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Advanced Mathematical Approaches to Engineering and Computational Problems
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Advanced Mathematical Approaches to Engineering and Computational Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (15 August 2023) | Viewed by 28920

Special Issue Editor

Prof. Dr. Junzo Watada

E-Mail Website
Guest Editor
Graduate School of Information, Production and Systems, Waseda University, Kitakyushu 808-0135, Japan
Interests: artificial intelligence; image processing; soft computing, including meta heuristics, fuzzy systems, rough set analysis; model building; optimization; data analytics; big data mining; management engineering; financial engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues

Today, various innovative approaches are being proposed to solve engineering and computational problems from real engineering problems and factorial problems to intelligence methodologies, meta-heuristic methodologies, and deep learning. This Special Issue emphasizes the advanced mathematical, statistical, and computational aspects of such methodologies including, but not limited to:

  • Meta-heuristics methodologies to solve various engineering, computational, and industrial problems;
  • Artificial intelligence methodologies to solve various engineering, computational, and industrial problems;
  • Statistical approaches to solving various engineering, computational, and industrial problems;
  • Deep learning approaches to solve various engineering, computational, and industrial problems;

The problems should include management, marketing, and behavioral problems. We are interested in updated advanced methodologies and new areas of problems.

Prof. Dr. Junzo Watada
Guest Editor

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Keywords

  • mathematics
  • statistics
  • advanced methodologies
  • meta-heuristics
  • artificial intelligence
  • deep learning
  • engineering problems
  • industrial problems
  • financial engineering problems
  • management problems
  • marketing problems
  • behavioral problems

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Published Papers (15 papers)

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Research

30 pages, 19564 KiB  
Article
A Novel Simulation-Based Optimization Method for Autonomous Vehicle Path Tracking with Urban Driving Application
by Yanzhan Chen and Fan Yu
Mathematics 2023, 11(23), 4762; https://doi.org/10.3390/math11234762 - 24 Nov 2023
Cited by 1 | Viewed by 971
Abstract
Autonomous driving technology heavily depends on accurate and smooth path tracking. Facing complex urban driving scenarios, developing a suite of high-performance and robust parameters for controllers becomes imperative. This paper proposes a stochastic simulation-based optimization model for optimizing the Proportional–Integral–Differential (PID) controller parameters, [...] Read more.
Autonomous driving technology heavily depends on accurate and smooth path tracking. Facing complex urban driving scenarios, developing a suite of high-performance and robust parameters for controllers becomes imperative. This paper proposes a stochastic simulation-based optimization model for optimizing the Proportional–Integral–Differential (PID) controller parameters, with tracking accuracy and smoothness as bi-objectives, and solves it using a domination-measure-based efficient global optimization (DMEGO) algorithm. In this model, the tracking accuracy and smoothness are indexed by the normalized dynamic time warping (NDTW) and the mean absolute lateral acceleration (MALA), respectively. In addition, we execute the PID controller in a realistic simulation environment using a CARLA simulator, which consider various city scenes, diverse routes, different vehicle types, road slopes, etc., to provide a comprehensive and reliable evaluation for the designed PID controller. In the DMEGO method, each solution undergoes evaluation using a fixed number of costly simulations. Then, utilizing the solutions and their estimated bi-objective values, two surrogate models for the bi-objectives are constructed using the Gaussian process (GP) model. The preliminary nondominated solutions can be obtained by optimizing the two surrogate models. Finally, a novel performance metric known as the domination measure is employed to evaluate the quality of each solution. This metric is then integrated with the crowding distance to selectively retain a candidate solution exhibiting superior performance and good diversity for the next iteration. In our numerical experiments, we first test the DMEGO algorithm against three other counterparts using a stochastic FON benchmark. The proposed approach is then employed to optimize the PID parameters considering the complexity and uncertainty of urban traffic. The numerical results demonstrate that the nondominated solutions obtained by DMEGO exhibit excellent performance in terms of tracking accuracy and smoothness under limited simulation budgets. Overall, the proposed approach may be a viable tool for solving multi-objective simulation-based optimization problem under uncertainties. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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17 pages, 392 KiB  
Article
Security Quantification for Discrete Event Systems Based on the Worth of States
by Sian Zhou, Jiaxin Yu, Li Yin and Zhiwu Li
Mathematics 2023, 11(17), 3629; https://doi.org/10.3390/math11173629 - 22 Aug 2023
Cited by 1 | Viewed by 942
Abstract
This work addresses the problem of quantifying opacity for discrete event systems. We consider a passive intruder who knows the overall structure of a system but has limited observational capabilities and tries to infer the secret of this system based on the captured [...] Read more.
