by region and level of solar penetration.

#### \* <0.1.

#### **5. Discussion**

This study aimed to analyze how the penetration of solar energy utility levels affects energy imbalances and the peak of power in the grid. Subsequently, in response to the research objective, the study shows the following main results. The difference between before and after (the massive integration of solar power plants) is not statistically significant (*p* < 0.05) in most of the regions analyzed when including net generation as a variable (see Table 7). The exception is the Southwest, as it had a considerable increase in solar power generation (3.2% to 21.0%). In the case of the New England and New York regions, it may be that the percentage of solar power generation is too low, 4.0% and 3.7%, respectively, to generate a significant impact on the imbalance of the systems. On the other hand, the California area, in the baseline, already had a high percentage of solar energy generation (16.2%), which increased almost the double (30.8%). For this reason, the impact when analyzing the net generation before and after the massive integration of solar plants was not significant in the California region (see Table 7). For massive integration of renewable energies in the grid, it is necessary to maintain a balance [50].

Unlike this study, a study conducted in Texas found significant differences in energy balances and peak power after the massive integration of solar plants [51]. Although this study did not find a significant impact on the energy balance in most regions, one of the solutions suggested to improve the balance in the grid was the implementation of storage systems [50]. The difference between net generation and demand is analyzed as a variable, the total amount of energy that each region must exchange with other balancing authorities. The results show that the difference when analyzing the hourly data is significant between before and after the integration of the hypothetical solar plants in the system in the regions with the highest generation of solar energy, California and Southwest. This implies an imbalance in energy exchanges with other balance authorities due to incorporating more solar generation into the systems. Having to carry out more significant

energy exchanges with other external systems could cause disturbances due to voltage and frequency differences. Like this study, NREL studies have shown that cooperation between balancing areas is essential when significantly increasing renewable energy generation [52,53]. Studies have shown that by having greater solar energy penetration, more significant power fluctuations in the network are produced due to the changes in solar irradiance, which impacts the energy balance and energy peaks [54].

Additionally, when analyzing different penetration levels, it is observed that the probability of generating disturbances in the system increases when solar generation increases. However, this depends on the percentage of solar generation of the system. For instance, in the case of New England and New York, it is not significant (the portion in both regions is 4% or less). Also, when analyzing the absolute error of the difference between net generation and demand, the results support an increase in the absolute exchanges of energy with other interconnected systems in the California and Southwest regions. This difference decreases as the level of penetration of solar energy decreases. It has been found that power peaks are generated on the grid, which are produced by large solar systems [55]. However, studies have shown that peaks of power can be minimized by incorporating a large number of small solar plants instead of a few large solar plants [55]. In contrast, regarding the daily peak of energy in the net generation, no significant difference was found (at *p* < 0.05, see Table 10) in any of the four regions analyzed. Particularly, in the New England and New York regions, the lack of difference in power peaks is due to the low percentage of solar generation (4% or less). In the cases of California and Southwest, although solar generation is much higher (30.8% and 21.0%, respectively), it is still not enough to generate an impact on energy peaks. The highest energy peaks can be produced at midday, which is when a greater amount of electrical energy is generated from solar systems [33]. For this reason, future studies would benefit from an hourly peak-energy analysis. In addition to being physically adjacent systems connected to the same substation, energy imbalances increase [33]. An analysis at the substation level could generate different results on the peak of energy in the grid.

In previous studies, it was found that substituting traditional electricity generation by photovoltaic systems impacts the stability of the electrical network about energy peaks [56]. In this study, fossil fuels plants were substituted by solar generation. However, no significant impact was found in the energy peaks when the peaks of energy in the difference between net generation and demand were analyzed, that is, the exchange of energy with other areas. It was found that power peaks did not increase with the massive incorporation of solar plants into the systems. The four regions analyzed have a high dependence on energy interchanges with the other areas of the United States electrical system. As interchanges occur hourly, which in some cases may exceed 30% of the energy demanded or produced in the area, it would be necessary for the generation of solar energy to be one of the main sources of generation to create an impact on the energy peaks. Finally, like all studies, this study has limitations. Only four regions were analyzed, and not all the interconnected systems in the United States. Hypothetical data from solar plants were used, which may differ from reality. Furthermore, only four levels of solar energy penetration were considered.

#### **6. Conclusions**

#### *6.1. Summary*

This study provides findings from a comparative analysis considering the massive integration of solar power plants in four regions of the United States electrical system: (1) California, (2) Southwest, (3) New England, and (4) New York. The analysis in the network was carried out per hour, considering the changes in net generation, the net generation error with demand, and the energy power peaks. Figure 1 summarizes the percentages of generation by energy resource before and after the massive incorporation of photovoltaic plants (100% penetration). These plots show that having 100% penetration of solar generation impacts the reduction of the use of fossil fuels. The greatest changes

between before and after were found in the region of California and Southwest, as seen in Figure 1, are those that generate the greatest amount of solar energy.

**Figure 1.** 100% Solar Penetration by region before and after.

The study sought to verify that there are more significant energy imbalances and higher peak power in the grid at a higher level of solar energy penetration. The findings show that when comparing the difference between net generation and demand before and after the massive integration of solar plants, there is a significant difference in the energy balance in the regions with the highest solar generation, namely California and the Southwest. Additionally, by increasing the penetration levels of solar energy, the results are intensified. On the other hand, no significant difference was found in any of the analyzed regions in relation to the energy peaks. However, the *p*-value of the statistical analysis decreases with increasing penetration levels of solar energy in each area. This indicates that when considering a higher penetration of solar energy, there is a greater probability that the energy peak will increase.

#### *6.2. Practical Implications*

The practical implications of this study are of vital importance for increasing solar energy adoption in different regions of the United States electrical system. It is essential to bear in mind that as the installed solar generation capacity increases, the potential energy imbalances that can be created in the electrical network also increase. By having a greater penetration of solar energy, the probability of generating disturbances in the grid will increase. There are several solutions to this problem. First, problems could be overcome by improving solar grid protection plants. By improving protection systems in solar plants and including them as a requirement for future solar plants installations, disturbances in the grid could be reduced. Second, energy storage systems can significantly help grid disturbances. With the development of new storage technologies, costs should decrease and make their deployment feasible on a large scale in the electrical system. A third solution is to improve and standardize the solar forecasting technologies in each of the balancing authorities in the US electrical system. By increasing the precision of solar generation and demand forecasting, the probability of events expected in the electrical grid will decrease. Fourth, the problem could be overcome with the future implementation of peer-to-peer

energy trading at the utility level. However, there are still no regulations and security levels necessary for the massive implementation of P2P models.

#### *6.3. Future Research*

Future studies should be carried out in different regions and with different statistical approaches. First, different time horizons may be included. The current study analyzes data hourly; nevertheless, future studies should be extrapolated to an analysis every 10 or 30 minutes. In this way, the energy fluctuations that could cause more significant energy peaks can be detected. Second, future research can include more levels of solar energy penetration and, in this way, achieve a more detailed sensitivity analysis. In addition, studies can be extended to other regions of the United States and other countries to compare and contrast the reality under different conditions of generation and consumption of energy. Fourth, there are several ways to reduce the impacts caused by the massive integration of solar energy. For example, it would be beneficial to incorporate technologies that reduce the adverse impacts on the electrical grid due to solar energy integration. Integrating energy storage in conjunction with solar plants would be an interesting scenario to assess the real impact of energy storage systems in reducing grid disturbances.

**Author Contributions:** Conceptualization, E.A.S.; methodology, E.A.S.; software, E.A.S.; validation, E.A.S.; formal analysis, E.A.S.; investigation, E.A.S.; resources, E.A.S.; data curation, E.A.S.; writing original draft preparation, E.A.S.; writing—review and editing, L.B.B., E.W., W.D.L.-S.; visualization, E.A.S.; supervision, L.B.B.; project administration, L.B.B.; funding acquisition, E.A.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the National Agency for Research and Development (ANID)/ Scholarship Program/DOCTORADO FULBRIGHT BIO/2015-*56150019*.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**


#### **References**


### *Article* **Efficient Identification of Jiles–Atherton Model Parameters Using Space-Filling Designs and Genetic Algorithms**

**Varun Khemani \*, Michael H. Azarian and Michael G. Pecht**

Center for Advanced Life Cycle Engineering (CALCE), University of Maryland, College Park, MD 20740, USA **\*** Correspondence: vkheman@terpmail.umd.edu

**Abstract:** The Jiles–Atherton model is widespread in the hysteresis description of ferromagnetic, ferroelectric, magneto strictive, and piezoelectric materials. However, the determination of model parameters is not straightforward because the model involves numerical integration and the solving of ordinary differential equations, both of which are error prone. As a result, stochastic optimization techniques have been used to explore the vast ranges of these parameters in an effort to identify the parameter values that minimize the error differential between experimental and modelled hysteresis curves. Because of the time-consuming nature of these optimization techniques, this paper explores the design space of the parameters using a space-filling design. This design provides a narrower range of parameters to look at with optimization algorithms, thereby reducing the time required to identify the optimal Jiles–Atherton model parameters. This procedure can also be carried out without using expensive hysteresis measurement devices, provided the desired transformer's secondary voltage is known.

**Keywords:** genetic algorithm; Jiles–Atherton model; space-filling design

### **1. Introduction**

Hysteresis phenomena are prevalent in various technological domains, resulting in a growing interest in models of the magnetization processes. Jiles and Atherton [1] proposed a model for describing the magnetization of soft magnetic materials. From an engineering point of view, this model is attractive because of the physical interpretation of the parameters that define it and the fact that it is based on the physical insight of hysteresis. However, as noted in [2], the iterative procedure of estimating model parameters poses convergence problems. The model is also extremely sensitive to initial parameter values and hence requires physical experimentation on the material to identify the starting point. Therefore, researchers have tried a host of different techniques to reduce the sum of squared errors (SSE) between experimental and modelled hysteresis curves. Some of these attempts include implementations of global optimization techniques, for example, simulated annealing methods [3], metaheuristic techniques such as genetic algorithms [4,5], machine learning techniques such as neural networks [6], or an exhaustive search in the solution space [7].

Section 2 shows that Jiles–Atherton model parameters are clearly connected with the physical properties of magnetic materials. However, there is no definitive method to calculate the value of each Jiles–Atherton model parameter. All of the methods use optimization algorithms to minimize the objective function, which is defined as the sum of squares of differences between the experimental hysteresis curve and the hysteresis curve as a result of modeling. Unfortunately, this sum exhibits many local minima, and hence gradient optimization techniques strongly depend on the starting point.

The traditional method of estimating model parameters [1] assumed knowledge of measured slopes *dH*/*dM* on several characteristic points on the hysteresis curve. This information facilitated the development of a set of nonlinear equations, which were solved itera-

**Citation:** Khemani, V.; Azarian, M.H.; Pecht, M.G. Efficient Identification of Jiles–Atherton Model Parameters Using Space-Filling Designs and Genetic Algorithms. *Eng* **2022**, *3*, 364–372. https://doi.org/10.3390/ eng3030026

Academic Editor: Huanyu Cheng

Received: 25 June 2022 Accepted: 16 August 2022 Published: 18 August 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

tively to obtain the values of model parameters using numerical Runge–Kutta-algorithmbased methods. The anhysteric magnetization equation for anisotropic materials has been solved with the Gauss–Konrod method. Optimization methods have been explored by fitting Jiles–Atherton hysteresis curves to measurement data by using techniques including nonlinear least-squares, simulated annealing [3], genetic algorithms (binary and real-coded) [4,5], levy whale optimization [8], particle swarm optimization [9], cuckoo search [10,11], the covariance matrix adaptation evolution strategy, and other differential evolution algorithms [12]. Trapanese [6] trained a neural network with the hysteresis data and corresponding Jiles–Atherton model parameters of several materials. The trained network was used to predict the unknown Jiles–Atherton model parameters for a test material.

As optimization algorithms are time-consuming, a trial-and-error approach to Jiles–Atherton model parameter determination has also been suggested. The original paper [1] provided plots of different Jiles–Atherton model parameters held constant while one of them was varied for isotropic materials, whereas Prigozy [13] provided plots for anisotropic materials.

This paper aims to reduce the solution space of the Jiles–Atherton model parameters to a smaller and more manageable set using space-filling designs. In essence, we are reducing the area of the solution space that these algorithms explore, thereby cutting down drastically on the solution space and the time required to reach an optimal solution. The solution space exploration is done efficiently with a space-filling design that is described in the following sections. Once a reduced solution space is obtained, any of the aforementioned algorithms can be used to exploit and further explore the reduced solution space in order to arrive at the optimal solution. However, we focus on the genetic algorithm because it is the most robust among the algorithms [14].

The remainder of the paper is organized as follows. Section 2 describes the Jiles–Atherton model in detail. Section 3 describes space-filling designs and its application to the Jiles–Atherton Model, and Section 4 describes the genetic algorithm for identifying the parameters of the Jiles Atherton Model. The conclusions follow in Section 5.

#### **2. Jiles–Atherton Model**

The Jiles–Atherton [1] accounts for all important features of the hysteresis curve (Figure 1)—initial magnetization curve, saturation of magnetization, coercivity, remanence/retentivity. The Jiles–Atheron model was developed for anhysteric magnetization (*M*an) using the mean field approach [1]. The effects of magnetic domain wall pinning on defect sites are then considered to account for hysteresis. Examples of defect sites include grain inhomogeneity, for example, angles of dislocation, inhomogeneous strain regions, etc.

**Figure 1.** Typical hysteresis loop.

The following expression represents the effective magnetic field,

$$H\_{\varepsilon} = H + \mathfrak{a}M\_{an} \tag{1}$$

where *α* is a parameter representing the experimentally determined inter-domain coupling, and *H* is the magnetizing field. For an isotropic material, the magnetization response to this effective field is expressed as

$$M = MS \* f(H\_c) \tag{2}$$

where *MS* is the saturation magnetization of the ferromagnetic material with unit A/m, and *f* is a function to be defined. This magnetization expression accounts for the magnetic field response and the mean magnetic interaction with the rest of the material using the term *αM,* and hence is only a statistical domain distribution. Hence, it does not account for pinning and is considered the anhysteric magnetization. The modified Langevin equation is considered for *f*, which leads to the following expression for anhysteric magnetization,

$$M\_{\rm an} = MS \left[ \coth \left[ \frac{H\_{\rm e}}{A} \right] - \left[ \frac{A}{H\_{\rm e}} \right] \right] \tag{3}$$

Here, *A* is the anhysteric behavior parameter which characterizes the shape of the anhysteric magnetization. When the work done by the field equals the magnetization energy of the sample, the domain wall displacement stops. On removal of the field, the domain wall returns to its original location. The domain wall translation causes an energy loss called the irreversible magnetization component *M*irr, and is given by

$$\frac{dM\_{\text{irr}}}{dH} = \frac{M\_{\text{an}} - M}{\frac{\delta K}{\mu} - a\left(M\_{\text{an}} - M\right)}\tag{4}$$

Here, *K* is the average energy to break the pinning location, *μ* is the initial permeability of the material, and

$$\mathcal{S} = \begin{cases} +1 \text{ for } \frac{\text{dFI}}{\text{dI}} > 0\\ -1 \text{ for } \frac{\text{dFI}}{\text{dI}} < 0 \end{cases} \tag{5}$$

The total magnetization is given by

$$\frac{dM}{dH} = \frac{1}{1+\mathcal{C}} \frac{M\_{\text{an}} - M}{\frac{\delta k}{\mu} - \alpha (M\_{\text{an}} - M)} + \frac{\mathcal{C}}{1+\mathcal{C}} \tag{6}$$

Here, *C* is the magnetization reversibility proportion.

Various modifications/additions were made to the Jiles–Atherton model by multiple researchers, for example:

(a) The original Jiles–Atherton model only considered isotropic materials. The anhysteric magnetization for anistropic materials is given by

$$M\_{\rm ah}^{\rm aniso} = MS \left[ \frac{\int\_0^\pi e^{\frac{E(1) + E(2)}{2}} \sin \theta \cos \theta d\theta}{\int\_0^\pi e^{\frac{E(1) + E(2)}{2}} \sin \theta d\theta} \right] \tag{7}$$

where *E* (*i*) is given by

$$E(i) = \frac{H\_{\rm eff}}{a} \cos \theta - \frac{K\_{\rm an}}{M\_s \mu\_0 a} \sin^2 \phi\_i \tag{8}$$

where *φ* is the angle between the applied field and easy magnetization axis, *θ* is the angle between the atomic magnetic moment and magnetizing field direction, and *K*an is the magnetic anisotropy energy density with units J/m3. In some materials such as constructional steels, isotropic and anisotropic phases can be mixed. In these cases, the total anhysteric magnetization is calculated as per Equation (9), where *t* is between 0 and 1.

$$M\_{\rm an} = tM\_{\rm an}^{\rm aniso} + (1 - t)M\_{\rm an}^{\rm iso} \tag{9}$$


$$\frac{dM}{dB} = \frac{(1-\mathcal{C})\frac{dM\_{\text{dir}}}{dB} + \frac{\mathcal{C}}{\mu\_0}\frac{dM\_{\text{dir}}}{dH\_{\text{cr}}}}{1 + \mu\_0(1-\mathcal{C})(1-\alpha)\frac{dM\_{\text{dir}}}{dB} + \mathcal{C}(1-\alpha)\frac{dM\_{\text{dir}}}{dH\_{\text{cr}}}} \tag{10}$$

#### **3. Space-Filling Design**

In deterministic modeling problems such as circuit SPICE simulations, the variability is negligible, so the traditional design of experiment features such as replication, randomization, and blocking to reduce experimental variability are unnecessary. Computer deterministic models are complex and can involve hundreds of variables with interactions. Space-filling designs are used to find a simpler model form of the complex computer model called a surrogate model. Space-filling designs find accurate representations of complex computer models by spreading out the design points as far apart from each other as possible while staying within the model parameter boundaries. As opposed to traditional designed experiments that have fixed levels for each factor for each simulation, spacefilling designs explore the design space between two levels more thoroughly by having different levels in every simulation. This leads to a higher coverage of the parametric space, which is extremely important in the case of the Jiles–Atherton model, which has multiple local minima.

Latin hypercube designs [15] spread out the points in the design space more evenly across all possible values as compared to sphere packing designs. The parametric space is partitioned into intervals, and a sample is selected from each interval. Uniform design [16] minimizes the discrepancy between the design points (which have an empirical distribution that approximates uniformity) and a theoretical uniform distribution.

The Latin hypercube was used to set up a space-filling design that explores the design space of the four Jiles–Atherton parameters *MS*, *A*, *C*, and *K* because of its computational efficiency compared to the other types of space-filling designs. By default, the number of simulations that need to be run is 10 times the number of factors, which, in this case, means 40 simulations need to be run. First, a linear model (11) is fit where the response SCORE represents the sum of squared errors (SSE) between the actual transformer's secondary voltage and the transformer's secondary voltage simulated on PSpice. The analysis is carried out using SAS JMP software.

$$\text{SCORE} = \beta\_0 + \beta\_1 MS + \beta\_2 A + \beta\_3 C + \beta\_4 K \tag{11}$$

The estimates of the regression coefficients of the linear model (11) are given in the 'Estimate' column in Table 1, whereas the column 'Std Error' gives the standard deviation of each of the parameters. The 't Ratio' column gives the t ratio metric, which tests whether the true value of the parameter is zero. It is a ratio of the estimate to its standard error, and under the null hypothesis (true value of parameter is zero), has a Student's t distribution. The 'Prob > |t|' column lists the *p*-value for the test where the true parameter value is

zero. A *p* value of less than 0.05 implies that the parameter is statistically significant at the 95% confidence level. The goodness of fit of the linear model (11), as measured by the metric RSquare Adjusted, which is the coefficient of determination adjusted to account for overfitting, is 0.71 or 71%. As can be seen from Table 2, as expected, all Jiles–Atherton model parameters are statistically significant to the SCORE at the 95% confidence level. JMP has the option of a prediction profiler (Figure 2) that can be used to vary the parameter values simultaneously to bring the SCORE (SSE) to zero (Figure 3).


**Table 1.** Parameter estimates of linear model effects.

**Table 2.** Parameter estimates of response surface model effects.


**Figure 2.** Prediction profiler for the linear model.

**Figure 3.** Prediction profiler for the optimized linear model.

Figures 2 and 3 show the individual response surfaces of the different Jiles–Atherton model parameters. The slopes of the response surfaces are the values in the 'Estimate' column of Table 1, which in turn are the regression coefficients of the linear model (11). The larger the absolute value in the 'Estimate column' of Table 1 of the Jiles Atherton model parameter, the larger its statistical significance and larger the slope of its response surface. The cross-hairs on the prediction profiler can be moved to reduce the response towards zero as much as possible. For example, reducing *MS* and increasing *A* would cause the response to move towards zero as shown in Figure 3. This results in a SCORE (SSE) value of 0.111449, but with a wide confidence interval from −797.13 to 797.357.

To improve the goodness of fit, we fit a response surface model (12) to check if there are any significant interactions or quadratic effects among the Jiles–Atherton model parameters.

$$\begin{array}{c} \text{SCORE} = \beta\_0 + \beta\_1 MS + \beta\_2 A + \beta\_3 C + \beta\_4 K + \beta\_{11} MS \ast MS + \beta\_{12} MS \ast A + \beta\_{13} MS \ast C + \beta\_{14} MS \ast K\\ \quad + \beta\_{22} A \ast A + \beta\_{23} A \ast C + \beta\_{23} A \ast K + \beta\_{33} C \ast C + \beta\_{34} C \ast K + \beta\_{44} K \ast K \end{array} \tag{12}$$

As can be seen from Table 2, as expected, all the Jiles–Atherton model parameters are significant to the SSE. However, the interaction effects between *MS* and *C*, *A* and *K*, and *C* and *K* are significant, too. Additionally, the quadratic effects of all the Jiles–Atherton model parameters are significant, too. The same is evident from the quadrature of the individual response surfaces in the prediction profiler, as can be seen in Figures 4 and 5.

**Figure 4.** Prediction profiler for the response surface model.

**Figure 5.** Prediction profiler for the optimized response surface model.

The goodness of fit of the response surface model, as measured by the metric RSquare Adjusted, is 0.84 or 84%. Since it is not a perfect fit i.e., 100%, we further explored the region near the values that give a zero response in the prediction profiler using stochastic optimization.

#### **4. Parameter Identification of The Jiles–Atherton Model**

Genetic algorithms [17] are based on the theory of evolution. A population consists of individuals with genetic material called genes, which reproduce to create the next generation. Genes from two parent individuals are combined using various crossover procedures to create offspring individuals for the next generation and so on and so forth. The selection of individuals in the parent generation to reproduce is dependent on their fitness, i.e., their evaluation of the objective function of the optimization problem. Usually, the individuals with the best fitness move on to the next generation without reproduction in order to propagate the best solution through a process called elitism. Individuals that are not elite reproduce through crossover. To introduce variety in the genes, random changes are introduced into the genes of a fraction of the individuals in the offspring generation. This is analogous to mutation in evolution and helps in avoiding local minima in the optimization of the objective function. This evolution process continues until there is no improvement in the fitness in consecutive generations or until the predefined number of generations is reached.

The genetic algorithm was implemented with 50 individuals in each generation and 50 maximum generations. A crossover probability of 90% and a mutation probability of 5% was used. The full ranges in SPICE and the reduced ranges for each variable after the space-filling design are shown in Table 3. The fitness function to be minimized corresponds to the total SSE between the actual and simulated transformer's secondary voltage. The optimal values in those ranges as found by the genetic algorithm are also shown in the table. SAS JMP Pro 15 was used for the space-filling design, and MATLAB was used to implement the genetic algorithm and communicate with the SPICE simulator (OrCAD PSpice). The code required for conducting the approach is available in the supplementary material. Due to the significant reduction (by about 85%) of the solution space of the Jiles–Atherton model parameters that the stochastic optimization algorithms have to explore, the computational time using this approach is significantly smaller than without the approach. The exact time required for the approach depends on the simulation time for the circuit of which the transformer is a part of.


**Table 3.** Allowable ranges and optimized values for Jiles–Atherton model parameters.

This modeling technique was developed to be able to simulate a large analog circuit with five transformers. The Jiles–Atherton model parameters learnt by the proposed technique were used to implement the transformers in the SPICE circuit model. The circuit output as a result of the usage of these Jiles–Atherton model parameters was verified with the circuit output of the actual circuit. This procedure confirmed the validity of the developed method. Additionally, this procedure also speaks to the advantage of this technique —estimation of the Jiles–Atherton model parameters without resorting to the need for hysteresis parameter measurement.