This work addresses the problem of quantifying opacity for discrete event systems. We consider a passive intruder who knows the overall structure of a system but has limited observational capabilities and tries to infer the secret of this system based on the captured information flow. Researchers have developed various approaches to quantify opacity to compensate for the lack of precision of qualitative opacity in describing the degree of security of a system. Most existing works on quantifying opacity study specified probabilistic problems in the framework of probabilistic systems, where the behaviors or states of a system are classified as secret or non-secret. In this work, we quantify opacity by a state-worth function, which associates each state of a system with the worth it carries. To this end, we present a novel category of opacity, called worthy opacity, characterizing whether the worth of information exposed to the outside world during the system’s evolution is below a threshold. We first provide an online approach for verifying worthy opacity using the notion of a run matrix proposed in this research. Then, we investigate a class of systems satisfying the so-called 1-cycle returned property and present a worthy opacity verification algorithm for this class. Finally, an example in the context of smart buildings is provided. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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20 pages, 10239 KiB  
Article
Realization of Intelligent Observer for Sensorless PMSM Drive Control
by Dwi Sudarno Putra, Seng-Chi Chen, Hoai-Hung Khong and Chin-Feng Chang
Mathematics 2023, 11(5), 1254; https://doi.org/10.3390/math11051254 - 5 Mar 2023
Cited by 2 | Viewed by 1975
Abstract
An observer is a crucial part of the sensorless control of a permanent magnet synchronous motor (PMSM). An observer, based on mathematical equations, depends on information regarding several parameters of the controlled motor. If the motor is replaced, then we need to know [...] Read more.
An observer is a crucial part of the sensorless control of a permanent magnet synchronous motor (PMSM). An observer, based on mathematical equations, depends on information regarding several parameters of the controlled motor. If the motor is replaced, then we need to know the motor parameter values and reset the observer’s parameters. This article discusses an intelligent observer that can be used for several motors with different parameters. The proposed intelligent observer was developed using machine learning methods. This observer’s core algorithm is a modified Jordan neural network. It processes Iα, Iβ, vα, and vβ to produce Sin θ and Cos θ values. It is combined with a phase-locked loop function to generate position and speed feedback information. The offline learning process is carried out using data acquired from the simulations of PMSM motors. This study used five PMSMs with different parameters, three as the learning reference sources and two as testing sources. The proposed intelligent observer was successfully used to control motors with different parameters in both simulation and experimental hardware. The average error in position estimated for the simulation was 0.0078 p.u and the error was 0.0100 p.u for the experimental realization. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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12 pages, 1252 KiB  
Article
The Two Stage Moisture Diffusion Model for Non-Fickian Behaviors of 3D Woven Composite Exposed Based on Time Fractional Diffusion Equation
by Hang Yu, Chenhui Zhu, Lu Yao, Yan Ma, Yang Ni, Shenkai Li, Huan Li, Yang Liu and Yuming Wang
Mathematics 2023, 11(5), 1160; https://doi.org/10.3390/math11051160 - 26 Feb 2023
Cited by 4 | Viewed by 1914
Abstract
The moisture diffusion behaviors of 3D woven composites exhibit non-Fickian properties when they are exposed to a hydrothermal environment. Although some experimental works have been undertaken to investigate this phenomenon, very few mathematical works on non-Fickian moisture diffusion predictions of 3D woven composites [...] Read more.
The moisture diffusion behaviors of 3D woven composites exhibit non-Fickian properties when they are exposed to a hydrothermal environment. Although some experimental works have been undertaken to investigate this phenomenon, very few mathematical works on non-Fickian moisture diffusion predictions of 3D woven composites are available in the literature. To capture the non-Fickian behavior of moisture diffusion in 3D woven composites, this study first utilized a time fractional diffusion equation to derive the percentage of moisture content of a homogeneous material under hydrothermal conditions. A two-stage moisture diffusion model was subsequently developed based on the moisture diffusion mechanics of both neat resin and 3D woven composites, which describes the initial fast diffusion and the long-term slow diffusion stages. Notably, the model incorporated fractional order parameters to account for the nonlinear property of moisture diffusion in composites. Finally, the weight gain curves of neat resin and the 3D woven composite were calculated to verify the fractional diffusion model, and the predicted moisture uptake curves were all in good agreement with the experimental results. It is important to note that when the fractional order parameter α < 1, the initial moisture uptake will become larger with a later slow down process. This phenomenon can better describe non-Fickian behavior caused by initial voids or complicated structures. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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28 pages, 5068 KiB  
Article
Exploration of New Optical Solitons in Magneto-Optical Waveguide with Coupled System of Nonlinear Biswas–Milovic Equation via Kudryashov’s Law Using Extended F-Expansion Method
by Wafaa B. Rabie, Hamdy M. Ahmed and Walid Hamdy
Mathematics 2023, 11(2), 300; https://doi.org/10.3390/math11020300 - 6 Jan 2023
Cited by 13 | Viewed by 1246
Abstract
Optical soliton solutions in a magneto-optical waveguide and other exact solutions are investigated for the coupled system of the nonlinear Biswas–Milovic equation with Kudryashov’s law using the extended F-expansion method. Various types of solutions are extracted, such as dark soliton solutions, singular soliton [...] Read more.
Optical soliton solutions in a magneto-optical waveguide and other exact solutions are investigated for the coupled system of the nonlinear Biswas–Milovic equation with Kudryashov’s law using the extended F-expansion method. Various types of solutions are extracted, such as dark soliton solutions, singular soliton solutions, a dark–singular combo soliton, singular combo soliton solutions, Jacobi elliptic solutions, periodic solutions, combo periodic solutions, hyperbolic solutions, rational solutions, exponential solutions and Weierstrass solutions. The obtained different types of wave solutions help in obtaining nonlinear optical fibers in the future. Furthermore, some selected solutions are described graphically to demonstrate the physical nature of the obtained solutions. The results show that the current method gives effectual and direct mathematical tools for resolving the nonlinear problems in the field of nonlinear wave equations. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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21 pages, 6805 KiB  
Article
A Novel ON-State Resistance Modeling Technique for MOSFET Power Switches
by Ionuț-Constantin Guran, Adriana Florescu and Lucian Andrei Perișoară
Mathematics 2023, 11(1), 72; https://doi.org/10.3390/math11010072 - 25 Dec 2022
Cited by 2 | Viewed by 2653
Abstract
Nowadays, electronic circuits’ time to market is essential, with engineers trying to reduce it as much as possible. Due to this, simulation has become the main testing concept used in the electronics domain. In order to perform the simulation of a circuit, a [...] Read more.