#### **5. Conclusions**

This paper demonstrated a novel way to identify parameters for the Jiles–Atherton model. A space-filling design was used to search the solution space optimally, which is advantageous because the Jiles–Atherton model has multiple local minima. The overall method can ascertain Jiles–Atherton model parameters without having to use expensive hysteresis measurement devices. The only prerequisite for the application of this method is that the transformer's secondary voltage (or current) waveforms must be known. This information can be measured by relatively inexpensive measurement devices.

Another advantage of this method is that it significantly reduces (by about 85%) the solution space of the Jiles–Atherton model parameters that the stochastic optimization algorithms have to explore. Additionally, by using space-filling designs, we have been able to discover previously unknown relations between Jiles–Atherton model parameters. For example, in addition to linear effects, the quadratic effects of the Jiles–Atherton model parameters are statistically significant at the 95% confidence level. We have observed that some of these interactions are also significant. A detailed simulation study is required to confirm these observations and possibly modify the Jiles–Atherton model to account for the new observations. This will be the focus of our future work.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/eng3030026/s1, Code.

**Author Contributions:** Conceptualization, methodology, investigation, software, writing—original draft, V.K.; writing—review and editing, M.H.A.; writing—review and editing, supervision, M.G.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Preliminary Siting, Operations, and Transportation Considerations for Licensing Fission Batteries in the United States**

**DaeHo Lee and Mihai A. Diaconeasa \***

Department of Nuclear Engineering, North Carolina State University, Raleigh, NC 27695, USA **\*** Correspondence: madiacon@ncsu.edu

**Abstract:** Nuclear energy is currently in the spotlight as a future energy source all over the world amid the global warming crisis. In the current state of miniaturization, through the development of advanced reactors, such as small modular reactors (SMRs) and micro-reactors, a fission battery is inspired by the idea that nuclear energy can be used by ordinary people using the "plug-and-play" concept, such as chemical batteries. As for design requirements, fission batteries must be economical, standardized, installed, unattended, and reliable. Meanwhile, the commercialization of reactors is regulated by national bodies, such as the United States (U.S.) Nuclear Regulatory Commission (NRC). At an international level, the International Atomic Energy Agency (IAEA) oversees the safe and peaceful use of nuclear power. However, regulations currently face a significant gap in terms of their applicability to advanced non-light water reactors (non-LWRs). Therefore, this study investigates the regulatory gaps in the licensing of fission batteries concerning safety in terms of siting, autonomous operation, and transportation, and suggests response strategies to supplement them. To figure out the applicability of the current licensing framework to fission batteries, we reviewed the U.S. NRC Title 10, Code of Federal Regulations (CFR), and IAEA INSAG-12. To address siting issues, we explored the non-power reactor (NPR) approach for site restrictions and the permit-by-rule (PBR) approach for excessive time burdens. In addition, we discussed how the development of an advanced human-system interface augmented with artificial intelligence and monitored by personnel for fission batteries may enable successful exemptions from the current regulatory operation staffing requirements. Finally, we discovered that no transportation regulatory challenge exists.

**Keywords:** fission battery; regulation; licensing; siting; transportation; autonomous operation

### **1. Introduction**

*1.1. Background*

Nuclear energy is one of the eco-friendly and low-carbon energy sources for our world currently struggling with pollution, severe climate change, and the resulting natural disasters. Historically, the power of nuclear energy was recognized and started to be used in the 1940s, and through continuous development, it has become a major energy source, accounting for 10% of the global electricity production and 20% of the United States' (U.S.) electricity production [1].

However, historical accidents from the previous generation, large-scale nuclear power plants (NPPs), have taken away trust in nuclear energy and instilled fear. As a result, the United Kingdom, France, South Korea, and Japan declared a gradual reduction in NPPs, although some have reconsidered their position due to recent global events and climate goals. In the U.S., cost considerations are forcing the early retirement of NPPs and weakening the national nuclear supply chain [2].

In this trend, nuclear experts are conducting research on the miniaturization of NPPs to reduce huge damage in the event of an accident and the economic burden from the large capital cost per plant of the current NPPs. Accordingly, advanced reactors, such

**Citation:** Lee, D.; Diaconeasa, M.A. Preliminary Siting, Operations, and Transportation Considerations for Licensing Fission Batteries in the United States. *Eng* **2022**, *3*, 373–386. https://doi.org/10.3390/eng3030027

Academic Editor: Antonio Gil Bravo

Received: 17 June 2022 Accepted: 30 August 2022 Published: 4 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

as SMRs and micro-reactors, are under development, where SMRs are expected to be commercialized in 2029 [1]. Going one step further, Idaho National Laboratory (INL) took the idea from batteries and established the fission battery initiative to make nuclear energy accessible to the public in any location with the vision of "plug and play", just like in chemical batteries, without the need for licensed operators.

Meanwhile, the commercialization of reactors is regulated by the U.S. Nuclear Regulatory Commission (NRC), and the safe and peaceful use of nuclear energy in terms of safety, security, and safeguards are supervised by the International Atomic Energy Agency (IAEA). However, current regulations focusing on current NPPs are facing significant regulatory gaps of applicability to advanced reactors. Therefore, this research investigates the regulatory challenges of the licensing of fission batteries concerning safety in terms of siting, autonomous operation, and transportation, and suggests potential response strategies to supplement it.

#### *1.2. Fission Batteries*

#### 1.2.1. Fission Battery Attributes

Five attributes, economical, standardized, installed, unattended, and reliable, support the vision and suggest the direction for development [3]. The fission battery attributes are defined as follows:


#### 1.2.2. Fission Battery Design Features

The fission battery design is expected to follow the micro-reactor design features, mainly gas-cooled reactors with tri-structural isotropic (TRISO) fuel or heat-pipe reactors with metal, oxide, or TRISO fuels. Fission batteries will be designed to be used for less than 1 year with an output of less than 25 MWth and cheaper than 0.1 billion USD to meet midsize customer energy demands [4], such as isolated grids, military bases, and electricity supply to electric vehicles [5]. A design example of an autonomous micro-reactor currently is the eVinci design, currently under development by Westinghouse [6,7].

The most notable feature of this design is that it aims for a dramatically enhanced safety performance compared to the current large light water reactors. This is achieved by active and passive safety features for reactivity control, heat removal, and containment for redundancy and diversity [7]. For reactivity control, three strategies were designed: control drum subsystem, emergency shutdown subsystem, and passive release of hydrogen from the moderator. The design includes two strategies for decay heat removal, one using heat channels through the power conversion system and the other through the reliance on the conduction of heat through the core block to the canister with natural air convection heat removal from the outside surface of the canister to an air duct system that channels air to the surrounding environment. For the containment function, the eVinci design includes three barriers to prevent the release of radioactive material: a monolith encapsulation of fuel, a solid core block, and a canister containment subsystem.

Fuel with high-assay low-enriched uranium (HALEU), enriched from 5% to 20%, is the most typically considered fuel type for advanced reactors, such as the eVinci microreactor design described above [8]. TRISO fuel is one of the representative fuels using

HALEU with the uranium form of uranium oxycarbide (UCO) or uranium dioxide (UO2). The TRISO particles are encapsulated with three layers of carbon and ceramic-based materials that prevent the release of most radioactive fission products and withstand very high temperatures without melting, ensuring good fission product retention even under extremely severe conditions, including temperatures of 1600 ◦C for hundreds of hours [9].

Moreover, since the thermal power level is hundreds of times smaller compared to light water reactors, the number of fission products that are produced and could potentially be released to the environment is also much smaller. This can be seen from the radiological consequence evaluations performed for the eVinci micro-reactor design configurations having thermal power output levels of 1 MWth and 14 MWth [10]. When considering three barriers, the maximum total effective dose equivalent (TEDE) to a dose receptor within 1 m was between 6.33 <sup>×</sup> <sup>10</sup>−<sup>12</sup> rem and 6.84 <sup>×</sup> <sup>10</sup>−<sup>8</sup> rem for a 1 MWth reactor, and for a 14 MWth reactor, it was between 6.33 <sup>×</sup> <sup>10</sup>−<sup>12</sup> rem and 9.58 <sup>×</sup> <sup>10</sup>−<sup>7</sup> rem in all accident scenarios [10]. This shows that the released doses are essentially zero for all practical purposes when compared to the average U.S. resident's annual background radiation from natural and anthropologic sources of approximately 6.2 <sup>×</sup> <sup>10</sup>−<sup>1</sup> rem [11]. Even when assuming only one barrier, the maximum total effective dose equivalent (TEDE) to a dose receptor within 1 m was between 5.11 <sup>×</sup> <sup>10</sup>−<sup>4</sup> rem and 5.59 rem for a 1 MWth reactor, and for a 14 MWth reactor, it was between 5.11 <sup>×</sup> <sup>10</sup>−<sup>4</sup> rem and 78.3 rem in all accident scenarios [10]. To put it into perspective, this is about the same order of magnitude of doses below which we have no data to establish a firm link between radiation exposure and cancer [11] and thousands smaller than the high doses 134 workers received while on the site during the early morning of 26 April 1986 after the Chernobyl accident, of which 28 were confirmed dead in the first three months due to radiation exposure [12].

In addition, the eVinci micro-reactor design supports the fission battery unattended attribute by including only one operator action of tripping the control drum system [10]. However, during emergency conditions, the reactivity control function is achieved without operator actions through the automatic emergency shutdown subsystem and the passive release of hydrogen from the moderator.

#### **2. Regulatory Review Methodology**

The regulatory review methodology used in this study is shown in Figure 1.

**Figure 1.** Regulatory review process in this study.

INSAG-12 "Basic Safety Principles for NPPs" [13] and the U.S. NRC Title 10, Code of Federal Regulations (CFR) [14] were reviewed to evaluate the specific safety principles essential for the licensing of NPPs and obtain regulatory information on the licensing process of 10 CFR Part 50 and 52 (Table 1).

The next step was to apply the current regulatory licensing framework to fission batteries in terms of siting, operation, and transportation, and figure out regulatory challenges considering the characteristics of fission batteries.


**Table 1.** List of U.S. NRC 10 CFR Part related to licensing commercial nuclear reactors.

Finally, response strategies were presented to support the licensing of fission batteries against the challenges. In this step, the non-power reactor approach was cited from the "Regulatory review of microreactors-Initial considerations" [15] and the permit-by-rule approach was referenced from "Key regulatory issues in nuclear microreactor transport and siting" [16]. In addition, an advanced human-system interface (HSI) for autonomous operation approach was derived from "Human-system interface to automatic systems: Review guidance and technical basis" [17] and "A method to select human-system interface for NPPs" [18].

#### **3. The Current Licensing Framework for NPPs**

#### *3.1. Basic Safety Principles for NPPs (INSAG-12)*

Internationally, the IAEA oversees the safe and peaceful use of nuclear energy, ensuring the protection of people and the environment from the harmful effects of radiation. INSAG-12 [13], written by the International Nuclear Safety Advisory Group (INSAG), provides three safety objectives, three fundamental safety principles, and eight specific principles. The specific principles present eight types of safety principles applied during the main design phases, from the early conceptual design phase to the decommissioning phase (Figure 2). Above all, siting and operation are recognized as top research priorities for licensing issues considering the features of fission batteries that would be used anywhere without on-site licensed operators.

**Figure 2.** Structure of specific principles.

#### *3.2. The Regulatory Licensing Framework of the U.S. NRC*

Title 10 of the CFR, established by the U.S. NRC, contains the requirements that need to be met by organizations using nuclear materials or operating nuclear facilities in the U.S. Currently, there are two ways to achieve a commercial license regulated by the U.S. NRC; 10 CFR Part 50 dividing construction permit (CP) and operating license (OL) or 10 CFR Part 52 supporting a combined process of construction and operating license (COL) [19].

According to Figures 3 and 4 describing the process of Part 50, initial public hearings, an environmental report, and an NRC review of the preliminary design for a CP are required, which is a pre-requisite for obtaining an OL issued with final mandatory public hearings and final safety and environmental requirements [20]. Through this process, obtaining a license normally takes more than 10 years [21].

**Figure 4.** OL process of 10 CFR Part 50.

In order to reduce the various economic and regulatory risks that may arise during the long period of the Part 50 process, Part 52 was introduced [21], combining CP and OL steps. As seen in Figure 5, the Part 52 process is conducted with an early site permit (ESP) and a design certification (DC) together prior to issuing a COL [20]. Through this streamlined process, it shortens the period to within 10 years. Figure 6 graphically shows, for power reactors, how the two kinds of licenses can be obtained with the process of Part 50 and Part 52, that is, prototype license and license through analysis and test [22].

**Figure 5.** COL process of 10 CFR Part 52.

However, the current licensing framework of Part 50 and Part 52 does not fully consider the features of advanced reactors, and so the U.S. NRC is taking the process for 10 CFR Part 53 "Licensing and Regulations of advanced nuclear reactors" mandated by the Nuclear Energy Innovation and Modernization Act (NEIMA). Currently, the preliminary rule language consists of 10 subparts based on a risk-informed and performance-based regulatory approach [23].

**Figure 6.** The U.S. NRC licensing structure.

#### **4. Applicability of the Current U.S. Licensing Framework to Fission Batteries** *4.1. Siting Regulations*

Siting is used to select an appropriate location for a safe operation, including the process of analyzing natural and anthropogenic hazards, such as the radiological impact on the public and the environment [13]. Accordingly, the NRC requires an environmental report (ER) during the licensing process for CP, which takes several years for the site investigation and requires detailed site-specific information, including impacts on area populations and surrounding environmental conditions. To minimize the impacts on the site, regulations and guidance are strictly stipulated by the U.S. NRC and IAEA. Table 2 shows in detail the current regulations and regulatory guides related to siting.

**Table 2.** Regulations and regulatory guides related to siting.


#### 4.1.1. Applicability of Siting Regulations to Fission Batteries

Considering the expansive use of target electricity markets by military bases, isolated grids, and electricity supply to electric vehicles, fission batteries are expected to be developed to enable multi-site deployment with the concept of "plug-and-play". However, the current regulations and guidance presented above, directly contradict the vision for

fission batteries, designed to be used anywhere, due to numerous prescriptive rules on the site selection.

In response to performance rules, such as doses at the exclusion areas under normal operation and emergency conditions, technology suppliers are designing enhanced passive safety systems for advanced reactors. Fission batteries are expected to have additional attributes such that any abnormal events will result in a significantly reduced source term and limit any radioactive materials release to within the site boundary or be limited to within a short distance of the exclusion area boundary [24]. Therefore, site restrictions may not be suitable for the universal use of fission batteries equipped with enhanced passive safety systems.

Additionally, the long duration, on the order of multiple years, for site evaluation in the current licensing process would interfere with the multi-site deployment and expedient site transfer required by user needs.

As a result, we conclude that the current site regulations and licensing process do not apply to the characteristics of fission batteries in terms of site restrictions and excessive time burdens for on-site evaluations.

4.1.2. Response Strategy to Site Restrictions: Non-Power Reactor Approach

The IAEA suggests an emergency planning zone (EPZ) where preparations are made to promptly shelter in place to perform environmental monitoring and to implement urgent protective actions. Table 3 shows the represented EPZ size [25]. Therefore, it can be inferred that the EPZ size of fission batteries whose output is [4] less than 25 MWth would be within 1.5 km.


**Table 3.** Suggested EPZ size for NPPs.

However, it seems to be reasonable to re-analyze the EPZ size of fission batteries that are expected to be equipped with enhanced passive safety systems, so those doses could be under the regulatory limit of 1 rem for non-power reactors [15]. Accordingly, applying the rules to non-power reactors is appropriate, and Table 4 shows the EPZ size of non-power reactors [26]. If it is applied to fission batteries, the EPZ size of the fission batteries would be reduced to approximately 400 m for power levels up to 20 MWth and even the operation boundary for power levels below 2 MWth.

#### **Table 4.** EPZ size for NPRs.


Meanwhile, SMR developers insist that the EPZ size for SMRs with an output of 300 MWth should be within 300 m or less to replace fossil fuel power plants located near big cities [27]. In Tables 3 and 4, we can see the relationships between EPZ size and power output. In Table 3, it shows that when power output increases 10 times from 10 MWth to 100 MWth, EPZ size also becomes 10 times larger, from 0.5 km to 5 km. Therefore, if we assume that the power level is proportional to the fission products that are produced and potentially released and that the relationship above could apply to advanced reactors, such as SMRs and fission batteries, we could expect that the EPZ size of fission batteries whose power output may be less than 25 MWth would be 25 m. These assumptions need to be confirmed by analysis; however, since the sudden request for a big regulatory change can be burdensome to the regulatory authorities, starting with the officially proven non-power reactor approach, it is desirable to request gradual deregulation, as the design of fission batteries is materialized, and its safety systems are verified and validated. Finally, the zero-EPZ concept should be applicable in the future [28], such that fission batteries can be widely used in highly populated areas.

#### 4.1.3. Response Strategy to Excessive Time Burdens: Permit-By-Rule Approach

A permit-by-rule is a pre-construction permit issued by a reviewing authority that may be applied to a number of similar emissions units or sources within a designated category [29]. It is widely used for safety-guaranteed facilities, for example, on-site power generation. Sites for fuel-burning equipment are applied to permit-by-rule in Georgia State [30]. The key to applying permit-by-rule is to prove high levels of safety and reliability at the design stage. Therefore, considering the enhanced safety features of fission batteries, permit-by-rule would be a fast and reliable regulatory approach for achieving multi-site deployment and expedient site transfer by reducing the time for siting to a few days or weeks instead of several years within the current regulation [16].

The permit-by-rule approach would be conducted with the analysis of the plant parameter envelope and site parameter envelope. Major steps for it may include [16]:


Therefore, defining a well-developed plant parameter envelope and a hypothetical site parameter envelope are essential for the permit-by-rule approach. A plant parameter envelope may be analyzed in the design process, and a site parameter envelope may be analyzed by modeling, applying simulation tools, and applying unsupervised machine learning technology for expected areas.

As a result, when fission battery design is mature enough and a high-quality enhanced safety system is verified and validated, permit-by-rule could be a reasonable approach that would sufficiently replace or complement the current years-long siting evaluation process for fission batteries that may require hundreds or thousands to be deployed simultaneously.

#### *4.2. Operations Staffing Regulations*

Operation is the key phase in the lifecycle of NPPs. Once NPPs begin operation, their safety performance depends on the reliability and capability of the facility equipment and human personnel, especially during abnormal conditions. As shown in Table 5, therefore, the composition of the control room and related staffing regulations are specified in 10 CFR Part 50 and Part 55. What stands out is that regulations prescriptively set the minimum required number of licensed operators on site during normal operation and emergencies. Even the preliminary language of 10 CFR Part 53 for advanced reactors still requires licensed human operators. As such, the operation and response to emergencies for NPPs are highly dependent on licensed human personnel.


**Table 5.** Regulations and regulatory guides related to operations staffing.

#### 4.2.1. Applicability of Operations Staffing Regulations to Fission Batteries

According to the un-attended fission battery attribute, fission batteries are expected to be developed for un-attended operation through resilience and automation. Investigations in the aftermath of the Three Mile Island and Chernobyl accidents showed that human errors resulted from equipment design and human factor deficiencies [31]. Therefore, the development of automation should be attained with the advanced design of passive safety systems, simplicity of operation, and limited important human actions based on innovative un-supervised machine learning technology [3].

However, the current operations staffing regulations covering licensed operators seem to be highly dependent on personnel and do not fully capture current automation capabilities. The exemption process for control room staffing requirements shows some benefits. For example, NuScale Power successfully obtained an exemption to reduce the number of staff for its SMR light-water design, but it was not a complete elimination [22].

Nevertheless, the designer community is still expected to develop fission batteries with high automation and remote monitoring and with no operator control or at least partial control [32]. This is because the un-attended operation is the most important attribute of fission batteries, that is, aiming to enable their use by ordinary people, such as chemical batteries. Therefore, current regulations related to operators cannot be applied to unattended operations of any advanced reactor, including fission batteries, for which a change in regulations is necessary.

#### 4.2.2. Response Strategy to Operations Staffing Regulations: Advanced Human-System Interface

Human-system interface technology is defined as the part of the nuclear reactor through which personnel interact to perform their functions and tasks with the systems. The primary purpose of the human-system interface is to provide the operator with a means to monitor and control the nuclear reactors and to restore them to a safe state when adverse conditions occur [18], and so it is widely used at present.

In advanced human-system interface systems with improved telecommunication technologies, an off-site space equipped with a set of computer displays and input devices may replace the control rooms and make it feasible for remote monitoring and control. Moreover, the enhanced safety systems and simplified design may allow one controller to manage multiple reactors. In the current state, human-system interface technology

still requires minimum human functions. However, for fission batteries equipped with un-supervised machine learning technology, un-supervised machine learning could replace human functions. Therefore, an advanced human-system interface managed by un-supervised machine learning would be the core technology required for autonomous operation of fission batteries.

Meanwhile, the advancements in automation systems and the development of computer performance have had a tremendous impact on the deployment of automation technologies and systems in many industries over the past years, such as a nearly autonomous management and control (NAMAC) system [33], where the digital twin (DT) and advanced machine learning algorithms play key roles in replacing human personnel.

Therefore, optimistic expectations on the progress of a complete remote-control system with advanced telecommunication technologies and human-system interface operated by un-supervised machine learning could make it possible for fission batteries to be exempted from current regulations related to operations staffing.

#### *4.3. Transportation Regulations*

Transportation in the nuclear industry means moving radioactive materials to the desired places. Related regulations are co-managed by 10 CFR 71 of the U.S. NRC and 49 CFR 173 of the U.S. Department of Transportation (DOT). Table 6 shows the currently regulated packaging types for the transportation of radioactive materials.

**Table 6.** Classification of packaging type for transportation of radioactive materials.


The packaging type is determined by the quantities of radioactive materials, and each package is required to resist certain conditions. In order to verify the safety performance of each package, the U.S. NRC requires specific tests on the normal conditions of transport (NCT) and hypothetical accident conditions (HAC). Especially, tests on the HAC for Type B packaging assuming possible severe transportation accidents are specified in 10 CFR 71.73 [34]. The need for the safety performance test is to prevent the leakage of radioactive material or to control it below a prescribed regulatory dose limit as described in Table 7 under all conditions.

**Table 7.** Regulated radiation dose limits for transportation of radioactive materials.


<sup>1</sup> Additional requirements for Type B packaging.

Therefore, even in the most severe transportation accidents, packages should be able to maintain their containment function and prevent the release of radioactive materials under regulatory the dose limit.

#### Applicability of Transportation Regulations to Fission Batteries

According to the installed fission battery attribute, fission batteries are expected to be installed at the factory, delivered to multiple users, and decommissioned with the fuel loaded. Considering this design goal, three transportation phases could be analyzed:


These new transportation phases for mobile reactors equipped with fuel pose technical and regulatory challenges. The third phase is especially critical for fission batteries since the used fuel will contain highly radioactive fission products.

When it comes to technical challenges, the key for fission battery transportation is to achieve complete safety reliability for radiation shielding, decay heat removal, and maintaining subcriticality, and capability for preventing the release of radioactive materials. However, when fission batteries are fully developed and commercialized, the technical challenges are expected to be addressed. Therefore, this study assumed that fission batteries would have adequate safety systems to meet the technical challenges associated with fission battery transportation.

For regulatory considerations, the current regulations for transporting radioactive materials stipulate the packaging type and the dose limit for packages. Currently, one of the most hazardous radioactive materials is used or spent nuclear fuel, which requires the use of Type B packaging as seen in Table 6.

Moreover, since fission battery transportation will include used fuel during the third transportation phase, it seems reasonable to assume the designers may try to meet the Type B packaging requirements, which is the safest and most robust cask in use nowadays. Accordingly, if fission battery designs meet the Type B packaging requirements at a reasonable cost and, implicitly, meet the regulatory dose limits, safe fission battery transportation is possible under current regulations without any foreseeable burdens due to the performance-based nature of transportation regulations [35].

#### **5. Discussion on the Applicability of the Current U.S. Licensing Framework to Fission Batteries**

This research indicates that the current regulatory framework is facing considerable challenges in terms of its applicability to fission batteries for siting and operations staffing; however, under certain design constraints for the fission batteries, it is feasible to meet the current transportation rules.