Nowadays, electronic circuits’ time to market is essential, with engineers trying to reduce it as much as possible. Due to this, simulation has become the main testing concept used in the electronics domain. In order to perform the simulation of a circuit, a behavioral model must be created. Metal-Oxide-Semiconductor Field-Effect Transistors (MOSFETs) are semiconductor devices found in a multitude of electronic circuits, and they are also used as power switches in many applications, such as low-dropout linear voltage regulators, switching regulators, gate drivers, battery management systems, etc. A MOSFETs’ behavior is extremely complex to model, thus, creating high-performance models for these transistors is an imperative condition in order to emulate the exact real behavior of a circuit using them. An essential parameter of MOSFET power switches is the ON-state resistance (RDSON), because it determines the power losses during the ON state. Ideally, the power losses need to be zero. RDSON depends on multiple factors, such as temperature, load current, and gate-to-source voltage. Previous studies in this domain focus on the modeling of the MOSFET only in specific operating points, but do not cover the entire variation range of the parameters, which is critical for some applications. For this reason, in this paper, there was introduced for the first time a novel ON-state resistance modeling technique for MOSFET Power Switches, which solves the entire RDSON dependency on the transistor’s variables stated above. The novel RDSON modeling technique is based on modulating the transistor’s gate-to-source voltage such that the exact RDSON value is obtained in each possible operating point. The method was tested as a real-life example by creating a behavioral model for an N-channel MOSFET transistor and the chosen simulation environment was Oregon, USA, Computer-Aided Design (OrCAD) capture. The results show that the model is able to match the transistor’s RDSON characteristics with a maximum error of 0.8%. This is extremely important for applications in which the temperatures, voltages, and currents vary over a wide range. The new proposed modeling method covers a gap in the behavioral modeling domain, due to the fact that, until now, it was not possible to model the RDSON characteristics in all operating corners. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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18 pages, 4247 KiB  
Article
Application of Computational Model Based Probabilistic Neural Network for Surface Water Quality Prediction
by Mohammed Falah Allawi, Sinan Q. Salih, Murizah Kassim, Majeed Mattar Ramal, Abdulrahman S. Mohammed and Zaher Mundher Yaseen
Mathematics 2022, 10(21), 3960; https://doi.org/10.3390/math10213960 - 25 Oct 2022
Cited by 8 | Viewed by 1821
Abstract
Applications of artificial intelligence (AI) models have been massively explored for various engineering and sciences domains over the past two decades. Their capacity in modeling complex problems confirmed and motivated researchers to explore their merit in different disciplines. The use of two AI-models [...] Read more.
Applications of artificial intelligence (AI) models have been massively explored for various engineering and sciences domains over the past two decades. Their capacity in modeling complex problems confirmed and motivated researchers to explore their merit in different disciplines. The use of two AI-models (probabilistic neural network and multilayer perceptron neural network) for the estimation of two different water quality indicators (namely dissolved oxygen (DO) and five days biochemical oxygen demand (BOD5)) were reported in this study. The WQ parameters estimation based on four input modelling scenarios was adopted. Monthly water quality parameters data for the duration from January 2006 to December 2015 were used as the input data for the building of the prediction model. The proposed modelling was established utilizing many physical and chemical variables, such as turbidity, calcium (Ca), pH, temperature (T), total dissolved solids (TDS), Sulfate (SO4), total suspended solids (TSS), and alkalinity as the input variables. The proposed models were evaluated for performance using different statistical metrics and the evaluation results showed that the performance of the proposed models in terms of the estimation accuracy increases with the addition of more input variables in some cases. The performances of PNN model were superior to MLPNN model with estimation both DO and BOD parameters. The study concluded that the PNN model is a good tool for estimating the WQ parameters. The optimal evaluation indicators for PNN in predicting BOD are (R2 = 0.93, RMSE = 0.231 and MAE = 0.197). The best performance indicators for PNN in predicting Do are (R2 = 0.94, RMSE = 0.222 and MAE = 0.175). Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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26 pages, 11505 KiB  
Article
Sizing and Design of a PV-Wind-Fuel Cell Storage System Integrated into a Grid Considering the Uncertainty of Load Demand Using the Marine Predators Algorithm
by Fayza S. Mahmoud, Ashraf M. Abdelhamid, Ameena Al Sumaiti, Abou-Hashema M. El-Sayed and Ahmed A. Zaki Diab
Mathematics 2022, 10(19), 3708; https://doi.org/10.3390/math10193708 - 10 Oct 2022
Cited by 19 | Viewed by 2521
Abstract
In this paper, the utility grid is integrated with hybrid photovoltaic (PV)/wind/fuel cells to overcome the unavailability of the grid and the single implementation of renewable energy. The main purpose of this study is smart management of hydrogen storage tanks and power exchange [...] Read more.
In this paper, the utility grid is integrated with hybrid photovoltaic (PV)/wind/fuel cells to overcome the unavailability of the grid and the single implementation of renewable energy. The main purpose of this study is smart management of hydrogen storage tanks and power exchange between the hybrid renewable energy and the grid to minimize the total cost of the hybrid system and load uncertainties. PV and wind act as the main renewable energy sources, whereas fuel cells act as auxiliary sources designed to compensate for power variations and to ensure continuous power flow to the load. The grid is considered a backup system that works when hybrid renewable energy and fuel cells are unavailable. In this study, the optimal size of the components of the hybrid energy system is introduced using two methods: the marine predators’ algorithm (MPA) and the seagull optimization algorithm (SOA). The optimal sizing problem is also run accounting for the uncertainty in load demand. The results obtained from the proposed optimization are given with and without uncertainty in load demand. The simulation results of the hybrid system without uncertainty demonstrate the superiority of the MPA compared with SOA. However, in the case of load uncertainty, the simulation results (the uncertainty) are given using the MPA optimization technique with +5%, +10%, and +15% uncertainty in load, which showed that the net present cost and purchase energy are increased with uncertainty. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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21 pages, 5001 KiB  
Article
Moore–Gibson–Thompson Photothermal Model with a Proportional Caputo Fractional Derivative for a Rotating Magneto-Thermoelastic Semiconducting Material
by Osama Moaaz, Ahmed E. Abouelregal and Meshari Alesemi
Mathematics 2022, 10(17), 3087; https://doi.org/10.3390/math10173087 - 27 Aug 2022
Cited by 6 | Viewed by 1606
Abstract
By considering the Moore–Gibson–Thompson (MGT) equation, the current work introduces a modified fractional photothermal model. The construction model is based on the proportional Caputo fractional derivative, which is a new definition of the fractional derivative that is simple and works well. In addition, [...] Read more.
By considering the Moore–Gibson–Thompson (MGT) equation, the current work introduces a modified fractional photothermal model. The construction model is based on the proportional Caputo fractional derivative, which is a new definition of the fractional derivative that is simple and works well. In addition, the theory of heat transfer in semiconductor materials was used in the context of optical excitation transfer and plasma processes. The proposed model was used to investigate the interaction of light and heat within a magnetized semiconductor sphere rotating at a constant angular speed. The Laplace transform was used to obtain solutions for optical excitation induced by physical field variables. Using a numerical method, Laplace transforms can be reversed. The figures show the effects of carrier lifetime, conformable fractional operator, and rotation on thermal and mechanical plasma waves, which are shown in the graphs. The theory’s predictions were compared and extensively tested against other existing models. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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15 pages, 3847 KiB  
Article
The Moisture Diffusion Equation for Moisture Absorption of Multiphase Symmetrical Sandwich Structures
by Hang Yu, Lu Yao, Yan Ma, Zhaoyuan Hou, Jiahui Tang, Yuming Wang and Yang Ni
Mathematics 2022, 10(15), 2669; https://doi.org/10.3390/math10152669 - 28 Jul 2022
Cited by 6 | Viewed by 1968
Abstract
When hydrophilic materials (such as natural fiber, epoxy resin or concrete) compose sandwich structures, the moisture absorption from hydrothermal environments may significantly affect their mechanical properties. Although some experimental works were carried out, few mathematical efforts have been made to describe the moisture [...] Read more.
When hydrophilic materials (such as natural fiber, epoxy resin or concrete) compose sandwich structures, the moisture absorption from hydrothermal environments may significantly affect their mechanical properties. Although some experimental works were carried out, few mathematical efforts have been made to describe the moisture diffusion of multiphase symmetrical sandwich structures thus far. In this paper, the moisture diffusion equation was developed to effectively predict the moisture diffusion behavior of multiphase symmetrical sandwich structures as the function of aging time. Both finite element analysis (FEA) and experimental works were carried out to validate the accuracy of the analytical method, and the analytical results show a good agreement with FEA and experimental data. The effect of the interface condition on the concentration at the interfaces was discussed; the difference between concentration and normalized concentration was illustrated; the correct interface condition, which is a continuous normalized concentration condition, was explained for the moisture diffusion behavior of sandwich structures. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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22 pages, 4590 KiB  
Article
Game Theory and an Improved Maximum Entropy-Attribute Measure Interval Model for Predicting Rockburst Intensity
by Yakun Zhao, Jianhong Chen, Shan Yang and Zhe Liu
Mathematics 2022, 10(15), 2551; https://doi.org/10.3390/math10152551 - 22 Jul 2022
Cited by 2 | Viewed by 1600
Abstract
To improve the accuracy of predicting rockburst intensity, game theory and an improved maximum entropy-attribute measure interval model were established. First, by studying the mechanism of rockburst and typical cases, rock uniaxial compressive strength σc, rock compression-tension ratio [...] Read more.