For siting regulations, strict site restrictions and excessive analysis and review-time burdens were presented as a limitation for the deployment of fission batteries. Thus, suggesting that the non-power reactors approach to resolve siting regulatory limitations. However, before applying the results of the non-power reactor approach, the fundamental difference should be considered, that is, a fission battery is a power reactor, unlike nonpower reactors. Nevertheless, since the safety features of fission batteries would be more adequate than non-power reactors, the non-power reactors approach may be reasonable considering that site inspection is focused on the safety aspects. Next, we proposed the permit-by-rule approach as a countermeasure to excessive analysis and review-time burdens. Similar to the non-power reactors approach, the permit-by-rule approach requires a reliable safety performance. Therefore, if regulatory authorities accept a permit-by-rule approach for fission batteries, multi-site deployment could be achievable.

In the case of operations staffing regulations, autonomous operation is an essential feature for fission batteries, thus, fission battery developers are working on applying unsupervised machine learning technologies to fission batteries to replace licensed operators. Therefore, for fission batteries controlled by un-supervised machine learning, human personnel will have the role of only monitoring the un-supervised machine learning control systems as necessary. As a result, an advanced human-system interface was suggested to support the role of an off-site un-supervised machine learning specialist for the successful exemption from regulations on control room operations staffing. If an advanced humansystem interface is applied to fission batteries controlled by un-supervised machine learning, the regulatory authorities will need to change their rules to accommodate the new role of

human personnel from licensed operators controlling the fission batteries directly to the certified personnel monitoring un-supervised machine learning control systems.

Finally, for transportation regulations, we have identified no regulatory gaps for the licensing of fission batteries, but it is necessary to consider whether to use Type B packaging requirements for fission batteries, which have their own safety features unlike used nuclear fuel, which may be too conservative. Therefore, using Type B packaging may be un-economical for nuclear vendors. As a result, it is necessary to carry out dedicated studies on the development of specific packaging for fission batteries and figure out which packaging is more reasonable to use in terms of safety and economic production of fission batteries.

#### **6. Conclusions**

In the development of innovative technologies, numerous regulatory barriers exist in all industries. Now that the transformation of nuclear reactors is taking place, fission batteries are at the peak of innovation, and accordingly, many challenges are expected. For this reason, this research was aimed at identifying possible regulatory challenges for the licensing of fission batteries and suggesting countermeasures to support their successful development and licensing. Among the many licensing topics, siting, operations staffing, and transportation were intensively studied, considering the five attributes of fission batteries.

For siting challenges, strict site restrictions to prevent impact on the public and several years of site inspections were presented. Considering the expansive use of fission batteries equipped with enhanced safety systems, the non-power reactor approach to relax site limitations and the permit-by-rule approach to shorten review time periods were proposed for site inspections to support simultaneous multi-site deployment.

Regarding operations staffing issues, un-attended operation is the core attribute of fission batteries. Currently, nuclear reactors are highly dependent on control room operators. However, fission batteries are envisioned to be operated by un-supervised machine learning control systems without the need for on-site staff. Therefore, the development of an advanced human-system interface supporting remote monitoring for fission batteries controlled by un-supervised machine learning may enable successful exemptions from the current regulatory requirements.

In terms of transportation regulations, fission batteries have the characteristic of needing to be transportable without removing the used fuel after an operation. If the fission battery designs meet the regulatory dose limits by adopting the certified Type B packaging requirements used for the transportation of used fuel from current reactors, fission battery transportation is achievable within the current regulatory framework.

Overall, the development of fission batteries in the U.S. is facing other regulatory challenges than the three discussed above. However, the status of present regulations should not hinder the development of innovative technologies in the future. Therefore, the necessary regulatory changes and the development of fission batteries should evolve in parallel through an open regulatory engagement process for the safe and practical deployment of advanced nuclear energy.

**Author Contributions:** Conceptualization, M.A.D.; Formal analysis, D.L.; Methodology, D.L. and M.A.D.; Supervision, M.A.D.; Validation, M.A.D.; Writing—original draft, D.L. and M.A.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was performed as part of DaeHo Lee's Master of Science degree at North Carolina State University in the Department of Nuclear Engineering supported by the Republic of Korea Army.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Investigating The Impact of Roadway Characteristics on Intersection Crash Severity**

**Mostafa Sharafeldin 1,\*, Ahmed Farid <sup>2</sup> and Khaled Ksaibati <sup>1</sup>**


**Abstract:** Intersections are commonly recognized as crash hot spots on roadway networks. Therefore, intersection safety is a major concern for transportation professionals. Identifying and quantifying the impact of crash contributing factors is crucial to planning and implementing the appropriate countermeasures. This study covered the analysis of nine years of intersection crash records in the State of Wyoming to identify the contributing factors to crash injury severity at intersections. The study involved the investigation of the influence of roadway (intersection) and environmental characteristics on crash injury severity. The results demonstrated that several parameters related to intersection attributes (pavement friction; urban location; roadway functional classification; guardrails; right shoulder width) and two environmental conditions (road surface condition and lighting) influence the injury severity of intersection crashes. This study identified the significant roadway characteristics influencing crash severity and explored the key role of pavement friction, which is a commonly omitted variable.

**Keywords:** crash injury severity; intersection safety; pavement friction; roadway characteristics; roadway geometric characteristics; intersection crash analysis

#### **1. Introduction**

Intersection-related crashes are responsible for more than 20% of road traffic fatalities, and more than 40% of total crash injuries in the United States. Complex traffic movements and the interaction between different transportation modes establish the intersections as hazardous locations for all road users [1–4]. In addition, intersection safety is facing new challenges with rapidly increasing traffic volumes and developing technologies. Planning for traffic control and safety at intersections can be even more challenging with multimodal operations. Therefore, the Federal Highway Administration (FHWA) and state Departments of Transportations (DOTs) are continuously striving to mitigate crash injury severity and reduce traffic-related fatalities [5–9]. The injury severity of traffic crashes can be related to different categories of contributing factors including crash, driver, environmental, and roadway attributes. While roadway characteristics are usually considered in traffic safety studies, pavement surface friction is a commonly omitted variable in crash analysis.

Pavement friction is the force resisting the relative motion between the vehicle tires and the pavement surface. The loss of skid resistance prevents drivers from safely maneuvering or stopping their vehicles, which leads to increased crash frequency and severity [10–12]. Tire-pavement interaction leads to aggregate polishing in the pavement surface layer, which reduces pavement friction supply over time. Thus, transportation agencies ought to consistently monitor the pavement surface friction levels. A recent survey of the roadway surface friction management practices revealed that only eleven of the surveyed thirty-two DOTs collect pavement friction data on specific road locations (such as ramps, curves, and intersections) to investigate safety concerns. The increase in wet pavement crashes

**Citation:** Sharafeldin, M.; Farid, A.; Ksaibati, K. Investigating The Impact of Roadway Characteristics on Intersection Crash Severity. *Eng* **2022**, *3*, 412–423. https://doi.org/ 10.3390/eng3040030

Academic Editor: Antonio Gil Bravo

Received: 20 September 2022 Accepted: 7 October 2022 Published: 8 October 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

is a grave safety concern, urging the need for friction-related data collection at locations experiencing such crashes [13].

Wet pavement crashes are typically linked to poor skid resistance, since wet pavement surfaces can substantially reduce the frictional force. Insufficient friction levels may lead to a similar issue on dry pavement surfaces [14,15]. The State of Wyoming has one of the highest snowfall rates in the United States. Therefore, non-dry pavement conditions are common in the state. A third of traffic crashes in Wyoming occur on non-dry pavement surface conditions, including snowy, icy, wet, or slushy road surfaces [16–18]. Pavement surface treatments play a critical role in supplying sufficient friction levels across the roadway network. Surface treatments are commonly applied to specific locations with high friction demand, such as intersections. These surface treatments include hot-mix asphalt (HMA) overlays, chip seals, open-graded friction courses (OGFC), micro-milling, and high friction surface treatments (HFST) [14,19–22].

The objective of this study was to investigate the roadway risk factors, including pavement friction, influencing the injury severity of intersection crashes. A set of roadwayrelated characteristics and critical environmental conditions were considered in the analysis. This paper is organized as follows. A review of the relevant studies in the traffic safety literature is discussed. Afterward, the methodology, data description, results of the empirical analysis, conclusion, and recommendations are all discussed.

#### **2. Literature Review**

This section provides a review of multiple studies related to the influence of roadway characteristics and pavement friction on crash injury severity. The limitations of the reviewed studies are identified, and the contribution of this research is discussed. The following studies did not consider pavement friction as a risk factor in the analysis.

Abdel-Aty and Keller [23] addressed different contributing factors to crash injury severity at signalized intersections in Florida using ordinal probit models. The results demonstrated that a combination of crash-related attributes and intersection characteristics influence crash injury severity. It was found that an increase in the number of lanes, the presence of medians, and right-turn channelization reduces the risk of sustaining severe injury. Even though the authors examined a wide set of roadway attributes, the pavement surface friction and road surface condition variables were not incorporated in the study.

Haleem and Abdel-Aty [24] selected multiple approaches, including two ordinal probit models, to examine crash injury severity at unsignalized intersections in Florida. The authors incorporated the driver's characteristics, intersection attributes, pavement surface type (concrete, asphalt, etc.), and road surface condition (dry, wet, etc.), among other factors. This study included the number of thorough lanes as a surrogate measure for traffic volume on the minor road. The authors identified several significant factors influencing the crash severity including intersection and driver characteristics. The left shoulder width, right shoulder width, and number of turning lanes were found to be among the influential factors. Yet, the authors did not account for pavement friction as a potential risk factor.

Anowar et al. [25] investigated the contributing factors to intersection crash severity in Bangladesh by utilizing a generalized ordinal logit model. The authors examined the impact of various crash, environmental, and roadway attributes. As per the results, undivided roads, dry pavement surfaces, and rural areas were found to raise the risk of incurring severe injury. Even though the authors considered the road surface condition, pavement friction was not considered in the analysis.

Oh [26] examined the contributing factors to crash injury severity at four-leg signalized intersections in rural areas. The author applied ordinal probit models to investigate the crash, weather, and roadway risk factors. The results indicated that tighter horizontal curves and higher speed limits contribute to severe crashes, while wider medians and the presence of protected left-turn phases are associated with less severe crashes. Yet, the author did not incorporate pavement surface friction as a potential contributing factor to crash injury severity.

Lee et al. [27] developed Bayesian ordinal logistic regression models to explore the impact of pavement surface conditions on the crash injury severity. The findings indicated that poor pavement surfaces increase the severity of multiple-vehicle crashes regardless of the posted speed limit. The findings also demonstrated that deteriorated pavement surfaces decrease the severity of single-vehicle crashes on low-speed roads (having posted speed limits of 35 mi/h or below) and increase such severity on high-speed roads (having speed limits of 50 mi/h or above). It should be noted that this study incorporated the pavement condition variable instead of the pavement friction in the analyses.

Zhao et al. [28] employed a multivariate Poisson log-normal model to analyze traffic crashes on the approaches of urban signalized intersections in the State of Nebraska. The study was focused on traffic and roadway geometric risk factors. The study's results demonstrated that intersection approaches on urban arterial roads have more frequent and higher severity crashes compared to collector roads. The results also indicated that the number of right-turn, left-turn, and through lanes influences crash frequency. The study did not consider any factors related to pavement condition or pavement friction.

The following study considered pavement friction as a risk factor, but they had other limitations, as follows.

Hussien et al. [29] investigated the effects of pavement resurfacing on intersection safety by conducting a before-after study on signalized intersections that were subjected to resurfacing in Melbourne, Australia. The authors incorporated multiple pavement condition data variables including roughness, skid resistance, and rutting. The authors also considered roadway characteristics and environmental conditions. The results demonstrated that pavement maintenance and improving skid resistance reduce the frequency and severity of crashes at signalized intersections. The results also identified other significant factors, including lighting, road surface condition, and interaction parameters, such as approach width interactions with the presence of a median, bus stop, or shared lane. Even though the authors incorporated pavement condition information including skid resistance and various roadway characteristics, the study's scope did not encompass rural intersections and the authors omitted several roadway characteristics. They include the roadway grade, horizontal curvature, roadway functional classification, and right shoulder attributes.

Sharafeldin et al. [30] developed a Bayesian ordinal probit model to investigate the impact of pavement friction, among other risk factors, on injury severity of the intersection crashes. The study concluded that insufficient pavement friction supply is one of the main contributors to severe crashes at intersections. Even though the study considered pavement friction as a potential risk factor, the study analyzed a limited data set and did not include other roadway attributes. Other related studies to this research topic include those of Chen et al. [31], Sharafeldin et al. [32], Karlaftis and Golias [33], Roy et al. [12], Chen et al. [34], Papadimitriou et al. [35], and Zhao et al. [36].

Generally, there is a growing interest in research about the relationship between pavement friction and traffic safety. However, to the best of the authors' knowledge, the investigation of the pavement friction's effect, among the other roadway attributes, on intersection crash severity is insufficient. In this research, the risk of observing severe injury crashes at intersections is modeled as a function of environmental and roadway factors, especially pavement surface friction.

#### **3. Research Methodology**

Ordered response modeling techniques have been widely adopted in crash injury severity studies to account for the ordinal nature of the injury severity levels. Ordinal probit and logit models were extensively utilized to study the risk factors of crash injury severity [37,38]. The ordinal probit model structure estimates the latent propensity, y∗ <sup>i</sup> , for each crash, i, as follows [39]:

$$\mathbf{y}\_{\text{i}}^{\*} = \beta\_0 + \beta\_1 \mathbf{X}\_{\text{i}1} + \beta\_2 \mathbf{X}\_{\text{2i}} + \dots + \beta\_{\text{p}} \mathbf{X}\_{\text{pi}} + \epsilon\_{\text{i}} \tag{1}$$

The predictors are described by the X's, while their regression coefficients are described by the β's, which are estimated using the maximum likelihood estimation (MLE) method. The random error term is defined by i, and it is assumed to be normally distributed. The response formulation is stated as follows [39], where ψ is a threshold that is estimated via the MLE technique.

$$\mathbf{y}\_{i} = \begin{cases} \mathbf{O}\_{\prime} & \mathbf{y}\_{i}^{\*} < 0 \\ \mathbf{BC}\_{\prime} & 0 < \mathbf{y}\_{i}^{\*} < \boldsymbol{\Psi} \\ \mathbf{KA}\_{\prime} & \mathbf{y}\_{i}^{\*} > \boldsymbol{\Psi} \end{cases} \tag{2}$$

The outcome probabilities, P(.)'s, are calculated by the following equations where F(.) is the cumulative standard normal distribution function [40]:

$$\mathbf{P}(\mathbf{y}\_i = \mathbf{O}) = \mathbf{F}\left(-\left(\beta\_0 + \sum\_{\mathbf{P}=1}^{\mathbf{P}} \beta\_{\mathbf{P}} \mathbf{x}\_{\mathbf{P}^i}\right)\right) \tag{3}$$

$$\mathbf{P(y\_i = BC)} = \mathbf{F}\left(\boldsymbol{\Psi} - \left(\boldsymbol{\beta}\_0 + \sum\_{\mathbf{p}=1}^{\mathbf{P}} \boldsymbol{\beta}\_\mathbf{p} \boldsymbol{\chi}\_{\mathbf{p}i}\right)\right) - \mathbf{F}\left(-\left(\boldsymbol{\beta}\_0 + \sum\_{\mathbf{p}=1}^{\mathbf{P}} \boldsymbol{\beta}\_\mathbf{p} \boldsymbol{\chi}\_{\mathbf{p}i}\right)\right) \tag{4}$$

$$\mathbf{P(y\_i = KA)} = 1 - \mathbf{F}\left(\boldsymbol{\psi} - \left(\beta\_0 + \sum\_{\mathbf{p}=1}^{\mathbf{P}} \beta\_\mathbf{p} \boldsymbol{\chi}\_\mathbf{p}\right)\right) \tag{5}$$

Confidence intervals of 90th were utilized to identify the statistically significant variables instead of the 95th intervals. This was to retain the valuable information usually lost by utilizing narrower confidence intervals. Marginal effects are estimated to identify the influences of contributing factors on crash injury severity. The marginal effect is the average change in the probability of incurring an injury of severity j, ΔP (y = j), as a result of the variable's influence, provided that all other variables are controlled [40].

#### **4. Data Collection**

This study involved the examination of crash data obtained from the Critical Analysis Reporting Environment (CARE) package of the Wyoming Department of Transportation (WYDOT). The crash records were collected by WYDOT from police crash reports and inputted into the package. The data were prepared such that each data point represented a unique intersection crash record, including the pavement friction number measured at the intersection in the crash year. The data included records of 9108 unique crashes at 359 intersections from January 2007 through December 2017, except for the years 2010 and 2011 due to friction data availability. Crashes specified as intersection crashes are those located within 250 feet (76.2 m) from the center of the intersection, as per the American Association of State Highway and Transportation Officials [41]. The crash records included information on the roadway and other characteristics as well.

WYDOT personnel collected the pavement friction data across the state using the locked-wheel tester. The locked-wheel tester is a trailer with two wheels having standard tires. The device tests the longitudinal friction by using either one or two wheels. The testing tires can be either smooth or ribbed. The smooth tire is sensitive to macrotexture while the ribbed tire is more sensitive to microtexture [10]. The locked-wheel device measures pavement friction by fully locking the testing wheel(s) and recording the average sliding force at which the fully locked state is achieved. Accordingly, the locked-wheel device can only measure friction at specific time intervals due to the full-lock requirement [42]. The friction number are usually reported as (FN40R), which is measured by using a locked wheel tester, fitted by a standard ribbed tire at 40 mile per hour. The Federal Highway Administration (FHWA) promotes utilizing the continuous pavement friction measurement (CPFM) technique to collect friction data continually along road networks, including special locations, such as curves, ramps, and intersections [43].

The field data were calibrated by WYDOT at the regional calibration center. Friction data were integrated with the obtained intersection crash data by matching the mile post of the intersection with the friction measurement's locations identified by mile posts. When the friction measure was not gauged exactly at the intersection location, the nearest two measurements (before and after the intersection) along the major route were averaged to calculate the friction at the intersection. Moreover, the friction numbers were estimated at the years with no friction data collection by averaging the measurements of the previous and the subsequent years at the study location. This approach was only applied at locations where friction numbers were declining. This indicated that no maintenance work was performed and the difference in friction numbers (FN40R) between the previous and the subsequent years was 10 or less, to ensure the validity of the averaged measurements. This method assumes that the pavement friction was deteriorating at a steady rate over the three years. The friction measurements were matched to the crash records that occurred in the same year of the friction measurement. Each row of the dataset represented a unique crash record with the friction number at the intersection, measured in the crash year.

#### **5. Data Description**

In this study, the crash injury severity is classified into three categories: O for property damage only (PDO) or no injury crashes, BC for possible or minor injury crashes, and KA for the highest severity level, which is disabling or fatal injury crashes. PDO crashes represented 75.9% of the total crash records. Possible and minor injury crashes accounted for 22.3%, while disabling and fatal injury crashes comprised 1.8% of the data. The investigated roadway attributes were pavement surface friction, intersection type, intersection location attributes, number of lanes, grade (uphill, downhill, and level), horizontal curvature, roadway functional classification, roadway surface type, guardrail presence, presence of rumble strips, median type, median width, right shoulder type, and right shoulder width. The pavement friction values (FN40R) ranged from 19 to 71 with an average of 40. Figure 1 illustrates the friction number distribution for the crash records.

Table 1 presents summary statistics of this study's data. As for the other roadway characteristics, the majority of the examined crashes occurred at signalized intersections, intersections with four or more legs, and intersections in urban areas. The intersections were identified as urban or rural according to the US Census Bureau's definition [44]. Limited proportions of crashes were at uphill and downhill intersections in contrast to crashes on level intersections. The data included the functional classification of the major roadways of the intersections. Most recorded crashes occurred at intersections of principal arterial roads, while smaller proportions occurred on interstate, minor arterial, and collector roads. Local roads were considered as the reference category for this variable in the modeling. It should be noted that the intersections with a functional classification of "Interstate" refer to intersections with interstate interchanges (on/off ramps).

Low proportions of crashes occurred at intersections having horizontal curves. The number of through lanes and road surface type were also considered. Low proportions of crashes occurred at intersections with guardrails or rumble strips. A total of 45% of the collected crash records occurred at intersections near schools, while a low proportion of them occurred near liquor stores.

As for the median type, almost half of the crashes involved a raised median, while a limited proportion involved a depressed median. The absence of a median was considered as the reference category in the modeling. Medians wider than 100 feet (30.5 m) were estimated as 120 feet (36.6 m) wide. As for the right shoulder type, more than a quarter of the crash records occurred at sites having asphalt shoulders, while a third of them occurred at sites having concrete shoulders. On the contrary, a small percentage occurred at sites with unpaved right shoulders. The absence of a right shoulder was considered as the

reference category for this variable in the modeling. Moreover, right shoulders that were wider than 8.5 feet (2.6 m) were estimated as 10 feet (3 m) wide.

**Figure 1.** Friction number distribution by crash frequency.

**Table 1.** Data's descriptive statistics.



**Table 1.** *Cont.*

When it comes to environmental conditions, almost a quarter of the crashes occurred under non-daylight conditions, such as nighttime, dawn, or dusk conditions. Moreover, a considerable proportion of crashes occurred during adverse weather conditions. The adverse weather categories included rain, snow, blizzard, hail, fog, and any other inclement weather conditions. Concerning the road surface condition, over a quarter of the crashes occurred on non-dry road surfaces such as wet, snowy, icy, slushy, and any other adverse conditions.

#### **6. Empirical Analysis**

An ordinal probit model was developed to analyze the intersection crash data. The aforementioned explanatory variables were all considered in the model. The 90th percentile confidence level was selected for ascertaining statistically significant variables and the log-likelihood ratio test was conducted to test for the model's significance. The results of the model are presented in Table 2. Note that statistically insignificant variables are not shown in the table.


**Table 2.** Ordinal probit model results.

The modeling results indicated that several roadway attributes, including pavement surface friction, and two environmental conditions, are significantly impacting the crash injury severity at intersections. The marginal effects of the significant risk factors are presented in Table 3. In Table 3, the ΔP(.)'s represent the changes in the risks of observing crash severity j, whether KA, BC, or O are as a result of the explanatory variable's effect. Each variable's effect on the injury severity was estimated assuming all other variables were controlled, and the continuous variables (pavement friction and right shoulder width) were at their average values.

The findings demonstrated that several intersection attributes had a strong impact on crash severity risk. As shown in Table 3, pavement surface friction substantially influences the severity of intersection crashes. It was estimated that, on average, increasing the pavement friction numbers (FN40R) at intersections from 25 to 45 reduces the risk of observing BC and KA injuries by 1.65% and 0.36%, respectively. Sharafeldin et al. [30] and Hussien et al. [29] reported relevant findings indicating that insufficient friction levels increase the risks of crash frequency and severity. This finding emphasizes the significance of maintaining sufficient pavement friction levels on roadway networks, especially at high-risk crash locations with a larger friction demand, such as intersections, ramps, and curves, to alleviate severe injury concerns.

Crashes at urban intersections were found to be associated with lower injury severity risk compared to crashes at rural intersections. It was estimated that, on average, an urban intersection crash would have a 6.44% and a 1.14% lower chance of resulting in BC and KA injuries, respectively, relative to rural intersection crashes. The higher severity of rural crashes is plausibly related to higher speed limits, higher chances of driver distraction, non-compliance with safety measures, and driver fatigue due to longer travel distances. In addition, medical assistance has better access to crash victims in urban areas compared to rural locations. These findings align with those of Anowar et al. [25] and Oh [26]. This finding shed light on the premise that crashes at rural intersections have higher injury severities. This is critical to the State of Wyoming, since it has a higher number of rural and semirural intersections.


**Table 3.** Marginal effects of the intersection crash severity factors.

Notes: ΔP (y = O) = change in the likelihood of observing no injury, ΔP (y = BC) = change in the likelihood of observing possible or suspected minor injury, ΔP (y = KA) = change in the likelihood of observing fatal or suspected serious injury.

The roadway functional classification was found to be a significant contributing factor to crash severity. Intersection crashes on principal and minor arterial roads were found to be severe compared to those that occurred on local roads. Crashes on principal arterials were found to have higher severity levels with marginal effects of 2.39% and 0.55% for BC and KA injuries, respectively. Crashes on minor arterials were found to have higher severity levels with marginal effects of 4.23% and 1.02% for BC and KA injuries, respectively. These findings are possibly attributed to the higher percentage of trucks and more complex traffic mixes on arterial roads compared to those on local roads. Zhao et al. [28] reported similar findings. The higher severity of crashes on minor arterials compared to that of principal arterials is plausibly related to the higher speed differentials among vehicles on minor arterials. The presence of guardrails was found to be associated with higher injury severity levels. Crashes on intersections with guardrails would have 7.02% and 1.86% higher chances of resulting in BC and KA injuries, respectively. Plausibly, this is because of the correlation between higher speed facilities and guardrail installation.