To improve the accuracy of predicting rockburst intensity, game theory and an improved maximum entropy-attribute measure interval model were established. First, by studying the mechanism of rockburst and typical cases, rock uniaxial compressive strength σc, rock compression-tension ratio σc/σt, rock shear compression ratio σθ/σc, rock elastic deformation coefficient Wet, and rock integrity coefficient Kv were selected as indexes for predicting rockburst intensity. Second, by combining the maximum entropy principle with the attribute measure interval and using the minimum distance Di−k between sample and class as the guide, the entropy solution of the attribute measure was obtained, which eliminates the greyness and ambiguity of the rockburst indexes to the maximum extent. Third, using the compromise coefficient to integrate the comprehensive attribute measure, which avoids the ambiguity about the number of attribute measure intervals. Fourth, from the essence of measurement theory, the Euclidean distance formula was used to improve the attribute identification mode, which overcomes the effect of the confidence coefficient taking on the results. Moreover, in order to balance the shortcomings of the subjective weights of the Analytic Hierarchy Process and the objective weights of the CRITIC method, game theory was used for the combined weights, which balances experts’ experience and the amount of data information. Finally, 20 sets of typical cases for rockburst in the world were selected as samples. On the one hand, the reasonableness of the combined weights of indexes was analyzed; on the other hand, the results of this paper’s model were compared with the three analytical models for predicting rockburst, and this paper’s model had the lowest number of misjudged samples and an accuracy rate of 80%, which was better than other models, verifying the accuracy and applicability. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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18 pages, 409 KiB  
Article
Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers
by V. Vinitha, N. Anbazhagan, S. Amutha, K. Jeganathan, Bhanu Shrestha, Hyoung-Kyu Song, Gyanendra Prasad Joshi and Hyeonjoon Moon
Mathematics 2022, 10(13), 2235; https://doi.org/10.3390/math10132235 - 26 Jun 2022
Cited by 4 | Viewed by 1733
Abstract
This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. [...] Read more.
This paper explores the random environment with two classes of suppliers and impulse customers. The system’s greatest inventory size is S, and it has an infinitely large orbit. In this case, there are two categories of suppliers: temporary suppliers and regular suppliers. Whenever the inventory approaches r, we place on order Q1 (=S−r) unit items to a temporary supplier. Similarly, when the inventory level drops to s (<Q1<r), we place an order for Q2 (=S−s>s+1) units of items to our regular supplier. Two types of suppliers’ lead times are considered to be exponentially distributed. Here, the customers who arrive from different states of the random environment (RE) are followed by the Markovian arrival process. If there is no inventory in the system when the customer arrives, they are automatically assigned to an orbit. The model was examined in steady state by using the matrix-analytic approach. Finally, the numerical examples for our structural model are discussed. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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10 pages, 2550 KiB  
Article
A Novel Method for Remaining Useful Life Prediction of Bearing Based on Spectrum Image Similarity Measures
by Bo Wu, Bo Zhang, Wei Li and Fan Jiang
Mathematics 2022, 10(13), 2209; https://doi.org/10.3390/math10132209 - 24 Jun 2022
Cited by 3 | Viewed by 1642
Abstract
Accurately predicting the remaining useful life (RUL) of bearing by analyzing vibration signals is challenging and meaningful. To address this issue, a novel method based on spectrum image similarity is proposed in this paper. First, spectrum images for the whole lifecycle data of [...] Read more.