The right shoulder width was found to significantly impact intersection crash injury severity. It was estimated that, on average, widening the right shoulders at intersections from 4 to 10 feet (1.2 to 3 m) raises the risk of observing BC and KA injuries by 2.73% and 0.64%, respectively. This finding may be attributed to the improper use of wide shoulders, which increases the risk of observing sideswipe and rear-end crashes. Such crashes are possibly severe at high-impact speeds. It should be noted that wider shoulders are typically utilized on high-speed roads. Haleem and Abdel-Aty [24] reported similar findings.

As for the environmental factors, two environmental conditions were found to have a significant impact on injury severity risk. Non-dry road surfaces were found to be inversely related to crash injury severity. It was estimated that, on average, crashes on non-dry road surfaces have 6.97% and 1.21% lower chances of resulting in BC and KA injuries, respectively, compared to crashes on dry surfaces. This finding is possibly attributed to the cautious driving behavior and lower speeds observed on non-dry roads. Comparable findings were reported by Anowar et al. [25]. The lighting condition at the time of the crash was found to influence crash injury severity. Crashes that occurred during non-daylight conditions would have 2.11% and 0.48% higher chances of resulting in BC and KA injuries, respectively, compared to crashes that occurred under daylight conditions. Haleem and Abdel-Aty [24] and Oh [26] reported similar findings.

#### **7. Conclusions and Recommendations**

In this study, an attempt was made to explore the influencing factors of crash injury severity at intersections. That is, intersection and environmental contributing factors were examined. An ordinal probit model was developed to investigate the crash severity risk factors. The analysis results demonstrated that several parameters significantly impact crash injury severity. Pavement friction was found to be a substantial effect, as increasing friction numbers at intersections was found to mitigate crash injury severity. It was also concluded that fatal and disabling injury crashes are more likely to occur at rural intersections compared to urban intersections. Therefore, rural intersections require more attention when it comes to maintaining adequate pavement friction levels and implementing crash mitigation measures. This finding is particularly valuable to the State of Wyoming, since it is characterized by rural and semi-rural areas. The functional classification of the roadway was also found to influence crash severity, as intersection crashes on arterial roads tend to have higher injury severity likelihoods compared to local roads. The widening of right shoulders and the deployment of guardrails were found to be associated with severe crashes. On the other hand, non-dry road surfaces were found to reduce the likelihood of observing severe crashes. Finally, crashes that occurred during daylight conditions were found to be less severe than those that occurred during other conditions.

It is recommended to raise pavement friction levels at intersections to adequate levels to mitigate crash injury severity and crash probability. It is also recommended to provide proper lighting at intersections, especially rural intersections, to lower the risk of observing severe crashes. Intersections on arterials, high-speed facilities, and rural intersections require more attention for countermeasure planning and implementation, since they are linked to high injury severity crashes. In addition, the findings related to the intersection characteristics can be further investigated to plan for the appropriate treatments. Implementing countermeasures that reduce severe crashes, such as those documented in the Crash Modification Factors (CMF) Clearinghouse [45], may be extensively reviewed.

#### **8. Study Limitations and Future Research**

The study had one main limitation, which is not including the traffic volume at intersection approaches due to data availability.

**Author Contributions:** Conceptualization, M.S., A.F. and K.K.; methodology, M.S.; software, M.S.; validation M.S., A.F. and K.K.; formal analysis, M.S.; investigation, M.S. and A.F.; resources, K.K.; data curation, M.S.; writing—original draft preparation, M.S.; writing—review and editing, M.S., A.F. and K.K.; visualization, M.S.; supervision, K.K.; project administration, K.K.; funding acquisition, K.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Wyoming Department of Transportation (WYDOT), grant number: RS05221.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data were collected from the Critical Analysis Reporting Environment (CARE) package, supported by the Wyoming Department of Transportation (WYDOT).

**Acknowledgments:** The authors gratefully acknowledge the effective financial support of WYDOT. All opinions are solely of the authors. The subject matter, all figures, tables, and equations, not previously copyrighted by outside sources, are copyrighted by WYDOT, the State of Wyoming, and the University of Wyoming. All rights reserved copyrighting in 2022.

**Conflicts of Interest:** The authors declare that they have no conflict of interest with all parties.

#### **References**


## *Article* **A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models †**

**Brian Andersen 1, Jason Hou 1,\*, Andrew Godfrey <sup>2</sup> and Dave Kropaczek <sup>2</sup>**


**Abstract:** This work presents the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for treatment of crud deposition as a constraint within light-water reactor core loading pattern optimization. The neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated. Analysis found that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence is presented that shows boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the methods employed provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

**Keywords:** convolutional neural network; genetic algorithm; crud; surrogate model; optimization

#### **1. Introduction**

Crud is a unique form of fouling in light water reactors (LWRs) caused by particulates such as iron and nickel—depositing on fuel rods in the reactor as a result of system corrosion [1]. Crud imposes operational challenges to the current fleet of operating LWRs [2] and is strongly associated with subcooled boiling and high-power fuel regions, such as within fresh fuel assemblies loaded into the reactor [3]. For pressurized water reactors (PWRs), the primary issues caused by crud deposition are crud-induced localized corrosion (CILC) and crud-induced power shift (CIPS) caused by the uptake of soluble boron within the crud layer. Crud deposition is also associated with a pressure drop in nuclear reactors as well [4]. Methods of managing crud are based on conservatively bounding the risk associated with the occurrence of CIPS and CILC through the reactor core reload design. Some of these techniques, such as flattening the power distribution to reduce the overall steaming rate, increase the fuel cycle cost of the reactor due to an increase in the number of fresh fuel assemblies.

CIPS, also known as the axial offset anomaly (AOA), is depicted in Figure 1. CIPS is an unexpected downward shift in the power distribution, which manifests as a decrease in the axial offset (AO) of the reactor [5] with the potential for rapid AO increase in the event of crud burst. CIPS is caused by boron coming out of solution from the moderator and uptaking into the crud layer. This introduces an extraneous neutron absorber in the upper

**Citation:** Andersen, B.; Hou, J.; Godfrey, A.; Kropaczek, D. A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models. *Eng* **2022**, *3*, 504–522. https://doi.org/10.3390/ eng3040036

Academic Editor: Antonio Gil Bravo

Received: 17 October 2022 Accepted: 20 November 2022 Published: 23 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

portion of crud-impacted assemblies [6]. Significant AO deviations from the operating target AO force reactor operators to decrease operating power to bring the reactor to a more stable operating regime. For example, Cycle 9 of the Callaway Plant had to reduce to 70% of rated operating power due to CIPS [7]. For a 1000 MWe PWR, every 1% decrease in operating power corresponds to an approximate loss of \$10,000 per day in revenue due to the need for replacement power purchases [8].

**Figure 1.** Comparison of the expected AO based on a neutronics analysis to the AO when CIPS occurs [9].

CILC is an increased rate of corrosion in the fuel cladding that arises from the insulating effect of crud on the fuel rod [10] and a higher temperature distribution across the fuel rod [11]. In addition, chemical interactions between the crud and cladding also play a role in increasing the rate of corrosion [12].

It is estimated that nuclear power plants spend \$2 million annually in operations and maintenance costs related to crud [13]. Several methods have been proposed for preventing crud deposition. Strict PH control of the moderating water has been proposed as a possible solution, but PH control becomes more difficult as fuel assemblies achieve high burnup levels [2]. Advanced material coatings for fuel rods have also been proposed as a method for preventing crud deposition [8,14]. Ultrasonic cleaning of fuel assemblies has become a standard practice for mitigating crud deposition in the operating PWR fleet. Ultrasonic cleaning effectively reduces the thickness of the crud layer on fuel assemblies reloaded into the reactor, and it reduces the total mass of crud within the reactor [2]. The aforementioned methods have successfully reduced occurrences of CIPS and CILC in the operating reactor fleet with limitations. For example, ultrasonic cleaners do not remove enough particulate to prevent crud-induced effects.

Therefore, advanced simulation tools for predicting crud growth and its impact on reactor performance and safety are highly desired by reactor core designers in order to minimize or completely eradicate the adverse effects of crud. Some efforts have been made in the nuclear industry in this regard. The boron offset anomaly toolbox (BOA) is a tool developed by the Electric Power Research Institute (EPRI) and Westinghouse capable of predicting the mass of boron that deposits within crud on a nodal basis. BOA is often used to check a PWR loading pattern's susceptibility to CIPS [2]. Finally, utilities have developed their own proprietary operating limits for lowering instances of CIPS and CILC based on correlated parameters such as number of fuel rods predicted to undergo subcooled boiling or maximum soluble boron concentration. However, the use of BOA or utility operating limits for preventing CIPS and CILC can lead to overly conservative core loading patterns that require an increase in fresh fuel loading.

This work provides the initial progress of a new methodology for reducing the effects of crud deposition within PWRs by using a genetic algorithm and a neural network surrogate model based on the crud chemistry code MAMBA [9] for designing loading patterns that mitigate the effects of CIPS and CILC without penalizing other loading pattern objectives such as enrichment or cycle length. The crud chemistry code MAMBA was chosen for this work because it performs the crud calculations at the pin level. This level of depth is desired in order to readily understand how the optimization algorithm is changing the loading pattern design in order to account for crud deposition. CrUdNET, the neural network surrogate model developed for this work, is a necessary replacement of MAMBA because MAMBA simulations are computational cost prohibitive for use with optimization algorithms. For example, solutions were evaluated in sixteen parallel processes. Directly running MAMBA in this way would require 896 processors and take approximately 400 h to perform the optimization. In addition, an experimental database suitable for training a neural network based crud chemistry code is not available, which makes the simulation data the only feasible option.

A neural network, a popular family of machine learning (ML) algorithms, is used in this work as a surrogate model for crud evaluation. ML is observing increasing application in the field of nuclear engineering. ML algorithms have been applied to cross section predictions [15], neutron transport acceleration [16], and accident classification [17]. Neural networks were used as surrogate models in loading pattern optimizations. For example, they have been applied as a core simulator for evaluating loading pattern solutions [18,19]. Additionally, ML algorithms have been a preemptive evaluator to reduce the computational burden of the optimization [20].

Genetic algorithms (GAs) were chosen to perform core loading pattern optimization due to their long history of application in the field. They were one of the first optimization algorithms applied to the core loading pattern problem [21]. They have been successfully applied numerous times to PWRs [22,23], and they have also been used for the loading pattern optimization of boiling water reactors [24–27]. Moreover, GAs have served as the yardstick by which new optimization methodologies are measured. For example, GA was one of the benchmarks used to evaluate development of Tabu algorithms for fuel loading pattern optimization [28,29]. Likewise, it has been used to test the development of various particle swarm algorithms [30,31]. GAs were also used in a wide comparison of optimization methodologies for BWR loading pattern optimization [32].

#### **2. Optimization Tools and Methods**

This work made use of the neural network surrogate model crUdNET and a GA within the Modular Optimization Framework (MOF) [33,34]. This section provides a brief discussion of these tools, and how they are employed for crud optimization.

#### *2.1. Neural Network for CRUD Modeling*

Pin-level crud calculations are desired to understand how changes in the loading pattern affect the crud distribution. This necessitates the use of the crud chemistry code MAMBA for its capability of calculating crud deposition on a pin level basis, as opposed to BOA which provides results on a nodal level.

MAMBA has been integrated into the core simulator VERA [9,35]. Through VERA, MAMBA is coupled to the neutronics solver MPACT [36] and subchannel thermal hydraulics code CTF [37]. MAMBA uses information provided by these two codes and Equation (1) to calculate the surface deposition of crud on every fuel rod across a PWR [9].

$$\mathbb{C}\_{\text{dens}}(t+\delta t) = \mathbb{C}\_{\text{dens}}(t) + \delta t \left( (k\_{s,nombil}^p + k\_{s,holi}^p q^{\prime\prime}\_{\text{s,bvil}}) \mathbb{N}\_{\text{cool}} - \gamma k\_{tkx} \right) \tag{1}$$

In Equation (1), *Cdens*(*t* + *δt*) represents the deposited crud molar density after timestep *δt*. *k p <sup>s</sup>*,*nonboil* represents the non-boiling crud deposition rate. *k p <sup>s</sup>*,*boil* represents the boiling deposition rate, and *q*"*s*,*boil* represents the boiling heat flux obtained through the VERA coupling. *k p <sup>s</sup>*,*nonboil*, *k p <sup>s</sup>*,*boil*, and *q*"*s*,*boil* are multiplied by the term *Ncool*, which represents the concentration of nickel-ferrite particulate in the reactor coolant. Lastly, *γ* and *ktke* represent the erosion rate and surface kinetic energy which account for the crud that erodes from the surface of the fuel rod [9].

MAMBA coupled within VERA requires significant numbers of processors and wallclock time. This makes a fully coupled MAMBA analysis unsuitable for use in an optimization algorithm. For this reason, MAMBA is replaced with a convolutional neural network (CNN) based on the U-NET neural network architecture [38] to assess crud deposition. Reference [33] details why the U-NET neural network architecture was selected for the surrogate model.

Figure 2 shows the architecture of the CNN surrogate model, crUdNET. CrUdNET was designed to predict the change in the crud distribution at a single axial layer of the 3D CTF mesh in a reactor core. In essence, crUdNET can be thought of as replacing Equation (1) with Equation (2) for performing reactor core crud deposition calculations.

$$\mathcal{C}\_{sur-dens}(t+\delta t) = \mathcal{C}\_{sur-dens}(t) + F(\Delta P, \mathcal{N}\_{cool}, B\_{cool}, E),\tag{2}$$

In Equation (2), *F* represents the change in the crud surface density as predicted by crUdNET, and the crud densities are altered from molar densities to surface mass densities at the beginning and end of a time step, *Csur*−*dens*(*t*), *Csur*−*dens*(*<sup>t</sup>* <sup>+</sup> *<sup>δ</sup>t*). The density is altered because VERA reports the surface mass density in units g/cm2, rather than the molar density mol/cm3. As the primary driver of crud deposition in MAMBA, *F* is naturally a function of the nickel-ferrite particulate in the coolant, *Ncool*, in parts per billion [9]. By using multiple trained networks, developed uniquely for each axial layer, a reconstruction of the three-dimensional (3D) crud distribution is obtainable. Thus, the use of crUdNET reformulates the crud deposition analysis from an analytical problem to a pattern recognition problem. The soluble boron concentration in the coolant in parts per million (ppm), *Bcool*, and end of time step cycle exposure in Giga-Watt-days/Metric-Ton-Uranium (GWD/MTU), *E* are also provided to aid in pattern recognition. In broad terms, cycle exposure accounts for the nuclear fuel residence time in the core, while soluble boron concentration reflects the reactivity of the fuel. The higher the soluble boron concentration, the more reactive the fuel is, and so more crud should likely deposit. In other words, less and less crud will deposit in the reactor towards the end of the cycle exposure. Lastly, *F* is a function of the change in the whole core pin power distribution, Δ*P*, given by Equation (3).

$$
\Delta P = P(t + \delta t) - P(t) \tag{3}
$$

The leakyReLU activation function, given in Equation (4), is used as the activation between all layers in crUdNET [39]. The number of nodes used in the layers of crUdNET are provided in Table 1. Convolutional layers used a window size of 3 × 3.

$$f(\mathbf{x}) = \begin{cases} -0.1 \ast \mathbf{x} & \mathbf{x} < 0 \\ \mathbf{x} & \mathbf{x} \ge 0 \end{cases} \tag{4}$$

The difference in the pin power distribution, Δ*P*, is provided as input to the "U" portion of the neural network. Here, the data is first normalized in the batch normalization layer before being transformed by a series of 2D convolutional and averaging nodes. These nodes transform the data, shaping it from a core-wide matrix of data to an assembly wide matrix which identifies which assemblies are most likely to see significant changes in crud deposition. Through a series of more convolutional nodes, upsampling nodes, and concatenation nodes, the network then transforms this data into the core-wide crud distribution, in relative quantities, for a single layer in the 3D CTF mesh. Meanwhile, the inputs *Ncool*, *Bcool*, and *E* are fed into the linear dense connections of the neural network

where they are transformed and normalized to determine the scale of the change in the crud deposition. Lastly the spatial distribution and scaling terms are multiplied together and output from the neural network in order to get the final change in the crud distribution. As Equation (2) shows, the cycle crud deposition can then be calculated by summing the outputs of the network over each timestep [40].

**Figure 2.** (**a**) The neural network architecture of the crUdNET surrogate model. (**b**) Key proivding each of the neural network layers used in crUdNET.


**Table 1.** Number of nodes used in the layers of crUdNET.

CrUdNET was trained based on a fixed time step, *δt*, of 0.5 GWd/MTU. Pin-powers, soluble boron concentrations, and cycle exposures are provided by a nodal analysis code. which was used to replace MPACT for nuclear analysis to reduce the computational burden of developing the training library, while this means that the CTF+MAMBA analyses are decoupled from neutronics, this does not impact this work [33].

CrUdNET was trained on a library of 6600 unique sets of input and output data in an 80/20 training/validation split. The performance of crUdNET was then tested against a further 1500 unique samples [33]. The training and testing inputs were developed through repeated core loading pattern optimizations to obtain Δ*P*, *Bcool*, and *E*. *Ncool* was obtained through random sampling. Figure 3 provides a comparison of MAMBA and crUdNET for a crud distribution at end of cycle (EOC) for a reactor predicted by crUdNET. Figure 3 shows that crUdNET provides acceptable agreement with MAMBA in predicting crud distributions. Figure 3 also represents a computational power reduction from 540 processors and 1 h of wall clock time to a single processor and 30 s of wall clock time. More detailed

explanations on the development and training process for crUdNET used in this work were previously presented in reference [33].

**Figure 3.** (**a**) The crud distribution at EOC as predicted by crUdNET. (**b**) The crud distribution at EOC as calculated by MAMBA for a reactor core.

#### *2.2. Genetic Algorithm*

The main features of a GA are crossover, mutation, and selections [41]. For this work, the GA was developed using MOF, an object-oriented code for facilitating the rapid development and application of optimization algorithms [34]. This GA utilized is relatively standard.A flowchart of the GA is provided in Figure 4.

The initial population of solutions is generated by randomly selecting assembly types allowed for each core location in all initial solutions. All solutions that pass the selection process become parents to the next generation of solutions. Solutions are selected to undergo either mutation or crossover, based on the mutation rate. For each solution a random number is drawn. If the number is less than the current mutation rate, the solution is selected to undergo mutation. Otherwise the parent solution will create a new solution through crossover. All solutions selected for crossover are designed to mate and undergo crossover with the most genetically similar solution. This mating is performed by selecting the first un-mated solution, and examining the remaining un-mated solutions for the highest number of fuel assembly types in the same position. These solutions are then mated for crossover. A solution can only be mated once for undergoing crossover.

Crossover is performed by exchanging fresh fuel assemblies in the same core location between the two genomes while the positions of reloaded fuel assemblies are shuffled within the core. These restrictions on crossover ensure that the inventory on fresh and burned fuel assemblies is preserved throughout the entire optimization. This is done in place of other techniques, such as throwing out solutions that violate the used fuel inventory and desired number of fresh fuel assemblies.

Mutation is performed in two ways. Fresh fuel assemblies are allowed to be freely replaced with other available fresh fuel assembly designs, or fresh fuel assemblies can swap their position in the core with another fuel assembly. Reloaded fuel assemblies are allowed to exchange positions only within the other fuel assemblies in the solution. The number of solutions that undergo mutation is determined by the mutation rate *R*, and Equation (5) [34].

$$R\_{new} = 1 - \Delta\_{mutation}(1 - R\_{current}),\tag{5}$$

where *Rnew* and *Rcurrent* are the updated and current mutation rate, respectively, and Δ*mutation* is defined by

$$\Delta\_{mutation} = \frac{\ln\left(\frac{1 - R\_{final}}{1 - R\_{initial}}\right)}{N},\tag{6}$$

where *Rinitial* and *Rfinal* are the initial and final mutation rate, respectively, [34].

Selection is performed using the tournament method [42]. The tournament method is completely random, allowing parents to compete against child solutions, child solutions to compete against other child solutions, and parent solutions to compete against other parents. Specific parameters of the GA, such as the mutation rate and population size, are provided with the relevant optimization performed.

**Figure 4.** Flowchart of the GA used for loading pattern optimization developed through MOF.

#### *2.3. Crud Optimization Methodologies*

Solutions generated by MOF are evaluated in a two-step process. In the first step, a neutronic analysis is performed to evaluate the loading pattern designed by the GA. This provides information on the radial rod power peaking, soluble boron concentrations, and cycle length. This also provides soluble boron concentrations, exposures, and the quartercore power distribution for crUdNET. In the second step, these values are combined with a nickel particulate concentration history to calculate the crud distribution produced by the solution. As previously mentioned, solutions were evaluated in sixteen parallel processes. This was a limit set by a system limit on the number of parallel nuclear simulation evaluations that could be performed in parallel.

In order to evaluate the effectiveness of optimizing crud, an initial optimization is first performed without any optimization objectives related to crud. The optimization is then re-performed. This second optimization includes an objective related to crud, and it begins from an initial random population just as the first optimization. The crud optimization is considered successful if the optimized solution provides similar results to the initial optimization in regard to the non-crud objectives, and must show improved performance in regard to crud over the first optimized solution when evaluated using CTF+MAMBA. For this work, the results of MAMBA calculations are taken as the true crud deposition.

Three optimization objectives unrelated to crud were used in each optimization. The first objective was maximizing the cycle length based on a fixed number of fresh fuel assemblies. This was used in place of meeting requirements on a specified cycle length and minimizing the core-wide enrichment. The second objective was minimizing the cycle peak soluble boron concentration. The third objective was minimizing radial rod power peaking (FΔH). This is calculated using Equation (7).

$$F\Delta H = \frac{\text{Peak Red Power}}{\text{Core Average Rod Power}} = \frac{\text{Max}\frac{1}{L}\int\_{0}^{L} P(x, y, z)dz}{\frac{1}{V\_{\text{Core}}} \int \int \int\_{V\_{\text{Core}}} P(x, y, z)dxdydz}.\tag{7}$$

Core loading pattern optimization was performed on the third cycle of a four-loop, 193 assembly, Westinghouse PWR. This model used geometry and operating conditions from the publicly available P9 progression problem published by CASL [43]. Heuristic restrictions were imposed on where certain types of fuel assemblies could be placed when generating initial solutions. This is a requirement and limitation of MOF in order to maintain the desired fuel inventory because MOF can only directly track the number of decision variables in a group, not how the placement of those decision variables affect total assembly count in a full core arrangement. Fuel assemblies were divided into four symmetry groups based on allowed location in the core (i.e., major and minor axis, nonaxis), and whether they were a fresh or previously burned fuel assembly. Figure 5 provides the allowed locations of assemblies for the four groups. 1's denote allowed locations and 0's denote prohibited locations. Figure 5 shows that fresh fuel assemblies are grouped based on octant or quarter symmetry depending on whether they are axis or non-axis locations.


**Figure 5.** Decision variable maps for the four fuel assembly groups used in each optimization case: (**a**) fresh fuel assemblies in octant symmetry, (**b**) fresh fuel assemblies in quarter symmetry, (**c**) burned fuel assemblies previously placed in quarter symmetry, (**d**) burned fuel assemblies previously placed in octant symmetry.

#### **3. Optimization Methodologies and Results**

Two optimization methodologies were tested. The first sought to reduce the total mass of crud in the core. The second sought to have a uniform amount of crud distribute on all fuel rods in the core.

#### *3.1. Total Crud Mass Reduction*

The logical first objective regarding crud deposition would be minimizing the total mass of crud that deposits within the reactor core. Reducing the total mass of crud that deposits in the core reduces the risk of CIPS and CILC. A methodology for reducing the total crud mass was proposed, however it turned out that this optimization objective could not be optimized using the chosen toolset.

The proposed optimization objective formulation for reducing the total core crud mass was quite simple. Three crUdNET models were trained. Each model predicted the crud distribution at a different axial elevation. Per Equation (8), these three predictions, *Nplanes*, are summed across all fuel rods, *Nrods*, to produce a single crud mass value.

$$m\_{total}^{cruid} = \sum\_{j=1}^{N\_{plames}} \sum\_{i=1}^{N\_{rods}} m\_{ij}^{cruid} \tag{8}$$

The crud mass optimization methodology was explored using six test cases. Cases differed in two ways: (1) whether the limiting value FΔH was 1.55 or 1.60, and (2) whether the case used 84, 88, or 92 fresh fuel assemblies. This exploratory study consisted of generating an optimized loading pattern using MOF based on each of the six cases using the previously described non-crud related optimization objectives. These objectives were maximizing cycle length, measured in effective full power days (EFPD), and meeting the described limits on maximum FΔH and a maximum soluble boron concentration less than 1300 ppm. These cases were then repeated with the inclusion of crUdNET and the crud mass objective described in Equation (8). The twelve optimized cases were then re-analyzed using CTF+MAMBA to determine if the combination of MOF and crUdNET had noticeably reduced the total mass of crud in the core. For this work, the results of MAMBA calculations are taken as the true crud deposition.

The loading pattern parameters for the cases optimized without crud are presented in Table 2. Results for the cases optimized with crud as an optimization objective, are presented in Table 3. Both tables also provide the mass of crud as predicted by crUdNET. This mass is significantly smaller than the total core crud mass because of the use of a subset of axial planes used in the analysis, as described previously. Figure 6 shows the FΔH values over the course of the cycle for the twelve highest fitness solutions, and Figure 7 provides the soluble boron concentration.

Tables 2 and 3 show that in five of the six cases optimized, crUdNET evaluation of the crud objective within the GA lowered the total mass of crud deposited. These tables also show that the highest fitness loading patterns for the 12 optimizations performed are unique. This is further reinforced by Figures 6 and 7, which show unique FΔH and soluble boron concentration histories for each of the 12 cases analyzed.

**Table 2.** Optimization objective values, including crud mass predicted by crUdNET, for highest fitness solution for optimizations performed without total crud mass optimization objective.


**Table 3.** Optimization objective values, including crud mass predicted by crUdNET, for highest fitness solution for optimizations performed with total crud mass optimization objective.


**Figure 6.** Comparison of FΔH versus exposure for the highest fitness solutions for the six optimization cases with and without crud objectives.

**Figure 7.** Comparison of the soluble boron concentration for the highest fitness solutions for the six optimization cases with and without crud objectives.

Figure 8 shows the total mass of crud within the core, as calculated by MAMBA, over the length of the cycle for the 12 cases. Table 4 provides the EOC total crud mass for the twelve cases.

**Figure 8.** Whole crud mass, as calculated by MAMBA, versus exposure for loading patterns analyzed in crud mass optimization.

**Table 4.** Comparison of total core crud mass, as calculated by MAMBA, at cycle exposure of 438 EFPD for the 12 highest fitness solutions for the total core crud mass optimization demonstrations.


Tables 2–4 and Figure 8 mean several things. The significant difference in mass between the crUdNET predictions and MAMBA calculations indicate that the use of a three-layer modeled by crUdNET is not sufficient to represent the whole-core crud mass. Additionally, MAMBA calculating the same crud mass for all twelve loading pattern designs indicate MAMBA is not mature in regard to the total crud mass deposited. It is unlikely for the nickel particulate concentration in the coolant to be the sole factor in determining the core wide crud mass, and for the power distribution to not significantly impact the core-wide crud mass.

Improvements in MAMBA will improve both itself and crUdNET, and further refinement of crUdNET will improve its predictive capability when it comes to total core crud mass. This work will make it possible to use crUdNET, in conjunction with an optimization algorithm, to design loading patterns that drive down the mass of crud that deposits within the reactor core. In the short term however, this means that a different optimization objective is required to demonstrate that crUdNET can successfully be used to optimize loading patterns in regard to crud deposition.

#### *3.2. Crud Deposition Analysis*

To demonstrate that crUdNET in conjunction with optimization algorithms could control crud deposition, an optimization objective to maximize the uniformity of the crud distribution over the entire reactor was adopted. In other words, the objective is to have as many fuel rods with the same amount of crud as possible. This methodology modeled a single axial layer. Deviation from a uniform distribution was measured via Equations (9) and (10):

$$M\_{\text{av}\epsilon} = \frac{\sum\_{i=1}^{N\_{\text{rods}}} M\_i}{N\_{\text{rods}}^2} \,\,\,\tag{9}$$

$$D = \sum\_{i=1}^{N\_{\text{rods}}^2} |M\_i - M\_{\text{avc}}| \,. \tag{10}$$

For Equations (9) and (10), *Mi* is the crud mass density for fuel pin *i*, *Mave* is the average crud mass density, and D is the deviation from the average value.

Equation (11) is the fitness equation for the deviation from uniform methodology analysis.

*Fitness* <sup>=</sup> *<sup>D</sup>* <sup>−</sup> <sup>10</sup> · *max*(*Lcycle* <sup>−</sup> *Tcycle*, 0) <sup>−</sup> <sup>1500</sup> · max(*F*Δ*Hm* <sup>−</sup> 1.55, 0) <sup>−</sup> <sup>2</sup> · max(*Csb <sup>m</sup>* − 1300, 0) (11)

> In Equation (11), *D* is the deviation from a uniform distribution given by Equation (10), *Lcycle* represents the solution cycle length, FΔ*Hm* is the maximum rod power peaking, and *Csb <sup>m</sup>* is the maximum soluble boron concentration.

> The GA used a population size of 30 and iterated solutions over 200 generations. Initially, 25% of solutions were mutated, but the number of solutions grew to 55% of solutions by the end of the optimization. Assemblies used in the optimization had enrichments of 4.4, 4.7, or 4.9 w/o. IFBA, gadolinium, and pyrex were used as burnable poisons in the fuel assemblies for all three enrichments. Fuel assemblies containing IFBA used 80 or 120 IFBA rods. Fuel assemblies using gadolinium had either 12 or 24 rods containing gadolinium. Gadolinium was utilized at 3%, 5%, and 8% w/o. Finally, assemblies containing pyrex as a burnable poison used a 12, 16, or 24 pyrex rod configuration.

#### 3.2.1. Optimization Results

Figure 9 provides the deviation of crud from a uniform distribution—as calculated by Equations (9) and (10)—in the reactor over the course of the cycle as predicted by crUdNET for the reference and test methodology optimizations. The reference optimization did not include the optimization objective related to crud. The test optimization methodology sought minimize the deviation from a uniform crud distribution. Figure 9 shows that the use of crUdNET significantly improved the uniformity of the crud distribution across the reactor core.

As mentioned, crUdNET and the optimization algorithm are considered to have successfully optimized the crud distribution if the optimization objective for the test methodology is improved over the reference value when solutions for both optimizations are evaluated using MAMBA. Figure 10 is reproduced Figure 9 using MAMBA, rather than crUdNET, to calculate the crud distribution for the population of solutions. It shows that although the difference between the two populations in terms of deviance from a uniform crud distribution is significantly smaller, the population of solutions optimized for crud clearly shows lower values, and thus a more uniform crud distribution than the reference optimization population.

Figure 10 shows that crUdNET and optimization algorithms can be combined to directly optimize crud distributions through the fuel loading pattern. This provides a significant advancement toward reducing the effects of CIPS and CILC within PWRs by providing core design engineers with a direct means of evaluating and manipulating the crud distribution when designing loading patterns. This is an improvement over current methods that seek to reduce crud deposition based on correlated parameters or evaluating crud as part of a post processing analysis.

**Figure 9.** Deviation from a uniform crud distribution using crUdNET with and without considering crud as an optimization objective.

**Figure 10.** Deviation from a uniform crud distribution using MAMBA with and without considering crud as an optimization objective

It is also important to understand how the genetic algorithm optimized the loading pattern in regard to crud. Figure 11 provides the loading patterns for the highest fitness solutions for the reference optimization and crud optimization test methodology. The comparison shows that the loading pattern for the test methodology has a larger concentration of fresh fuel assemblies toward the outer edge of the reactor core.

**Figure 11.** (**a**) The loading pattern for the highest fitness solution in the reference optimization. (**b**) The loading pattern for the highest fitness solution in the test methodology optimization. The loading pattern optimized in the test methodology has far fewer fresh assemblies towards the center of the core than the reference optimization loading pattern.

The effects are shown in Figures 12 and 13, which compare the power distributions between the loading patterns at beginning of cycle (BOC) and middle of cycle (MOC), respectively. The figures show that the loading pattern optimized for crud maintains higher and denser power concentrations over the reference optimization.

**Figure 12.** (**a**) The BOC power distribution for the highest fitness solution of the reference optimization. (**b**) The BOC power distribution for the highest fitness solution of the crud test methodology. The solution optimized for crud shows higher power concentrations over the reference solution.

**Figure 13.** (**a**) The MOC power distribution for the highest fitness solution in the reference population. (**b**) The MOC power distribution for the highest fitness solution in the crud test methodology population. The crud optimized solution shows continued higher power concentrations than the reference case, which has more distributed power.

Figure 14 illustrates the effect of these higher power concentrations on the crud distribution in the loading patterns. Figure 14 indicates that the GA optimized the loading pattern to have a minimal deviation from uniform crud distribution by concentrating the power distribution so that crud grows very densely on a small number of assemblies. This results in most fuel rods having no crud on them, and so the deviation from a uniform distribution is minimized.

**Figure 14.** (**a**) The EOC crud distribution for the highest fitness solution in the reference optimization population. (**b**) The EOC crud distribution for the highest fitness solution in the crud test methodology. The GA optimized the deviation from uniform crud distribution objective by designing the loading pattern to concentrate the power. This causes crud to grow in only a few assemblies.

This shows that there is room for improvement in both MAMBA and the surrogate model crUdNET. However, the needs for improvement do not discount this work. Improvements in both crUdNET and MAMBA will only increase the effectiveness of the methods discussed here. The optimization objective demonstrated that the combination of crUdNET and a GA can be successfully used for a multi-objective optimization that designs the crud distribution in a given way while also meeting other requirements such as rod power peaking and cycle length. However, in practice, dense distributions of crud, such as the one shown in Figure 14, created through the optimization are undesirable. Refinement of MAMBA, crUdNET, and the crud optimization objective will significantly improve reactor performance with respect to CIPS and CILC.

#### 3.2.2. Note on the Mass of Boron in Crud

Although not the focus, the boron mass deposited in crud was calculated as part of the MAMBA crud deposition analysis. The total boron mass in crud over cycle exposure for cases analyzed in MAMBA are presented in Figure 15. Figure 15 shows that there is nearly a 50 g range mass of boron that uptakes into the crud layer. This implies that loading pattern optimization with a reduced-order model or fast surrogate model trained for boron in crud prediction could effectively reduce the impact or occurrence of CIPS without penalizing other parameters such as enrichment or cycle length.

#### **4. Conclusions and Future Work**

This work presents a proof of concept demonstration that neural network surrogate models combined with optimization algorithms such as the GA can optimize properties related to crud deposition in nuclear reactors via loading pattern optimization. Deficiencies in both MAMBA and the modeling approach taken with crUdNET prevented optimization of the mass of crud that deposits in the core. However, by setting a crud related optimization objective to minimize the deviation from a uniform crud distribution, it was shown that the GA could successfully use crUdNET to develop loading patterns that outperformed a reference optimization regarding this parameter without sacrificing other objectives of the loading pattern optimization including power peaking, cycle length, and maximum soluble boron concentration.

CrUdNET's accuracy requires some improvement. The most immediate way in which the fidelity of crUdNET could be improved is through the introduction of ensemble modeling. Ensemble modeling is a powerful tool for increasing the predictive capability of neural networks, and the expansion of the surrogate modeling used in this work to multiple neural network architectures trained using varying data sets would greatly increase the accuracy of crUdNET. Additionally, it was shown that there is need for improvement in MAMBA, particularly regarding the crud mass calculations. As MAMBA matures the strength of the neural network surrogate models and the efficacy of the methods demonstrated here will only improve.

These improvements will also allow for the further exploration of optimization objectives related to crud. The deviation from a uniform crud distribution was used here based on the current capabilities of both MAMBA and crUdNET. Improvements to MAMBA and crUdNET will allow for the inclusion of other optimization objectives such as the core crud mass or maximum density of crud on fuel assemblies. Lastly, Figure 15 showed that there is a significant amount of variance between loading pattern designs in the total mass of boron that uptakes into the crud distribution. This provides the motivation for developing a surrogate model dedicated to predicting the boron uptake into the crud layer. The development of such a model would allow for the direct analysis and inclusion within the optimization of a loading patterns risk to CIPS using the methods demonstrated in this work.

**Author Contributions:** Conceptualization, J.H., A.G. and D.K.; Methodology, B.A., J.H., A.G. and D.K.; Software, J.H. and A.G.; Formal analysis, B.A.; Investigation, B.A. and D.K.; Data curation, B.A.; Writing—original draft, B.A.; Writing—review & editing, J.H. and D.K.; Visualization, B.A.; Supervision, D.K.; Funding acquisition, D.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Consortium for Advanced Simulation of Light Water Reactors (www.casl.gov), an Energy Innovation Hub (http://www.energy.gov/hubs) for Modeling and Simulation of Nuclear Reactors under US Department of Energy (DOE) contract no. DE-AC05- 00OR22725. This research used resources of the Compute and Data Environment for Science at the Oak Ridge National Laboratory, which is supported by the DOE Office of Science under contract no. DE-AC05-00OR22725. This research used the resources of the High Performance Computing Center at Idaho National Laboratory, which is supported by the DOE Office of Nuclear Energy and the Nuclear Science User Facilities under contract no. DE-AC07-05ID14517.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to express their thanks to researchers at Oak Ridge National Laboratory for their work on VERA and MAMBA, as well as for their help on this project.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Dispersive Optical Solitons for Stochastic Fokas-Lenells Equation with Multiplicative White Noise**

**Elsayed M. E. Zayed 1, Mahmoud El-Horbaty 1, Mohamed E. M. Alngar 2,\* and Mona El-Shater <sup>1</sup>**


**\*** Correspondence: mohamed.hassan@cs.mti.edu.eg

**Abstract:** For the first time, we study the Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise in Itô sense. Four integration algorithms are applied, namely, the method of modified simple equation (MMSE), the method of sine-cosine (MSC), the method of Jacobi elliptic equation (MJEE) and ansatze involving hyperbolic functions. Jacobi-elliptic function solutions, bright, dark, singular, combo dark-bright and combo bright-dark solitons are presented.

**Keywords:** stochastic F L equation; modified simple equation method; sine-cosine method; Jacobielliptic function expansion method; ansatze method

### **1. Introduction**

Nonlinear differential equations (NLDEs) play a very important role in scientific fields and engineering such as optical fibers, the heat flow, plasma physics, solid-state physics, chemical kinematics, the proliferation of shallow water waves, fluid mechanics, quantum mechanics, wave proliferation phenomena, etc. One of the fundamental physical problems for these models is to obtain their traveling wave solutions. As a consequence, the search for mathematical methods to create exact solutions of NLDEs is an important and essential activity in nonlinear sciences. In recent years, many articles have studied optical solitons' form in telecommunications industry. These soliton molecules form the information transporter across intercontinental distances around the world. Lastly, the nonlinear Schrödinger's equation (NLSE) has been discussed with the help of many models [1–38]. The aspect of stochasticity is one of the features that is less touched upon and there are hardly any papers that have debated this point [3–9]. The Fokas–Lenells equation (FLE) appears as a model which appoints nonlinear pulse propagation in optical fibers. The FLE is a completely integrable equation which has arisen as an integrable generalization of the NLSE using bi-Hamiltonian methods [10]. On the other hand, the FLE models have the propagation of nonlinear light pulses in monomode optical fibers when certain higher-order nonlinear effects are considered in optics field [11]. The complete integrability of the FLE has been presented by using the inverse scattering transform (IST) method [12]. In the main, a Lax pair and a few conservation laws connected to it have been obtained using the bi-Hamiltonian structure and the multi-soliton solutions have been derived by using the dressing method [13]. One more main characteristic of the FLE is that it is the first negative flow of the integrable hierarchy of the derivative NLSE [14].

In the present article, we will study the FLE with multiplicative white noise in the Itô sense. Our results are presented after a comprehensive analysis obtained in this article.

### **2. Governing Model**

The dimensionless structure of the stochastic perturbed FLE in polarization preserving fiber with multiplicative white noise in the Itô sense is written, for the first time, as:

**Citation:** Zayed, E.M.E.; El-Horbaty, M.; Alngar, M.E.M.; El-Shater, M. Dispersive Optical Solitons for Stochastic Fokas-Lenells Equation with Multiplicative White Noise. *Eng* **2022**, *3*, 523–540. https://doi.org/ 10.3390/eng3040037

Academic Editor: Antonio Gil Bravo

Received: 28 October 2022 Accepted: 22 November 2022 Published: 28 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

$$\left[iq\_1 + a\_1q\_{xx} + a\_2q\_{xt} + |q|^2(bq + icq\_x) + \sigma(q - ia\_2q\_x)\frac{dW(t)}{dt} = i\left[aq\_x + \lambda\left(|q|^2q\right)\_x + \mu\left(|q|^2\right)\_xq\right],\tag{1}$$

where *q*(*x*, *t*) is a complex-valued function that represents the wave profile, while *a*1, *a*2, *b*, *c*, *<sup>σ</sup>*, *<sup>α</sup>*, *<sup>λ</sup>*, *<sup>μ</sup>* are real-valued constants and *<sup>i</sup>* <sup>=</sup> √−1. The first term in Equation (1) is the linear temporal evolution, *a*<sup>1</sup> is the coefficient of chromatic dispersion (CD), *a*<sup>2</sup> is the coefficient of spatio-temporal dispersion (STD), *b* is the coefficient of self-phase modulation (SPM), *c* is the coefficient of nonlinear dispersion term, *σ* is the coefficient of the strength of noise, the Wiener process is denoted by *W*(*t*), while *dW*(*t*)/*dt* represents the white noise. Also, the term *dW*(*t*)/*dt* is the time derivative of the standard Wiener process *W*(*t*) which is called a Brownian motion and has the following properties [7]: (i) *W*(*t*), *t* ≥ 0, is a continuous function of *t*, (ii) For *s* < *t*, *W*(*t*) − *W*(*s*) is independent of increments. (iii) *W*(*t*) − *W*(*s*) has a normal distribution with mean zero and variance (*t* − *s*).

Next, *α* is the coefficient of inter-modulation dispersion (IMD), *λ* is the coefficient of self-steepening (SS) term, and finally *μ* is the coefficient of higher-order nonlinear dispersion term. If *σ* = 0, Equation (1) reduces to the familiar FLE which is studied in [1,2,37]. The authors [37] studied Equation (1) with variable coefficients and *σ* = 0. The motivation of adding the stochastic term *<sup>σ</sup>*(*<sup>q</sup>* <sup>−</sup> *ia*2*qx*) *dW*(*t*) *dt* to Equation (1) is to formulate the stochastic FLE with noise or fluctuations depending on the time, which has been recognized in many areas via physics, engineering, chemistry and so on. This stochastic term has been constructed with the help of the two terms *iqt* and *a*2*qxt*. Therefore, in general, the stochastic model means that the model of differential equations should contain the white noise term (*σ* = 0). The physical importance of the stochastic FL Equation (1) is to find its traveling wave stochastic solutions which appoint the nonlinear pulse propagations in optical fibers.

The aim of this article is to use the method of MMSE in Section 3, the method of MSC in Section 4, the method of MJEE in Section 5 and the ansatze involving hyperbolic functions in Section 6 to find the bright, dark, singular soliton solutions, as well as the Jacobi elliptic function solutions of Equation (1). Some numerical simulations are obtained in Section 7. Finally, conclusions are illustrated in Section 8.

#### **3. On Solving Equation (1) by MMSE**

In order to solve the stochastic Equation (1), we use a wave transformation involving the noise coefficient *σ* and the Wiener process *W*(*t*) in the form:

$$q(\mathbf{x}, t) = \phi(\xi) \exp i \left[ -\kappa \mathbf{x} + \nu t + \sigma \mathcal{W}(t) - \sigma^2 t \right],\tag{2}$$

where the transformation *ξ* = *x* − *vt* is used. Here, *κ*, *w*, *v*, are real constants, such that *κ* represents the wave number, *w* represents the frequency and *v* represents the soliton velocity. The function *φ*(*ξ*) is real function which represents the amplitude part. When we put Equation (2) into Equation (1), we obtain the ordinary differential equation (ODE):

$$[a\_1 - a\_2 \upsilon] \phi'''' + \mathcal{Y} \phi + [b + \kappa(\varepsilon - \lambda)] \phi^3 = 0,\tag{3}$$

and the soliton velocity,

$$v = \frac{Y}{(a\_2 \kappa - 1)}, \quad a\_2 \kappa \neq 1 \tag{4}$$

as well as the constraint condition,

$$x - 3\lambda - 2\mu = 0,\tag{5}$$

where *Y* = (*<sup>w</sup>* <sup>−</sup> *<sup>σ</sup>*2)(*a*2*<sup>κ</sup>* <sup>−</sup> <sup>1</sup>) <sup>−</sup> *<sup>a</sup>*1*κ*<sup>2</sup> <sup>−</sup> *ακ* and <sup>=</sup> *<sup>d</sup>*<sup>2</sup> *<sup>d</sup>ξ*<sup>2</sup> . We have the balance number *N* = 1 by balancing *φ* with the *φ*<sup>3</sup> in Equation (3). According to the method of MSE [15–20], the solution of Equation (3) is written as:

$$\phi(\xi) = A\_0 + A\_1 \left[ \frac{\psi'(\xi)}{\psi(\xi)} \right],\tag{6}$$

where *ψ*(*ξ*) is a new function of *ξ*, and *A*0, *A*<sup>1</sup> are constants to be determined later, provided *A*<sup>1</sup> = 0, *ψ*(*ξ*) = 0 and *ψ* (*ξ*) = 0.

Inserting Equation (6) into Equation (3), and collecting all the coefficients of *ψ*−*<sup>i</sup>* (*ξ*) (*i* = 0, 1, 2, 3), we obtain the equations:

$$
\psi^0 : A\_0 \mathcal{Y} + A\_0^3 [b + \kappa (c - \lambda)] = 0,\tag{7}
$$

$$
\psi^{-1}: A\_1 \psi^{\prime\prime\prime}[a\_1 - a\_2 v] + A\_1 \psi Y + 3A\_0^2 A\_1 \psi^{\prime}[b + \kappa(c - \lambda)] = 0,\tag{8}
$$

$$
\Psi^{-2}: -3A\_1 \psi' \psi'' [a\_1 - a\_2 \upsilon] + 3A\_0 A\_1^2 \psi'^2 [b + \kappa(\varepsilon - \lambda)] = 0,\tag{9}
$$

$$
\psi^{-3}: 2A\_1 \psi'^3 [a\_1 - a\_2 v] + A\_1^3 \psi'^3 [b + \kappa(c - \lambda)] = 0. \tag{10}
$$

By solving Equations (7) and (10), we obtain:

$$A\_0 = 0, \ A\_0 = \pm \sqrt{-\frac{Y}{[b + \kappa(c - \lambda)]}}, \ A\_1 = \pm \sqrt{-\frac{2[a\_1 - a\_2 v]}{[b + \kappa(c - \lambda)]}},\tag{11}$$

provided [*b* + *κ*(*c* − *λ*)]*Y* < 0 and [*b* + *κ*(*c* − *λ*)][*a*<sup>1</sup> − *a*2*v*] < 0.