Accurately predicting the remaining useful life (RUL) of bearing by analyzing vibration signals is challenging and meaningful. To address this issue, a novel method based on spectrum image similarity is proposed in this paper. First, spectrum images for the whole lifecycle data of reference bearings are obtained by performing fast Fourier transformation (FFT). Second, the similarity is calculated between the current monitored data of operating bearing and run-to-failure images of reference bearings. Then, the weights of reference bearings are derived based on the similarity measures. Finally, the RUL of the operating bearing is estimated with the weighted average of the RULs of referenced bearings. The proposed method is demonstrated based on 2012 PHM Data Challenge Competition data, which shows its effectiveness and practicality. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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20 pages, 6453 KiB  
Article
Anomalous Areas Detection in Rocks Using Time-Difference Adjoint Tomography
by Feiyue Wang, Xin Xie, Zhongwei Pei and Longjun Dong
Mathematics 2022, 10(7), 1069; https://doi.org/10.3390/math10071069 - 26 Mar 2022
Cited by 3 | Viewed by 2102
Abstract
Detecting anomalous areas (such as caves, faults, and weathered layers) in rocks is essential for the safety of facilities and personnel in subsurface engineering. Seismic tomography has been proved to be an effective exploration technology in engineering geophysics. However, the complexity, anisotropy, and [...] Read more.
Detecting anomalous areas (such as caves, faults, and weathered layers) in rocks is essential for the safety of facilities and personnel in subsurface engineering. Seismic tomography has been proved to be an effective exploration technology in engineering geophysics. However, the complexity, anisotropy, and uncertainty in rock environments pose challenges to the resolution and robustness of tomography methods. Traditional tomography methods have difficulty balancing reliability and efficiency. Therefore, we developed a time-difference adjoint tomography method combining the arrival-time difference and the adjoint state method. The effectiveness was verified by numerical experiments and a laboratory-scale acoustic experiment. The effectiveness of the proposed method was demonstrated by the experimental results. The adjoint scheme avoids additional ray tracing and improves the efficiency of the inversion, which allows the use of finer forward grids in practice. By considering the differential arrivals of receiver pairs, the proposed method is robust in the face of systematic errors and relatively stable against large random noises. Moreover, the velocity contrast obtained by the proposed method is sharper than for first-arrival tomography in the areas where the rays are not dense, resulting in a clearer indication of the anomalous areas in the tomographic image. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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20 pages, 9246 KiB  
Article
Prevention of Hazards Induced by a Radiation Fireball through Computational Geometry and Parametric Design
by Joseph M. Cabeza-Lainez, Francisco Salguero-Andújar and Inmaculada Rodríguez-Cunill
Mathematics 2022, 10(3), 387; https://doi.org/10.3390/math10030387 - 27 Jan 2022
Cited by 10 | Viewed by 2476
Abstract
Radiation fireballs are singular phenomena which involve severe thermal radiation and, consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects [...] Read more.
Radiation fireballs are singular phenomena which involve severe thermal radiation and, consequently, they need to be duly assessed and prevented. Although the radiative heat transfer produced by a sphere is relatively well known, the shadowing measures implemented to control the fireball’s devastating effects have frequently posed a difficult analytical instance, mainly due to its specific configuration. The objective of this article is to develop a parametric algorithm that provides the exact radiative configuration factors for the most general case in which the fireball is located at any distance and height above the ground, partially hidden by a protective wall over an affected area at different positions with respect to the said fireball. To this aim we use methods based on Computational Geometry and Algorithm-Aided Design; tools that, departing from the projected solid-angle principle, provide exact configuration factors, in all cases, even if they do not present a definite analytical solution. This implies dealing with spatially curved radiative sources which had not been addressed formerly in the literature due to their mathematical difficulties. Adequate application of this method may improve the safety of a significant number of facilities and reduce the number casualties among persons exposed to such risks. As a similar radiative problem appears in volcanic explosions; we hope that further extensions of the method can be adapted to the issue with advantage. Full article
(This article belongs to the Special Issue Advanced Mathematical Approaches to Engineering and Computational Problems)
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