By solving Equations (8) and (9), we conclude that *A*<sup>0</sup> = 0 is rejected. Therefore, *A*<sup>0</sup> = 0. Now, Equation (9) reduces to the ODE :

$$\left[a\_1 - a\_2 v\right] \psi'' - A\_0 A\_1 \left[b + \kappa (c - \lambda)\right] \psi' = 0,\tag{12}$$

which has the solution

$$\Psi'(\xi) = \xi\_0 \exp\left[\frac{A\_0 A\_1 \left[b + \kappa(c - \lambda)\right]}{\left[a\_1 - a\_2 v\right]} \xi\right],\tag{13}$$

where *ξ*<sup>0</sup> = 0 is a constant. From Equation (11) and Equation (13), we can show that Equation (8) is valid. Hence, we have the results:

$$\psi(\xi) = \frac{\mathfrak{J}\_0[a\_1 - a\_2 v]}{A\_0 A\_1[b + \kappa(c - \lambda)]} \exp\left[\frac{A\_0 A\_1[b + \kappa(c - \lambda)]}{[a\_1 - a\_2 v]} \xi\right] + \mathfrak{J}\_{1\prime} \tag{14}$$

where *ξ*<sup>1</sup> is a nonzero constant of integration. Now, the exact solution of Equation (1) has the form:

$$q(\mathbf{x},t) = \left\{ A\mathbf{u} + A\_1 \frac{\frac{\mathbf{r}\_0}{\beta\_0} \exp\left[\frac{A\_0 A\_1 [\mathbf{b} + \mathbf{x}(c-\lambda)]}{[a\_1 - a\_2 v]}(\mathbf{x} - vt)\right]}{\frac{\mathbf{r}\_0}{\beta\_1} + \frac{\frac{\mathbf{r}\_0}{\beta\_0} [a\_1 - a\_2 v]}{A\_0 A\_1 [\mathbf{b} + \mathbf{x}(c-\lambda)]} \exp\left[\frac{A\_0 A\_1 [\mathbf{b} + \mathbf{x}(c-\lambda)]}{[a\_1 - a\_2 v]}(\mathbf{x} - vt)\right]} \right\} \exp\left[-\mathbf{x}\mathbf{x} + vt + \sigma \mathcal{W}(t) - \sigma^2 t\right].\tag{15}$$

In particular, if we set,

$$\xi\_1^x = \frac{\xi\_0^x[a\_1 - a\_2v]}{A\_0 A\_1[b + \kappa(c - \lambda)]},\tag{16}$$

we have the dark soliton solution:

$$q(\mathbf{x}, t) = \pm \sqrt{-\frac{Y}{[b + \kappa(c - \lambda)]}} \tanh\left[\sqrt{\frac{Y}{2[a\_1 - a\_2 v]}} (\mathbf{x} - vt)\right] \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right],\tag{17}$$

while, if we set,

$$\zeta\_1^\chi = -\frac{\zeta\_0^\chi [a\_1 - a\_2 \upsilon]}{A\_0 A\_1 [b + \kappa(\varepsilon - \lambda)]},\tag{18}$$

we have the singular soliton solution:

$$q(\mathbf{x},t) = \pm \sqrt{-\frac{\mathbf{y}}{[\mathbf{b} + \mathbf{x}(\varepsilon - \lambda)]}} \coth\left[\sqrt{\frac{\mathbf{y}}{2[\mathbf{a}\_1 - \mathbf{a}\_2 \mathbf{z}]}} (\mathbf{x} - \mathbf{v}t)\right] \exp\left[-\mathbf{x}\mathbf{x} + \mathbf{w}t + \sigma \mathcal{W}(t) - \sigma^2 t\right],\tag{19}$$

provided,

$$[b + \kappa(c - \lambda)]\mathcal{Y} < 0,\\
[a\_1 - a\_2v]\mathcal{Y} > 0. \tag{20}$$

On comparing our above results (17) and (19) with the results (19) and (20) obtained in [37], we deduce that they are equivalent when *σ* = 0.

#### **4. On Solving Equation (1) by MSC**

To apply this method according to [21–25], assume that Equation (3) has the sinesolution form:

$$\phi(\xi) = \begin{cases} \lambda\_1 \sin^{\beta\_1}(\mu\_1 \xi) \text{, if } |\xi| < \frac{\pi}{\mu\_1}, \\\\ 0 & \text{, otherwise.} \end{cases} \tag{21}$$

Substituting Equation (21) into Equation (3), we obtain:

$$\begin{aligned} \left[a\_1 - a\_2 v\right] \left[\lambda\_1 \mu\_1^2 \beta\_1 (\beta\_1 - 1) \sin^{\beta\_1 - 2} (\mu\_1 \underline{\epsilon}) - \lambda\_1 \mu\_1^2 \beta\_1^2 \sin^{\beta\_1} (\mu\_1 \underline{\epsilon})\right] \\ + \lambda\_1 \lambda\_1 \sin^{\beta\_1} (\mu\_1 \underline{\epsilon}) + [b + \kappa (c - \lambda)] \lambda\_1^3 \sin^{3\beta\_1} (\mu\_1 \underline{\epsilon}) = 0. \end{aligned} \tag{22}$$

From (22), we deduce that *β*<sup>1</sup> − <sup>2</sup> = <sup>3</sup>*β*<sup>1</sup> which leads *β*<sup>1</sup> = −1. Consequently, we have the results:

$$
\mu\_1^2 = \frac{Y}{[a\_1 - a\_2 v]}, \quad \lambda\_1^2 = -\frac{2Y}{[b + \kappa(c - \lambda)]}.\tag{23}
$$

Now, the periodic solution of Equation (1) is:

$$q(\mathbf{x},t) = \pm \sqrt{-\frac{2Y}{[b+\kappa(c-\lambda)]}} \csc\left[\sqrt{\frac{Y}{[a\_1-a\_2v]}}(\mathbf{x}-vt)\right] \exp i\left[-\kappa\mathbf{x}+\nu t+\sigma W(t)-\sigma^2 t\right],\tag{24}$$

provided [*b* + *κ*(*c* − *λ*)]*Y* < 0 , [*a*<sup>1</sup> − *a*2*v*]*Y* > 0.

Since csc(*ix*) = −*i*csch*x*, then the singular soliton solution of Equation (1) is written as:

$$q(\mathbf{x},t) = \pm \sqrt{\frac{2Y}{[b+\kappa(\varepsilon-\lambda)]}} \text{csch}\left[\sqrt{-\frac{Y}{[a\_1-a\_2v]}}(\mathbf{x}-\nu t)\right] \exp\left[-\kappa \mathbf{x} + \nu t + \sigma W(t) - \sigma^2 t\right], \tag{25}$$

provided *Y*[*b* + *κ*(*c* − *λ*)] > 0 , [*a*<sup>1</sup> − *a*2*v*]*Y* < 0.

In parallel, if we allow that Equation (3) has the cosine-solution:

$$\phi(\xi) = \begin{cases} \begin{array}{c} \lambda\_1 \cos^{\beta\_1}(\mu\_1 \xi) \end{array}, \text{ if } |\xi| < \frac{\pi}{2\mu\_1}, \\\\ 0 \end{cases} \tag{26}$$

Putting Equation (26) into Equation (3), we obtain

$$\begin{aligned} \left[a\_1 - a\_2 \upsilon\right] \left[-\mu\_1^2 \beta\_1^2 \lambda\_1 \cos^{\theta\_1}(\mu\_1 \underline{\chi}) + \lambda\_1 \mu\_1^2 \beta\_1 (\beta\_1 - 1) \cos^{\theta\_1 - 2}(\mu\_1 \underline{\chi})\right] \\ + \mathcal{Y} \lambda\_1 \cos^{\theta\_1}(\mu\_1 \underline{\chi}) + [b + \kappa(c - \lambda)] \lambda\_1^3 \cos^{3\theta\_1}(\mu\_1 \underline{\chi}) &= 0. \end{aligned} \tag{27}$$

From Equation (27), we deduce that *β*<sup>1</sup> − 2 = 3*β*1, which leads *β*<sup>1</sup> = −1. Therefore, we have the solutions:

$$q(\mathbf{x},t) = \pm \sqrt{-\frac{2\mathbf{y}}{[b+\kappa(\varepsilon-\lambda)]}} \sec\left[\sqrt{\frac{\mathbf{y}}{[a\_1-a\_2v]}}(\mathbf{x}-vt)\right] \exp\left[-\mathbf{x}\mathbf{x}+\sigma t+\sigma W(t)-\sigma^2 t\right],\tag{28}$$

with conditions [*b* + *κ*(*c* − *λ*)]*Y* < 0 , [*a*<sup>1</sup> − *a*2*v*]*Y* > 0. Since, sec(*ix*) = sech*x*, we have the bright soliton solution:

$$q(\mathbf{x}, t) = \pm \sqrt{-\frac{2Y}{[b + \kappa(c - \lambda)]}} \text{sech}\left[\sqrt{-\frac{Y}{[a\_1 - a\_2v]}} (\mathbf{x} - vt)\right] \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right],\tag{29}$$

$$\text{provided}[b + \kappa(c - \lambda)]Y < 0, \, [a\_1 - a\_2v]Y < 0.$$

#### **5. On Solving Equation (1) by MJEE**

If we multiply Equation (3) by *φ* (*ξ*) and integrate, we have the JEE as:

$$
\phi'^{'2}(\xi) = l\_0 + l\_2 \phi^2(\xi) + l\_4 \phi^4(\xi),
\tag{30}
$$

where,

$$l\_0 = \frac{2c\_1}{\left[a\_1 - a\_2v\right]}, l\_2 = -\frac{Y}{\left[a\_1 - a\_2v\right]}, l\_4 = -\frac{\left[b + \kappa(c - \lambda)\right]}{2\left[a\_1 - a\_2v\right]},\tag{31}$$

and *c*<sup>1</sup> is the integration constant, [*a*<sup>1</sup> − *a*2*v*] = 0. It is noted [26–30] that Equation (30) has the Jacobi-elliptic solutions in the forms:

$$\text{(1)}\text{ If }l\_0 = 1, l\_2 = -\left(1 + m^2\right), l\_4 = m^2, 0 < m < 1 \text{, then,}$$

$$\phi(\xi) = \text{sn}(\xi) \text{ or } \phi(\xi) = \text{cd}(\xi). \tag{32}$$

Then, Equation (1) has the JEE solution:

$$\begin{aligned} q(\mathbf{x}, t) &= \mathfrak{sn}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma W(t) - \sigma^2 t \right], \\ \text{or} \\ q(\mathbf{x}, t) &= \mathbf{c} \mathbf{d}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma W(t) - \sigma^2 t \right], \end{aligned} \tag{33}$$

where,

$$\begin{array}{l} c\_1 = \frac{1}{2}(a\_1 - a\_2 v), \\ Y = (1 + m^2)(a\_1 - a\_2 v), \\ b + \kappa(c - \lambda) = -2m^2(a\_1 - a\_2 v), \end{array} \tag{34}$$

and consequently, we obtain

$$\Upsilon = -\frac{(1+m^2)}{2m^2}[b+\kappa(c-\lambda)].$$

Particularly, if *m* → 1, we get,

$$q(\mathbf{x},t) = \tanh(\mathbf{x} - vt) \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right].\tag{35}$$

Note that the solution Equation (35) is equivalent to the solution Equation (17) under the conditions of Equation (34).

**(2)** If *<sup>l</sup>*<sup>0</sup> <sup>=</sup> *<sup>m</sup>*2, *<sup>l</sup>*<sup>2</sup> <sup>=</sup> <sup>−</sup> 1 + *m*<sup>2</sup> , *l*<sup>4</sup> = 1, 0 < *m* < 1, then,

$$
\phi(\xi) = \text{ns}(\xi) \quad \text{or} \quad \phi(\xi) = \text{dc}(\xi). \tag{36}
$$

Then, we obtain the JEE solution for Equation (1),

$$\begin{aligned} q(\mathbf{x}, t) &= \mathbf{ns}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma W(t) - \sigma^2 t \right], \\ \text{or} \\ q(\mathbf{x}, t) &= \mathbf{dc}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma W(t) - \sigma^2 t \right], \end{aligned} \tag{37}$$

where,

$$\begin{array}{l} c\_1 = \frac{1}{2}m^2(a\_1 - a\_2v), \\ Y = (1 + m^2)(a\_1 - a\_2v), \\ b + \kappa(c - \lambda) = -2(a\_1 - a\_2v), \end{array} \tag{38}$$

and consequently, we have,

$$\Upsilon = -\frac{(1+m^2)}{2}[b + \kappa(c - \lambda)].$$

Particularly, if *m* → 1, we obtain,

$$q(\mathbf{x},t) = \coth(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t \right]. \tag{39}$$

Note that the solution in Equation (39) is equivalent to the solution in Equation (19) under the conditions in Equation (38).

**(3)** If *<sup>l</sup>*<sup>0</sup> <sup>=</sup> <sup>1</sup> <sup>−</sup> *<sup>m</sup>*2, *<sup>l</sup>*<sup>2</sup> <sup>=</sup> <sup>2</sup>*m*<sup>2</sup> <sup>−</sup> 1, *<sup>l</sup>*<sup>4</sup> <sup>=</sup> <sup>−</sup>*m*2, 0 <sup>&</sup>lt; *<sup>m</sup>* <sup>&</sup>lt; 1, then,

$$\phi(\mathcal{J}) = \text{cn}(\mathcal{J}).\tag{40}$$

Now, we have the JEE solution for Equation (1),

$$q(\mathbf{x},t) = \text{cn}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + wt + \sigma W(t) - \sigma^2 t \right],\tag{41}$$

where,

$$\begin{array}{l} c\_1 = \frac{1}{2}(1 - m^2)(a\_1 - a\_2v), \\ Y = -(2m^2 - 1)(a\_1 - a\_2v), \\ b + \kappa(c - \lambda) = 2m^2(a\_1 - a\_2v), \end{array} \tag{42}$$

and consequently, we have,

$$\Upsilon = -\frac{(2m^2 - 1)}{2m^2} [b + \kappa(c - \lambda)].$$

Particularly, if *m* → 1, we obtain,

$$q(\mathbf{x}, t) = \text{sech}(\mathbf{x} - vt) \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right] \tag{43}$$

Note that the solution of Equation (43) is equivalent to the solution of Equation (29) under the conditions of Equation (42).

**(4)** If *<sup>l</sup>*<sup>0</sup> <sup>=</sup> <sup>−</sup>*m*<sup>2</sup> <sup>1</sup> <sup>−</sup> *<sup>m</sup>*<sup>2</sup> , *<sup>l</sup>*<sup>2</sup> <sup>=</sup> <sup>2</sup>*m*<sup>2</sup> <sup>−</sup> 1, *<sup>l</sup>*<sup>4</sup> <sup>=</sup> 1, 0 <sup>&</sup>lt; *<sup>m</sup>* <sup>&</sup>lt; 1, then,

$$\phi(\emptyset) = \text{ds}(\emptyset). \tag{44}$$

Consequently, we have the JEE solution for Equation (1),

$$q(\mathbf{x},t) = \text{ds}(\mathbf{x} - vt) \exp i \left[ -\kappa \mathbf{x} + \omega vt + \sigma \mathcal{W}(t) - \sigma^2 t \right],\tag{45}$$

where,

$$\begin{array}{l} c\_1 = -\frac{m^2}{2}(1 - m^2)(a\_1 - a\_2v), \\ \mathcal{Y} = -(2m^2 - 1)(a\_1 - a\_2v), \\ b + \kappa(c - \lambda) = -2(a\_1 - a\_2v), \end{array} \tag{46}$$

and we have,

$$\mathcal{Y} = \frac{1}{2}(2m^2 - 1)[b + \kappa(c - \lambda)].$$

Particularly, if *m* → 1, we obtain

$$q(\mathbf{x},t) = \text{csch}(\mathbf{x} - vt) \exp\left[-\kappa\mathbf{x} + vt + \sigma\mathcal{W}(t) - \sigma^2 t\right],\tag{47}$$

Note that the solution of Equation (47) is equivalent to the solution of Equation (25) under the conditions of Equation (46).

**(5)** If *l*<sup>0</sup> = <sup>1</sup> <sup>4</sup> , *<sup>l</sup>*<sup>2</sup> <sup>=</sup> <sup>1</sup> <sup>2</sup> (<sup>1</sup> <sup>−</sup> <sup>2</sup>*m*2), *<sup>l</sup>*<sup>4</sup> <sup>=</sup> <sup>1</sup> <sup>4</sup> , 0 < *m* < 1, then,

$$\phi(\xi) = \frac{\mathrm{sn}(\xi)}{1 \pm \mathrm{cn}(\xi)}.\tag{48}$$

Now, we have the JEE solution for the Equation (1),

$$q(\mathbf{x},t) = \frac{\text{sn}(\mathbf{x} - vt)}{1 \pm \text{cn}(\mathbf{x} - vt)} \exp\left[-\kappa\mathbf{x} + wt + \sigma\mathcal{W}(\mathbf{t}) - \sigma^2 \mathbf{t}\right],\tag{49}$$

where,

*c*<sup>1</sup> = <sup>1</sup> <sup>8</sup> (*a*<sup>1</sup> − *a*2*v*), *<sup>Y</sup>* <sup>=</sup> <sup>−</sup><sup>1</sup> <sup>2</sup> (<sup>1</sup> <sup>−</sup> <sup>2</sup>*m*2)(*a*<sup>1</sup> <sup>−</sup> *<sup>a</sup>*2*v*), *<sup>b</sup>* <sup>+</sup> *<sup>κ</sup>*(*<sup>c</sup>* <sup>−</sup> *<sup>λ</sup>*) <sup>=</sup> <sup>−</sup><sup>1</sup> <sup>2</sup> (*a*<sup>1</sup> − *a*2*v*), (50)

and consequently, we have,

$$\mathcal{Y} = (1 - 2m^2)[b + \kappa(c - \lambda)].$$

Particularly, if *m* → 1, we obtain the combo dark-bright soliton solutions:

$$q(\mathbf{x}, t) = \frac{\tanh(\mathbf{x} - vt)}{1 \pm \mathrm{sech}(\mathbf{x} - vt)} \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right]. \tag{51}$$

**(6)** If *<sup>l</sup>*<sup>0</sup> <sup>=</sup> <sup>1</sup>−*m*<sup>2</sup> , *<sup>l</sup>*<sup>2</sup> <sup>=</sup> <sup>1</sup>+*m*<sup>2</sup> , *<sup>l</sup>*<sup>4</sup> <sup>=</sup> <sup>1</sup>−*m*<sup>2</sup> , 0 < *m* < 1, then,

$$\phi(\xi) = \frac{\text{cn}(\xi)}{1 \pm \text{sn}(\xi)}.\tag{52}$$

Then, we have the JEE solution for Equation (1),

$$q(\mathbf{x},t) = \frac{\text{cn}(\mathbf{x} - vt)}{1 \pm \text{sn}(\mathbf{x} - vt)} \exp\left[-\kappa\mathbf{x} + wt + \sigma\mathcal{W}(t) - \sigma^2 t\right],\tag{53}$$

where

$$\begin{array}{l} c\_1 = \frac{1}{8}(1 - m^2)(a\_1 - a\_2v), \\ Y = -\frac{1}{2}(1 + m^2)(a\_1 - a\_2v), \\ b + \kappa(c - \lambda) = -\frac{1}{2}(1 - m^2)(a\_1 - a\_2v). \end{array} \tag{54}$$

Particularly, if *m* → 1, we obtain the combo bright-dark soliton solutions:

$$q(\mathbf{x},t) = \frac{\text{sech}(\mathbf{x} - vt)}{1 \pm \tanh(\mathbf{x} - vt)} \exp\left[-\kappa \mathbf{x} + wt + \sigma \mathcal{W}(t) - \sigma^2 t\right]. \tag{55}$$

Finally, there are many other Jacobi elliptic solutions which are omitted here for simplicity.

#### **6. Ansatze Involving Hyperbolic Functions**

To this aim, we first write Equation (3) in the simple form,

$$A\boldsymbol{\phi}^{\prime\prime} + \boldsymbol{\Upsilon}\boldsymbol{\phi} + \mathbb{C}\boldsymbol{\phi}^{\cdot} = \boldsymbol{0},\tag{56}$$

where,

$$\begin{array}{l} A = a\_1 - a\_2 v, \\ C = b + \kappa(c - \lambda). \end{array} \tag{57}$$

Along these lines, the main steps of the proposed ansatze have been presented according to the ansatze involving the hyperbolic functions method [31].

#### *6.1. Combo Bright-Dark Solitons*

We assume the ansatz,

$$\phi(\xi) = \frac{\varkappa\_1 \text{sech}(\mu\_1 \xi)}{1 + \lambda\_1 \tanh(\mu\_1 \xi)}.\tag{58}$$

where *α*1, *λ*1, *μ*<sup>1</sup> are parameters to be determined. Now, we obtain

$$\boldsymbol{\phi}^{\boldsymbol{\eta}^{\boldsymbol{\eta}}}(\boldsymbol{\xi}^{\boldsymbol{\eta}}) = \frac{a\_{1}\mu\_{1}^{2}(2\lambda\_{1}^{2}-1)\mathsf{sech}\mathfrak{h}(\mu\_{1}\boldsymbol{\xi}) + 2a\_{1}\lambda\_{1}\mu\_{1}^{2}\mathsf{sech}\mathfrak{h}(\mu\_{1}\boldsymbol{\xi})\tanh(\mu\_{1}\boldsymbol{\xi}) + a\_{1}\mu\_{1}^{2}(2-\lambda\_{1}^{2})\mathsf{sech}\mathfrak{h}(\mu\_{1}\boldsymbol{\xi})\tanh^{2}(\mu\_{1}\boldsymbol{\xi})}{\left(1+\lambda\_{1}\tanh(\mu\_{1}\boldsymbol{\xi})\right)^{3}}.\tag{59}$$

Substituting Equations (58) and (59) into Equation (56), combining all the coefficients of sech*p*(*ξ*)tanh*<sup>q</sup>* (*ξ*) (*p* = 1, *q* = 0, 1, 2), we obtain the set of equations:

$$\begin{array}{l} A\alpha\_1 \mu\_1^2 (2\lambda\_1^2 - 1) + \Upsilon \alpha\_1 + \mathbb{C} \alpha\_1^3 = 0, \\ 2A\alpha\_1 \lambda\_1 \mu\_1^2 + 2\Upsilon \alpha\_1 \lambda\_1 = 0, \\ A\alpha\_1 \mu\_1^2 (2 - \lambda\_1^2) + \Upsilon \alpha\_1 \lambda\_1^2 - \mathbb{C} \alpha\_1^3 = 0. \end{array} \tag{60}$$

By resolving the Equation (60), we have the results:

$$
\mu\_1^2 = \frac{-Y}{A}, \\
AY < 0, \ \lambda\_1^2 = \frac{2Y + \mathcal{Ca}\_1^2}{2Y} > 0, \mathcal{a}\_1 \neq 0.
$$

Now, we obtain

$$q(\mathbf{x},t) = \left\{ \frac{a\_1 \text{sech}\left[\sqrt{\frac{-Y}{A}}(\mathbf{x}-vt)\right]}{1 \pm \sqrt{\frac{2Y + \text{Ca}\_1^2}{2Y} \tanh\left[\sqrt{\frac{-Y}{A}}(\mathbf{x}-vt)\right]}} \right\} \exp\left[-\kappa\mathbf{x} + \nu t + \sigma W(t) - \sigma^2 t\right]. \tag{61}$$

which represent the combo-bright-dark soliton solutions and are equivalent to the solutions Equation (55) of Section 5, if *A* = −*Y*, *C* = 0 and *α*<sup>1</sup> = 1.

#### *6.2. Combo Dark-Bright Solitons*

We assume the ansatz

$$\phi(\xi) = \frac{\varkappa\_1 \tanh(\mu\_1 \xi)}{1 + \lambda\_1 \mathrm{sech}(\mu\_1 \xi)},\tag{62}$$

where *α*1, *λ*1, *μ*<sup>1</sup> are parameters to be determined. Now, we obtain

$$\phi''(\xi) = \frac{a\_1 \mu\_1^2 (\lambda\_1^2 - 2) \text{sech}^2(\mu\_1 \xi) \tanh(\mu\_1 \xi) - a\_1 \lambda\_1 \mu\_1^2 \text{sech}(\mu\_1 \xi) \tanh(\mu\_1 \xi)}{\left(1 + \lambda\_1 \text{sech}(\mu\_1 \xi)\right)^3}. \tag{63}$$

Substituting Equations (62) and (63) into Equation (56), combining all the coefficients of tanh*p*(*ξ*)sech*<sup>q</sup>* (*ξ*) (*p* = 1, *q* = 0, 1, 2), we obtain the algebraic equations:

$$\begin{array}{c} \text{Ya}\_1 + \text{C}\boldsymbol{\alpha}\_1^3 = 0, \\ -A\boldsymbol{\alpha}\_1\lambda\_1\mu\_1^2 + 2\text{Y}\boldsymbol{\alpha}\_1\lambda\_1 = 0, \\ A\boldsymbol{\alpha}\_1\mu\_1^2(\lambda\_1^2 - 2) + \text{Y}\boldsymbol{\alpha}\_1\lambda\_1^2 - \text{C}\boldsymbol{\alpha}\_1^3 = 0. \end{array} \tag{64}$$

Solving the algebraic Equation (64), we obtain the results:

$$
\mu\_1^2 = \frac{2Y}{A}, \\
AY > 0, \\
\alpha\_1^2 = \frac{-Y}{C}, \\
YC < 0, \\
\lambda\_1^2 = 1.
$$

Now, Equation (1) has the combo dark-bright soliton solutions:

$$q(\mathbf{x},t) = \pm \sqrt{\frac{-\mathcal{Y}}{\mathcal{C}}} \left\{ \frac{\tanh\left[\sqrt{\frac{2\mathcal{Y}}{\mathcal{A}}}(\mathbf{x}-\mathbf{v}t)\right]}{1 \pm \mathrm{sech}\left[\sqrt{\frac{2\mathcal{Y}}{\mathcal{A}}}(\mathbf{x}-\mathbf{v}t)\right]} \right\} \exp\left[-\kappa\mathbf{x} + \mathbf{v}t + \sigma\mathcal{W}(t) - \sigma^2 t\right]. \tag{65}$$

which are equivalent to the solutions Equation (51) of Section 5, if *A* = 2*Y* and *Y* = −*C*.

#### **7. Numerical Simulations**

In this section, we present the graphs of some solutions for Equation (1). Let us now examine Figures 1–15, as it illustrates some of our solutions obtained in this paper. To this aim, we select some special values of the obtained parameters.

Figure 1: The numerical simulations of the solutions (17) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values

*a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 0, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 3, −5 ≤ *x*, *t* ≤ 5.

**Figure 1.** The profile of the dark soliton solutions (17).

Figure 2: The numerical simulations of the solutions (17) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 1, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 4, −5 ≤ *x*, *t* ≤ 5.

**Figure 2.** The profile of the dark soliton solutions (17).

Figure 3: The numerical simulations of the solutions (17) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 2, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 8, −5 ≤ *x*, *t* ≤ 5.

**Figure 3.** Shows the profile of the dark soliton solutions (17).

Figure 4: The numerical simulations of the solutions (19) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 0, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 3, −5 ≤ *x*, *t* ≤ 5.

**Figure 4.** Shows the profile of the singular soliton solutions (19).

Figure 5: The numerical simulations of the solutions (19) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 1, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 4, −5 ≤ *x*, *t* ≤ 5.

**Figure 5.** Shows the profile of the singular soliton solutions (19).

Figure 6: The numerical simulations of the solutions (19) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 2, *α* = 1, *κ* = 2, *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = 8, −5 ≤ *x*, *t* ≤ 5.

**Figure 6.** Shows the profile of the singular soliton solutions (19).

Figure 7: The numerical simulations of the solutions (29) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 0, *α* = 1, *κ* = <sup>1</sup> <sup>2</sup> , *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = −2, −5 ≤ *x*, *t* ≤ 5.

**Figure 7.** Shows the profile of the bright soliton solutions (29).

Figure 8: The numerical simulations of the solutions (29) 3D and 2D (with *t* = <sup>1</sup> <sup>2</sup> ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 4, *α* = 4, *κ* = <sup>1</sup> <sup>4</sup> , *w* = 16, *λ* = 2, *μ* = 2, *c* = 10, *v* = −6, −5 ≤ *x*, *t* ≤ 5.

**Figure 8.** Shows the profile of the bright soliton solutions (29).

Figure 9: The numerical simulations of the solutions (29) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = 1, *σ* = 2, *α* = 2, *κ* = <sup>1</sup> <sup>2</sup> , *w* = 2, *λ* = 1, *μ* = 1, *c* = 5, *v* = −10, −5 ≤ *x*, *t* ≤ 5.

**Figure 9.** Shows the profile of the bright soliton solutions (29).

Figure 10: The numerical simulations of the solutions (51) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 4, *a*<sup>2</sup> = 2, *b* = −16, *σ* = 0, *α* = 1, *κ* = 2, *w* = 10, *λ* = 2, *μ* = 2, *c* = 10, *v* = 2, −5 ≤ *x*, *t* ≤ 5.

**Figure 10.** The profile of the combination of dark-bright soliton solutions (51).

Figure 11: The numerical simulations of the solutions (51) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 4, *a*<sup>2</sup> = 1, *b* = −21, *σ* = 1, *α* = 1, *κ* = 2, *w* = 24, *λ* = 2, *μ* = 2, *c* = 10, *v* = −6, −5 ≤ *x*, *t* ≤ 5.

**Figure 11.** The profile of the combination of dark-bright soliton solutions (51).

Figure 12: The numerical simulations of the solutions (51) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 6, *a*<sup>2</sup> = 1, *b* = −16, *σ* = 2, *α* = 1, *κ* = 2, *w* = 30, *λ* = 2, *μ* = 2, *c* = 10, *v* = 6, −5 ≤ *x*, *t* ≤ 5.

**Figure 12.** The profile of the combination of dark-bright soliton solutions (51).

Figure 13: The numerical simulations of the solutions (55) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = −16, *σ* = 0, *α* = 2, *κ* = 2, *w* = 2, *λ* = 2, *μ* = 2, *c* = 10, *v* = −7, −5 ≤ *x*, *t* ≤ 5.

**Figure 13.** The profile of the combination of bright-dark soliton solutions (55).

Figure 14: The numerical simulations of the solutions (55) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *<sup>a</sup>*<sup>1</sup> <sup>=</sup> 1, *<sup>a</sup>*<sup>2</sup> <sup>=</sup> 1, *<sup>b</sup>* <sup>=</sup> <sup>−</sup>16, *<sup>σ</sup>* <sup>=</sup> 1, *<sup>α</sup>* <sup>=</sup> <sup>−</sup><sup>5</sup> <sup>3</sup> , *κ* = 2, *w* = 2, *λ* = 2, *μ* = 2, *c* = 10, *v* = <sup>4</sup> <sup>3</sup> , −5 ≤ *x*, *t* ≤ 5.

**Figure 14.** The profile of the combination of bright-dark soliton solutions (55).

Figure 15: The numerical simulations of the solutions (55) 3D and 2D (with *t* = <sup>1</sup> 2 ) with the parameter values *a*<sup>1</sup> = 1, *a*<sup>2</sup> = 1, *b* = −16, *σ* = 2, *α* = 2, *κ* = 2, *w* = 2, *λ* = 2, *μ* = 2, *c* = 10, *v* = −9, *c*<sup>1</sup> = 0, −5 ≤ *x*, *t* ≤ 5.

**Figure 15.** The profile of the combination of bright-dark soliton solutions (55).

Let us now explain the effect of multiplicative white noise in the obtained solutions as follows:

In Figures 1, 4, 7, 10 and 13 when the noise *σ* = 0, we note that the surface is less planer. But in Figures 2, 3, 5, 6, 8, 9, 11 and 12 when the noise *σ* increases (*σ* = 1, 2, 4), we note that the surface becomes more planer after small transit behaviors. This means the multiplicative noise effects on the solutions and it makes the solutions stable.

#### **8. Conclusions**

In this article, we have obtained the solutions of the stochastic FLE in the presence of multiplicative white noise in the Itô sense. The modified simple equation method, the sine-cosine method, the Jacobi-elliptic function expansion method and the ansatze method are applied. Dark solitons, bright solitons, singular solitons, combo dark-bright solitons, combo bright-dark solitons, as well as Jacobi-elliptic solutions are given. Without noise (*σ* = 0) the authors [1,2,37] studied a number of methods to get the exact solutions of FL equation while the stochastic FL Equation (1) is not yet studied. So, on comparing our stochastic solutions (*σ* = 0) obtained in our present article with the non- stochastic solutions (*σ* = 0) obtained in [1,2,37] we deduce that the stochastic solutions are more general than the non-stochastic solutions. Finally, in future, this work will be extended in birefringent fibers, in fiber Bragg gratings and in magneto-optic waveguides. Also, we will study the stochastic FL Equation (1) with variable coefficients [37] when *σ* = 0, to get stochastic solutions.

**Author Contributions:** Conceptualization, E.M.E.Z. and M.E.-S.; methodology, M.E.-S. and M.E.-H.; software, M.E.-S.; writing—original draft preparation, M.E.-S. and E.M.E.Z.; writing—review and editing, M.E.M.A. and M.E.-H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** All data generated or analyzed during this study are included in this manuscript.

**Acknowledgments:** The authors thank the anonymous referees whose comments helped to improve the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Evaluation of Color Anomaly Detection in Multispectral Images for Synthetic Aperture Sensing**

**Francis Seits, Indrajit Kurmi and Oliver Bimber \***

Institute of Computer Graphics, Johannes Kepler University Linz, 4040 Linz, Austria

**\*** Correspondence: oliver.bimber@jku.at; Tel.: +43-732-2468-6631

**Abstract:** In this article, we evaluate unsupervised anomaly detection methods in multispectral images obtained with a wavelength-independent synthetic aperture sensing technique called Airborne Optical Sectioning (AOS). With a focus on search and rescue missions that apply drones to locate missing or injured persons in dense forest and require real-time operation, we evaluate the runtime vs. quality of these methods. Furthermore, we show that color anomaly detection methods that normally operate in the visual range always benefit from an additional far infrared (thermal) channel. We also show that, even without additional thermal bands, the choice of color space in the visual range already has an impact on the detection results. Color spaces such as HSV and HLS have the potential to outperform the widely used RGB color space, especially when color anomaly detection is used for forest-like environments.

**Keywords:** multispectral; image processing; anomaly detection; search and rescue; unmanned aerial vehicles; airborne optical sectioning

#### **1. Introduction**

Color anomaly detection methods identify pixel regions in multispectral images that have a low probability of occurring in the background landscape and are therefore considered to be outliers. Such techniques are used in remote sensing applications for agriculture, wildlife observation, surveillance, or search and rescue. Occlusion caused by vegetation, however, remains a major challenge.

Airborne Optical Sectioning (AOS) [1–13] is a synthetic aperture sensing technique that computationally removes occlusion in real-time by registering and integrating multiple images captured within a large synthetic aperture area above the forest (cf. Figure 1). With the resulting shallow-depth-of-field integral images, it becomes possible to locate targets (e.g., people, animals, vehicles, wildfires, etc.) that are otherwise hidden under the forest canopy. Image pixels that correspond to the same target on the synthetic focal plane (i.e., the forest ground) are computationally aligned and enhanced, while occluders above the focal plane (i.e., trees) are suppressed in strong defocus. AOS is real-time and wavelength-independent (i.e., it can be applied to images in all spectral bands), which is beneficial for many areas of application. Thus far, AOS has been applied to the visible [1,11] and the far-infrared (thermal) spectrum [4] for various applications, such as archeology [1,2], wildlife observation [5], and search and rescue [8,9]. By employing a randomly distributed statistical model [3,10,12], the limits of AOS and its efficacy with respect to its optimal sampling parameters can be explained. Common image processing tasks, such as classification with deep neural networks [8,9] or color anomaly detection, [11] are proven to perform significantly better when applied to AOS integral images compared with conventional aerial images. We also demonstrated the real-time capability of AOS by deploying it on a fully autonomous and classification-driven adaptive search and rescue drone [9]. In [11,13], we presented the first solutions to tracking moving people through densely occluding foliage.

**Citation:** Seits, F.; Kurmi, I.; Bimber, O. Evaluation of Color Anomaly Detection in Multispectral Images for Synthetic Aperture Sensing. *Eng* **2022**, *3*, 541–553. https://doi.org/ 10.3390/eng3040038

Academic Editor: Antonio Gil Bravo

Received: 3 November 2022 Accepted: 25 November 2022 Published: 29 November 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Figure 1.** Airborne optical sectioning (AOS) is a synthetic aperture sensing technique that computationally combines multiple aerial images captured within a synthetic aperture area (**a**) to an integral image, which enhances targets on the synthetic focal plane while suppressing occluders above it. Right: People covered by forest canopy. Single aerial image (thermal channel) that suffers from strong occlusion (**b**), and corresponding integral image of the same environment with occlusion removed (**c**).

Anomaly detection methods for wilderness search and rescue have been evaluated earlier [14], and bimodal systems using a composition of visible and thermal information were already used to improve detection rates of machine learning algorithms [15,16]. However, none of the previous work considered occlusion.

With AOS, we are able to combine multispectral recordings into a single integral image. Our previous work has shown that image processing tasks, such as person classification with deep neural networks [8–10], perform significantly better on integral images when compared to single images. These classifiers are based on supervised architectures, which have the disadvantage that training data must be collected and labeled in a time-consuming manner and that the trained neural networks do not generalize well into other domains. It was also shown in [11] that the image integration process of AOS decreases variance and covariance, which allows better separation of target and background pixels when applying the Reed–Xiaoli (RX) unsupervised anomaly detection [17].

In this article, we evaluate several common unsupervised anomaly detection methods being applied to multispectral integral images that are captured from a drone when flying over open and occluded (forest) landscapes. We show that their performance can significantly be improved by the right combination of spectral bands and choice of color space input format. Especially for forest-like environments, detection rates of occluded people can be consistently increased if visible and thermal bands are combined and if HSV or HLS color spaces are used for the visible bands instead of common RGB. Furthermore, we also evaluate the runtime behavior of these methods when considered for time-critical applications, such as search and rescue.

#### **2. Materials and Methods**

For our evaluation, we applied the dataset from [8], which was used to prove that integral images improve people classification under occluded conditions. It consists of RGB and thermal images (pairwise simultaneously) captured with a drone prototype over multiple forest types (broadleaf, conifer, mixed) and open landscapes, as shown in Figure 2. In all images, targets (persons laying on the ground) are manually labeled. Additional telemetry data (GPS and IMU sensor values) of the drone during capturing are also provided for each image.

(**b**) Open Landscapes

**Figure 2.** Our evaluation dataset consists of several forest (**a**) and open (**b**) landscape images captured with a drone from an altitude of about 35m AGL. Each scenery (F0, F1, F5, O1, O3, O5) contains about 20 consecutive single images taken in the visible (RGB) and thermal spectrum, which are combined into integral images. Rectangles indicate manually labeled persons lying on the ground.

While the visible bands were converted from RGB to other color spaces (HLS, HSV, LAB, LUV, XYZ, and YUV), the thermal data were optionally added as a fourth (alpha) channel, resulting in additional input options (RGB-T, HLS-T, HSV-T, LAB-T, LUV-T, XYZ-T, and YUV-T).

All images had a resolution of 512x512 pixels, so the input dimensions where either (512, 512, 3) or (512, 512, 4). Methods that do not require spatial information used flattened images with (262144, 3) or (262144, 4) dimensions.

The publicly available C/C++ implementation of AOS Source Code: https://github. com/JKU-ICG/AOS (accessed on 28 November 2022) was used to compute integral images from single images.

#### *2.1. Color Anomaly Detectors*

Unsupervised color anomaly detectors have been widely used in the past [17–22], with the Reed–Xiaoli (RX) detector [17] being commonly considered as a benchmark. Several variations of RX exist, where the standard implementation calculates global background statistics (over the entire image) and then compares individual pixels based on the Mahalanobis distance. In the further course of this article, we will refer to this particular RX detector as Reed–Xiaoli Global (RXG).

The following briefly summarizes the considered color anomaly detectors, while details can be found through the provided references:

The Reed–Xiaoli Global (RXG) detector [17] computes a *Kn*×*<sup>n</sup>* covariance matrix of the image, where *n* is the number of input channels (e.g., for RGB, *n* = 3 and for RGB-T, *n* = 4). The pixel under test is the *n*-dimensional vector *r*, and the mean is given by the *n*-dimensional vector *μ*:

$$
\mu\_{RXG}(r) = (r - \mu)^T K\_{n \times n}^{-1}(r - \mu).
$$

The Reed–Xiaoli Modified (RXM) detector [18] is a variation of RXG, where an additional constant *<sup>κ</sup>* <sup>=</sup> ||*<sup>r</sup>* <sup>−</sup> *<sup>μ</sup>*||−<sup>1</sup> is used for normalization:

$$
\mathfrak{a}\_{\mathbb{R}X\mathcal{M}}(r) = \kappa \cdot \mathfrak{a}\_{\mathbb{R}X\mathcal{G}}(r) = \left(\frac{r-\mu}{||r-\mu||}\right)^{T} \mathcal{K}\_{n\times n}^{-1}(r-\mu).
$$

The Reed–Xiaoli Local (RXL) detector computes covariance and mean over smaller local areas and, therefore, does not use global background statistics. The areas are defined by an inner window (*guard*\_*win*) and an outer window (*bg*\_*win*). The mean *μ* and covariance *K* are calculated based on the outer window but excludes the inner window. Window sizes were chosen to be *guard*\_*win* = 33 and *bg*\_*win* = 55, based on the projected pixel sizes of the targets in the forest landscape.

The principal component analysis (PCA) [19] uses singular value decomposition for a linear dimensionality reduction. The covariance matrix of the image is decomposed into eigenvectors and their corresponding eigenvalues. A low-dimensional hyperplane is constructed by selected (*n*\_*components*) eigenvectors. Outlier scores for each sample are then obtained by their euclidean distance to the constructed hyperplane. The number of eigenvectors to use was chosen to be *n*\_*components* = *n*, where *n* is the number of input channels (e.g., for RGB, *n* = 3 and for RGB-T, *n* = 4).

The Gaussian mixture model (GMM) [20] is a clustering approach, where multiple Gaussian distributions are used to characterize the data. The data are fit to each of the single Gaussians (*n*\_*components*), which are considered as a representation of clusters. For each sample, the algorithm calculates the probability of belonging to each cluster, where low probabilities are an indication of being an anomaly. The number of Gaussians to use was chosen to be *n*\_*components* = 2.

The cluster based anomaly detection (CBAD) [21] estimates background statistics over clusters instead of sliding windows. The image background is partitioned (using any clustering algorithm) into clusters (*n*\_*cluster*), where each cluster can be modeled as a Gaussian distribution. Similar to GMM, anomalies have values that deviate significantly from the cluster distributions. Samples are each assigned to the nearest background cluster, becoming an anomaly if their value deviates farther from the mean than background pixel values in that cluster. The number of clusters to use was chosen to be *n*\_*cluster* = 2.

The local outlier factor (LOF) [22] uses a distance metric (e.g., Minkowski distance) to determine the distances between neighboring (*n*\_*neighbors*) data points. Based on the inverse of those average distances, the local density is calculated. This is then compared to the local densities of their surrounding neighborhood. Samples that have significantly lower densities than their neighbors are considered isolated and, therefore, become outliers. The number of neighbors to use was chosen to be *n*\_*neighbors* = 200.

#### *2.2. Evaluation*

The evaluation of the methods summarized above was carried out on a consumer PC (Intel Core i9-11900H @ 2.50GHz) for the landscapes shown in Figure 2.

Precision (Equation (1)) vs. recall (Equation (2)) was used as metrics for performance comparisons.

The task can be formulated as a binary classification problem, where positive predictions are considered anomalous pixels. The data we want to classify (image pixels) is highly unbalanced, as most of the pixels are considered as background (majority class) and only some of the pixels are considered anomalies (minority class).

The true positive (TP) pixels are determined by checking whether they lie within one of the labeled rectangles, as shown in Figure 2. Pixels detected outside these rectangles are considered false positives (FP) and pixels inside the rectangle but not classified anomalously are considered false negatives (FN). Since the dataset only provides rectangles for labels and not perfect masks around the persons, the recall results are biased (in general, not as good as expected). As we are mainly interested in the performance difference between individual methods and the errors introduced are always constant (rectangle area—real person mask), the conclusions drawn from the results should be the same, even if perfect masks were used instead.

The precision (Equation (1)) quantifies the number of correct positive predictions made, and recall (Equation (2)) quantifies the number of correct positive predictions made out of all positive predictions that could have been made. :

$$Precision = \frac{TP}{TP + FP'} \tag{1}$$

$$Recall = \frac{TP}{FN + TP}.\tag{2}$$

Precision and recall both focus on the minority class (anomalous pixels) and are therefore less concerned with the majority class (background pixels), which is important for our unbalanced dataset.

Since the anomaly detection methods provide probabilistic scores on the likelihood of a pixel being considered anomalous, a threshold value must be chosen to obtain a final binary result.

The precision–recall curve (PRC) in Figure 3 shows the relationship between precision and recall for every possible threshold value that could be chosen. Thus, a method performing well would have high precision and high recall over different threshold values. We use the area under the precision–recall curve (AUPRC), which is simply the integral of the PRC, as the final evaluation metric.

**Figure 3.** The area under the precision–recall curve (AUPRC) is used as a metric for comparing the performance of the evaluated anomaly detection methods. We consider true positives (TP), false positives (FP), and false negatives (FN) pixels for each image and calculate precision and recall. The example above illustrates precision–recall curves of all landscapes for RXG and with RGB-T input.

The AUPRC metric provides comparable results on the overall performance of a method but is not well suited when it comes to finding the best threshold for a single image. To obtain the best threshold value for a single image, we use the F*β*-score (Equation (3)), which is also calculated from precision and recall:

$$F\_{\beta} = \left(1 + \beta^2\right) \cdot \frac{Precision \cdot Recall}{\left(\beta^2 \cdot Precision\right) + Recall} \tag{3}$$

where *β* is used as a weighting factor that can be chosen such that recall is considered *β*-times more important than precision.

The balanced F1-score is the harmonic mean of precision and recall and is widely used. However, as we care more about minimizing false positives than minimizing false negatives, we would select a *β* < 1. A grid search of *β* values has given the best results for *β* = <sup>1</sup> <sup>2</sup> . With this setting, precision is weighted more heavily than recall. The *F<sup>β</sup>* metric is only used to threshold the image scores for comparison purposes, as shown in Figure 6.

#### **3. Results**

Figure 4 shows the AUPRC values across different color spaces and methods. The methods are evaluated on each color space, once with three channels (visible spectrum only) and once with four channels (visible and thermal spectrum). The results of the forest landscape are average values over F0, F1 and F5, and the results of the open landscape are average values over O1, O3 and O5.

As expected (and as we have also seen in Figure 3), the overall AUPRC of the open landscapes is much higher than the AUPRC values of the more challenging forest landscapes. The reason is an occlusion in the presence of forests.

The AUPRC values of the four-channel (color + thermal) and three-channel (color only) inputs are overlayed in the same bar. The slightly lighter colored four-channel results are always higher than the three-channel results—regardless of the method or the color space used. However, the difference is more pronounced for the forest landscapes than for the open landscapes. This shows that regardless of the scenery and regardless of the method and the color space used, the additional thermal information always improves the performance of anomaly detection.

With a look at the AUPRC values in the forest landscapes, we can observe that RXL gives the overall best results and outperforms all other methods. Utilizing the additional thermal information gives, in this case, even a 2× gain. This can also be observed visually in the anomaly detection scores shown in Figure 6, where FP's detections highly decrease and TP's detections highly increase if the thermal channel is added (e.g., F1, in the visible spectral band, many background pixels are considered anomalous, with the additional thermal information those misclassified pixels are eliminated).

Looking at the AUPRC values in the open landscapes, we can observe that the difference between the methods is not as pronounced as in the forest landscapes. An obvious outlier, however, seems to be LOF, which nevertheless performs very well (second best) in the forest landscapes. This can be explained by the fact that hyper-parameters of the methods were specifically chosen for the forest landscape. In the case of LOF, the *n*\_*neighbors* parameter was set to be 200, which seems suboptimal for the open landscapes. The same holds for RXL (window sizes), CBAD (number of clusters), GMM (number of components) and PCA (number of components). All other methods do not require hyper-parametrization.

Another observation that can be made is that some color spaces consistently give better results than others. In the forest landscapes, HSV(-T) usually gives the best results, regardless of the methods being used. In the open landscapes, it is not as clear which color space performs best, but HSV(-T) still gives overall good results. In general, and especially for RXM, the improvements achieved by choosing HSV(-T) over other color spaces are clearly noticeable.

**Figure 4.** Results of area under the precision–recall curve (AUPRC) values for multiple color spaces and color anomaly detection methods. The results of the forest landscape are average values over F0, F1, and F5, and the results of the open landscape are average values over O1, O3, and O5. The stacked bar charts highlight the improvement gains caused by the additional thermal channel.

The individual results plotted in Figure 4 are also shown in Tables 1 and 2, where the mean values over all color spaces (last row) may give a useful estimate of the method's overall performance. The highest AUPRC value for the forest and open scenery is highlighted in bold.

Since anomaly detection for time-critical applications should deliver reliable results in real-time, we have also measured their runtimes, as shown in Table 3. The best-performing methods on the forest landscapes in terms of AUPRC values are RXL and LOF. In terms of runtime, both are found to be very slow, as they consume 20 to 35 s for computations, where all other algorithms provide anomaly scores in under a second (cf. Figure 5).

**Figure 5.** Performance in AUPRC (left bars) vs. runtime in *ms* (right bars): Color anomaly detection methods that produce results in less than a second. Reed–Xiaoli local (RXL) and local outlier factor (LOF) performed well but needed more than 20 seconds and are, therefore, not practicable for applications with real-time demands.

**Table 1.** Area under the precision–recall curve (AUPRC) values for each color space and color anomaly detection method. The scores are obtained from integral images and are averaged over forest landscapes. The last row is the mean AUPRC value over all color spaces. The best performance is highlighted in bold.


**Table 2.** Area under the precision–recall curve (AUPRC) values for each color space and anomaly detection method. The scores are obtained from integral images and are averaged over open landscapes. The last row is the mean AUPRC value over all color spaces. Best performance is highlighted in bold.


**CBAD GMM LOF PCA RXG RXL RXM HLS** 887 219 18,440 98 39 36,647 28 **HSV** 883 225 18,094 102 40 36,346 **27 LAB** 877 219 19,833 99 36 36,495 29 **LUV** 888 212 19,975 96 41 36,166 29 **RGB** 925 216 19,367 96 40 35,732 29 **XYZ** 872 224 19,107 100 40 36,367 **27 YUV** 874 228 20,485 100 42 36,409 **27** Runtime 887 221 19,329 99 40 36,309 28 **CBAD GMM LOF PCA RXG RXL RXM HLS-T** 878 243 28,054 104 43 36,002 30 **HSV-T** 882 237 28,235 107 40 35,801 30 **LAB-T** 879 230 28,005 108 32 35,876 31 **LUV-T** 893 229 27,506 105 45 36,059 32 **RGB-T** 904 230 27,323 98 37 35,618 32 **XYZ-T** 880 241 24,395 108 43 36,047 29 **YUV-T** 877 238 27,146 107 40 36,180 29

**Table 3.** Runtime for each input format and method in milliseconds. The input format (color spaces) does not have an influence on the runtime, but addition channels (thermal) may increase the runtime for some algorithms. The last row is the mean runtime of an algorithm. Best performance is highlighted in bold.

#### **4. Discussion**

The AUPRC results in Figure 4 show that all color anomaly detection methods benefit from additional thermal information, but especially in combination with the forest landscapes.

Runtime 885 236 27,238 105 40 35,940 31

In challenging environments, where the distribution of colors has a much higher variance (e.g., F1 in Figure 6, due to bright sunlight), the additional thermal information improves results significantly. If the temperature difference between targets and the surrounding is large enough, the thermal spectral band may add spatial information (e.g., distinct clusters of persons), which is beneficial for methods that calculate results based on locality properties (e.g., RXL, LOF).

In forest-like environments, the RXL anomaly detector performs best regardless of the input color space. This could be explained by the specific characteristics of an integral image. In the case of occlusion, the integration process produces highly blurred images caused by defocused occluders (forest canopy) above the ground, which results in a much more uniformly distributed background. Since target pixels on the ground stay in focus, anomaly detection methods such as RXL, which calculate background statistics on a smaller window around the target, benefit from the uniform distributed (local) background. The same is true for LOF, where the local density in the blurred background regions is much higher than the local density in the focused target region, resulting in overall better outlier detection rates. Since most objects in open landscapes are located near the focal plane (i.e., at nearly the same altitude above the ground), there is no out-of-focus effect caused by the integration process. Thus, these methods do not produce similarly good results for open landscapes.

(**a**) Forest Landscapes (**b**) Open Landscapes

**Figure 6.** Color anomaly detection scores for forest (**a**) and open (**b**) landscapes, comparing the overall good performing HSV(-T) inputs. The first rows per scenery show anomaly scores of the best (RXL) algorithm without considering runtime and the best (RXM) and second-best (CBAD) method when considering runtime. The second rows per scenery are the anomaly scores after thresholding.

For the forest landscapes, the HSV(-T) and HSL(-T) color spaces consistently give better results than others. The color spaces HSV (hue, saturation, value) and HSL (hue, saturation, lightness) are both based on cylindrical color space geometries and differ mainly in their last dimension (brightness/lightness). The first two dimensions (hue, saturation) can be considered more important when distinguishing colors, as the last dimension only describes the value (brightness) or lightness of a color. We assume that the more uniform background resulting from the integration process also has a positive effect on the distance metric calculations when those two color spaces are used, especially if the background mainly consists of a very similar color tone. This is again more pronounced for the forest landscapes than for the open landscapes.

Although the AUPRC results obtained from RXL and LOF are best for forest landscapes, the high runtime indicates that these methods are impractical for real-time applications. A trade-off must be made between good anomaly detection results and fast runtime; therefore, we consider the top-performing methods that provide reliable results within milliseconds further.

Based on the AUPRC and runtime results shown in Figure 5, one could suggest that the RXM method may be used. The AUPRC results combined with HSV-T are the best among methods that run under one second, regardless of the landscape. Since this method does not require a-priory settings to be chosen (only the final thresholding value) and the runtime is one of the fastest, it would be well suited for usage in forests and open landscapes. The second-best algorithm based on the AUPRC values would be CBAD, with the disadvantage that it requires a hyper-parameter setting and does not generalize well for open landscapes.

#### **5. Conclusions**

In this article, we have shown that the performance of unsupervised color anomaly detection methods applied to multispectral integral images can be further improved by an additional thermal channel. Each of the evaluated methods performs significantly better when thermal information is utilized in addition, regardless of the landscape (forest or open). Another finding is that even without the additional thermal band, the choice of input color space (for the visible channels) already has an influence on the results. Color spaces such as HSV and HLS can outperform the widely used RGB color space, especially in forest-like landscapes.

These findings might guard decisions on the choice of color anomaly detection method, input format, and applied spectral band, depending on individual use cases. Occlusion cause by vegetation, such as forests, remains challenging for many of them. In the future, we will investigate anomalies caused by motion in the context of synthetic aperture sensing. In combination with color and thermal anomaly detection, motion anomaly detection has the potential to further improve detection results for moving targets, such as people, animals, or vehicles.

**Author Contributions:** Conceptualization, O.B. and F.S.; methodology, F.S.; software, F.S. and I.K.; validation, F.S., I.K. and O.B.; formal analysis, F.S.; investigation, F.S.; resources, I.K.; data curation, I.K.; writing—original draft preparation, F.S. and O.B.; writing—review and editing, F.S. and O.B.; visualization, F.S.; supervision, O.B.; project administration, O.B.; funding acquisition, O.B. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Austrian Science Fund (FWF) under grant number P32185- NBL and by the State of Upper Austria and the Austrian Federal Ministry of Education, Science and Research via the LIT–Linz Institute of Technology under grant number LIT-2019-8-SEE114.

**Data Availability Statement:** The data and source code used in the experiments can be downloaded from https://doi.org/10.5281/zenodo.3894773 and https://github.com/JKU-ICG/AOS (accessed on 28 November 2022).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


### *Article* **Infrared Spectroscopy for the Quality Control of a Granular Tebuthiuron Formulation**

**Joel B. Johnson 1,\*, Hugh Farquhar 2, Mansel Ismay 3,† and Mani Naiker <sup>1</sup>**

<sup>2</sup> Cirrus Ag, 171 Alexandra St, Kawana, Rockhampton, QLD 4701, Australia

<sup>3</sup> Independent Researcher, Gladstone, QLD 4680, Australia


**Abstract:** Tebuthiuron is a selective herbicide for woody species and is commonly manufactured and sold as a granular formulation. This project investigated the use of infrared spectroscopy for the quality analysis of tebuthiuron granules, specifically the prediction of moisture content and tebuthiuron content. A comparison of different methods showed that near-infrared spectroscopy showed better results than mid-infrared spectroscopy, while a handheld NIR instrument (MicroNIR) showed slightly improved results over a benchtop NIR instrument (Antaris II FT-NIR Analyzer). The best-performing models gave an R2 CV of 0.92 and RMSECV of 0.83% *w*/*w* for moisture content, and R2 CV of 0.50 and RMSECV of 7.5 mg/g for tebuthiuron content. This analytical technique could be used to optimise the manufacturing process and reduce the costs of post-manufacturing quality assurance.

**Keywords:** process analytical technology; quality assurance; non-destructive assessment; NIRS

#### **1. Introduction**

Tebuthiuron is a thiadiazolyl urea herbicide (Figure 1) primarily used for the control of woody plants. Application is typically via pellet-type (granular) formulations containing tebuthiuron (200–400 mg/g), which may be applied from the ground (either by hand or mechanically), or aerially dispersed if a large area is to be treated. As tebuthiuron is highly water-soluble [1], it leaches from the granules into the soil [2], where it is subsequently absorbed by the roots and translocated to the leaf tissue [3]. Its mode of action is through inhibition of Photosystem II, thus preventing photosynthesis in the affected plant [4]. The degradation and persistence of tebuthiuron is still an area under investigation, with studies reporting half-lives between 20 days [5] and 16–22 days [6], to as high as one year [7], 12.9 months [8], 'considerably greater' than 15 months [9] and even 2–7 years [10]. du Toit and Sekwadi [11] reported that tebuthiuron residue remained active in soil for 8 years after application.

iations.

eng3040041

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Citation:** Johnson, J.B.; Farquhar, H.; Ismay, M.; Naiker, M. Infrared Spectroscopy for the Quality Control of a Granular Tebuthiuron Formulation. *Eng* **2022**, *3*, 596–619. https://doi.org/10.3390/

Academic Editor: Antonio Gil Bravo Received: 14 November 2022 Accepted: 30 November 2022 Published: 2 December 2022 **Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil-

**Figure 1.** The chemical structure of tebuthuiron. Retrieved from http://www.chemspider.com/ (accessed on 28 September 2022) under Creative Commons 4.0 license.

<sup>1</sup> School of Health, Medical & Applied Sciences, Central Queensland University, Bruce Highway, Rockhampton, QLD 4701, Australia

The structure of tebuthiuron includes two amide bonds (sharing the one carbonyl group) and a unique aromatic thiadiazolyl group (Figure 1), which should make it wellsuited to detection by non-destructive analytical techniques such as infrared spectroscopy. Both of these chemical moieties would be expected to show distinct spectral characteristics in the mid-infrared (MIR) and near-infrared (NIR) regions. Additionally, the high concentration of tebuthiuron in most commercial tebuthiuron products (200–400 mg/g), should make it relatively simple to detect using MIR/NIR spectroscopy. The benefits of infrared spectroscopy over traditional analytical techniques include its speed (real-time), no ongoing costs related to traditional analysis costs, non-destructiveness and versatility (many units are portable; some are even handheld).

The previous literature has documented the use of NIR spectroscopy for the prediction of pesticide concentrations in liquid solutions [12], although this particular study did not analyse pesticides present in granular/powder form. Other authors have used MIR spectroscopy for the production quality control of numerous pesticides in liquid and solid forms [13]. Consequently, there is increasing interest in the use of infrared spectroscopy as a process analytical technology (PAT) tool [14]. However, no previous studies were found using infrared spectroscopy for the analysis of tebuthiuron content in any sample matrices.

Consequently, the aim of this work was to investigate the prospect of using infrared spectroscopy for a rapid, non-invasive method for the assessment of tebuthiuron and moisture, another important analyte in the manufacturing quality assurance process. This included a comparison of the performance of different infrared spectrophotometers for this purpose.

#### **2. Materials and Methods**

#### *2.1. Sample Description*

Sixty-eight (68) granular tebuthiuron samples (Regain™ brand) were manufactured by Cirrus Ag (North Rockhampton, Australia) over a period of approximately 10 months (April 2021–February 2022). These were each collected at specific time points as the final product came off the manufacturing line. The samples were stored in an air-conditioned room (approx. 20 ◦C) after receipt at the laboratory. Additionally, five samples of tebuthiuron powder (>95% purity) were included for comparative purposes, although they were not included in the quantitative modelling.

Two types of Regain formulation were produced by Cirrus Ag: one containing 200 mg/g of the active ingredient (i.e., tebuthiuron) and the other containing 400 mg/g. Throughout the manuscript, these are abbreviated at Regain200 and Regain400, respectively. The exact composition of the Regain granules is a trade secret, hence cannot be disclosed in this paper.

#### *2.2. Sample Preparation*

To ensure representative sampling of the granules upon receipt at the laboratory, each sample bag was thoroughly shaken and pellets were subsampled from at least 6 different locations throughout the bag. Approximately half of the sample (20–30 g) was subsampled, with the pellets then ground to a fine powder (Breville Coffee & Spice Grinder; Botany, NSW, Australia). When weighing out the required mass of powder for each extraction, care was taken to ensure that powder from at least 3 different locations within the sample subset was included.

#### *2.3. Analysis of Moisture Content*

The moisture content was measured on the intact (unground) Regain samples. Approximately 3 g of each sample was weighed into a pre-weighed aluminium foil tray, before being dried in a laboratory oven (Memmert 400; Buechenbach, Germany) at 110 ◦C overnight (16 h) until reaching a constant mass. After cooling to room temperature, the samples were reweighed, with the moisture content was determined as the loss in mass

upon drying. Only one replicate was performed for each sample; however, triplicate analyses were performed on one sample to assess the reproducibility of the method.

To provide an extra data point for the NIR prediction of moisture content, the dried granules from all 68 samples were combined and mixed thoroughly. This aggregate granule sample was taken to have a moisture content of 0%, as it had been already dried at 110 ◦C for 16 hrs and did not lose any mass upon further drying.

#### *2.4. Tebuthiuron Extraction Protocol*

The extraction method was adapted from Lydon et al. [15] and validated by our laboratory. Approximately, 30 mg of the finely ground Regain powder was weighed into a 50 mL centrifuge tube. The total mass of the tube + sample was then recorded, before 20 mL of 90% *v*/*v* methanol was added using a calibrated bottle-top dispenser. The tube + sample + methanol was then re-weighed, with the determined mass of methanol converted to volume using the density of 90% methanol (0.823 ± 0.001 g/mL; *n* = 6 independent measurements). This allowed for the added volume of methanol to be determined with a much higher level of accuracy than that which could be obtained using a calibrated pipette.

The powder was extracted using an end-over-end shaker (Ratek RM-4; Boronia, VIC, Australia) operating at 50 rpm for 30 min. The extract was then centrifuged (1000 rcf for 5 min) and the supernatant collected for direct HPLC analysis (no dilution required). All samples were extracted and analysed in triplicate.

#### *2.5. Tebuthiuron Analysis by HPLC*

The tebuthiuron content of the methanol extracts was determined by high-performance liquid chromatography (HPLC). The HPLC analysis method used was adapted from Ferracini et al. [16]. Tebuthiuron was quantified on an Agilent 1100 HPLC system, comprising a G1313A autosampler, G1322A vacuum degasser, G1311A quaternary pump and G1315B diode array detector. A reversed-phase C18 column was used (Agilent Eclipse XDB-C18; 250 × 4.6 mm; 5 μm pore size; Agilent Technologies, Santa Clara, CA, USA) along with a C18 guard column (Agilent Eclipse XDB-C18; 12.5 × 4.6 mm; 5 μm pore size). The injection volume was 5 μL and the detection wavelength was 254 nm. The elution method was an isocratic mixture of 50% methanol/50% water, at a flow rate of 1 mL min−1. The total run time was 15 min.

The tebuthiuron concentration of the samples was determined using an external calibration of analytical-grade tebuthiuron standard (Sigma-Aldrich Australia; North Ryde. NSW, Australia), ranging between 100–1000 mg L−1. Results were expressed as mg/g, on an as-is basis.

Figure 2 shows a typical chromatogram obtained from the extract of a Regain400 sample, demonstrating the absence of any interfering compounds at the selected wavelength.

**Figure 2.** A typical HPLC chromatogram of a Regain extract, with the location of the tebuthiuron peak indicated.

There was no clear consistency in the literature for the λmax or detection wavelength for tebuthiuron. Weber [17] reported λmax values of 252 nm in neutral solution and 261 nm in acidic conditions for tebuthiuron. Lourencetti et al. [18] found a λmax of 255 nm, while more recently, Ferreira et al. [19] reported the λmax of tebuthiuron to be 253 nm. Similarly, Lydon et al. [15] used a wavelength of 254 nm for the quantification of tebuthiuron via HPLC, while other authors have used 245 nm [20] and 247 nm [16,18].

Consequently, preliminary investigations were conducted to determine the optimum detection wavelength to use for HPLC analysis, through HPLC-DAD analysis and scanning tebuthiuron solutions using a Thermo Scientific Genesys 10S UV-Vis spectrophotometer (Sydney, Australia).

#### *2.6. Validation of the HPLC Method*

To assess the linearity of the HPLC method, tebuthiuron standards were prepared between 0.1–1000 mg L−<sup>1</sup> and analysed using HPLC.

To assess the intra-day precision of the method, six replicate injections of 100 mg L−<sup>1</sup> tebuthiuron standard were analysed on the same day. Similarly, the inter-day precision was assessed by injecting a sample of 100 mg L−<sup>1</sup> tebuthiuron standard over six different days and comparing the peak areas.

To assess the stability of the methanolic tebuthiuron extracts, one Regain extract was analysed immediately following extraction and re-analysed after it had been stored for 8 days at room temperature.

The reproducibility of the finalised extraction method was determined by extracting and analysing 20 Regain samples each in triplicate, with the %CV calculated for each sample. In addition, the reproducibility of the extraction and HPLC method was assessed by performing 7 replicate extractions on one sample of homogenised Regain400 powder.

#### *2.7. Assessment of Sample Variation*

Based on preliminary results and observations during the manufacturing process, it was thought that there could be a high level of variation in tebuthiuron content between different portions of each Regain batch. To test this hypothesis, ten samples were randomly selected from different parts of one Regain400 sample (see Figure 3). These were then ground, extracted and analysed separately (each in triplicate).

**Figure 3.** Sampling of the ten spatial replicates of the Regain400 sample. The red circles show the sampled areas.

#### *2.8. Collection of FTIR Spectra*

Mid-infrared (MIR) spectra were collected from the powdered samples using a Bruker Alpha FTIR (Fourier transform infrared) spectrophotometer (Bruker Optics Gmbh, Ettlingen, Germany) fitted with a platinum diamond attenuated total reflectance (ATR) single reflection module. FTIR spectroscopy requires the samples to be in a powdered form, as it necessitates firm contact between the sample and the ATR platform used to collect the spectra. Consequently, the FTIR spectra could only be collected from the powdered Regain samples, not the whole granular product.

The reflection module was covered with powder (approximately 100–200 mg) and pressure was applied to achieve uniform contact between the ATR interface and powder. Air was used as a reference background; the background measurement was performed every 15 min. Cross-contamination of samples was minimised by cleaning and drying the platform with isopropyl alcohol and laboratory Kimwipes® between samples. Using the OPUS software version 7.5 (Bruker Optics Gmbh, Ettlingen, Germany), the FTIR spectra were recorded between 4000 and 400 cm−<sup>1</sup> as the average of 24 scans at a resolution of 4 cm−1. Three spectra were collected from each sample, repacking the instrument with fresh powder each time.

#### *2.9. Collection of NIR Spectra—Benchtop Instrument*

Near-infrared (NIR) spectra were collected from both the granular and powdered Regain samples using Antaris II FT-NIR Analyzer (Thermo Scientific; Madison, WI, USA). This instrument provides a high level of accuracy and reproducibility, making it highly suitable for method development purposes. Throughout the report, this is referred to as the "benchtop" NIR method.

The instrument was operated in reflectance mode, using the integrating sphere with a rotating sample cup (30 mm diameter). Spectra were collected between 1000–2500 nm (10,000–4000 cm−1), as the mean of 32 scans (resolution of 8 cm−1). The optimised gain was found to be 2×, with an empty attenuator screen. Background (dark) reference measurements were collected every hour. Spectra were collected in triplicate, repacking the sample cup with fresh granules or powder each time. The spectra were exported in \*.csv format, with the mean of the triplicate spectra for each sample used in subsequent data analysis.

#### *2.10. Collection of NIR Spectra—Handheld Instrument*

NIR spectra were also collected from the granular Regain samples using a handheld NIR instrument, in order to determine the typical accuracy that could be obtained using portable NIR instrumentation. Handheld instrumentation would be greatly beneficial in an industrial setting due to its portability and lower cost (less than 1/3 of the benchtop Antaris instrument). Furthermore, instruments such as the MicroNIR may be suitable for installation as in-line sensors in an industrial setting.

A MicroNIR OnSite handheld spectrometer (Viavi; Santa Rosa, CA, USA) was used for this work. Spectra were collected across the full wavelength range of this instrument (908–1676 nm); the integration time was set to 100 ms. Reference dark and light spectra were collected every 10 min. Again, spectra were collected in triplicate and exported in \*.csv format. The mean of the triplicate spectra for each sample was used in subsequent data analysis.

#### *2.11. Independent Test Set—Using Handheld NIR*

The best-performing infrared spectrophotometer was applied to an independent test set (i.e., samples not used in the model calibration). For this, thirteen additional samples (12 of Regain400 and 1 of Regain200) were sourced from Cirrus Ag (Rockhampton, Australia). NIR spectra were collected from the granules using the MicroNIR instrument and predictions made using the optimum model for each analyte.

#### *2.12. Data Analysis*

Chemometric analysis of the infrared spectra was conducted in the Unscrambler X 10.5 software (Camo ASA, Oslo, Norway). A variety of pre-processing methods were trialled, including the use of the standard normal variate (SNV) algorithm and the 1st and 2nd derivatives were calculated using a Savitzky–Golay algorithm with varying numbers of smoothing points. These are abbreviated as number–letter combinations showing the derivative number and number of smoothing points, e.g., 1d5 indicates 1st derivative with 5 smoothing points.

Partial least squares regression (PLSR) was used as the regression method. The maximum number of components considered in each model was set to 7, to reduce the possibility of overfitting. Full cross-validation of the PLSR models was conducted using the leave-one-out method.

To avoid creating a 'two-point' model, only Regain400 samples were included in the models for tebuthiuron content. The spectra and loadings were plotted using R Studio running R 4.2.2 (R Foundation for Statistical Computing, Vienna, Austria) [21].

#### **3. Results and Discussion**

#### *3.1. Validation of the HPLC Method*

Analysis of the tebuthiuron peak using HPLC-DAD showed that the maximum absorbance was located at 254 nm (Figure 4). This was confirmed by subsequent UV spectral scans of pure tebuthiuron standard in 100% methanol, which revealed a λmax of 253.5 nm. Hence, a detection wavelength of 254 nm was chosen for this work, agreeing with Lydon et al. [15].

**Figure 4.** The UV spectra of a Regain extract, showing the λmax at 254 nm.

For the analysis of linearity, the tebuthiuron standards were found to be linear over the range of 0.1–1000 mg L−1, with an R2 value of 0.9999 (Figure 5).

**Figure 5.** Linearity of the tebuthiuron standards.

As can be seen in Table 1, the intra-day precision of the HPLC method was quite high, with a mean relative error (coefficient of variation) of 0.35%. The inter-day precision was slightly poorer than the intra-day precision (Table 1), with a mean coefficient of variation of 0.95%.

**Table 1.** Intra-day and inter-day precision of replicate injections of 100 mg L−<sup>1</sup> tebuthiuron standards analyzed using the HPLC method.


For the assessment of extract stability at room temperature, there was virtually no change in the tebuthiuron concentration (CV = 0.07%), indicating high stability of the tebuthiuron content over the 8 day storage period (Table 2).

**Table 2.** Stability of the Regain methanolic extract after 8 days of storage at room temperature.


Reproducibility of the Extraction and HPLC Method

In order to create accurate prediction models using infrared spectroscopy, it is essential to have accurate analytical protocols for quantifying the analyte in question. In other words, the "reference" values used to calibrate the IR models must be accurate; otherwise, the IR models will be of no use.

For the reproducibility of the finalised extraction method, the mean %CV of the 20 samples extracted and analysed in triplicate was 2.1 ± 1.8% (*n* = 20), indicating an acceptable level of reproducibility.

Additionally, for the seven extractions performed on a single homogenised, powdered sample of Regain400, most of the replicate measurements showed good agreement with one another. One result (Replicate 2) was identified as an outlier and removed from subsequent calculations (Table 3). The mean content of the remaining samples was 401.3 ± 7.0 mg/g tebuthiuron, corresponding to a coefficient of variation of 1.74%.

**Table 3.** Replicate tebuthiuron content measurements performed on replicate extracts from one powdered, homogenised Regain400 sample.

