Search Results (11)

Tool wear modeling in CNC turning processes is critical for proactive maintenance and process optimization in intelligent manufacturing. However, traditional physics-based models lack adaptability, while machine learning approaches are often limited by poor interpretability. This study develops Kolmogorov–Arnold Networks (KANs) to address the trade-off between accuracy and interpretability in lathe tool wear modeling. Three KAN variants (KAN-A, KAN-B, and KAN-C) with varying complexities are proposed, using feed rate, depth of cut, and cutting speed as input variables to model flank wear. The proposed KAN-based framework generates interpretable mathematical expressions for tool wear, enabling transparent decision-making. To evaluate the performance of KANs, this research systematically compares prediction errors, topological evolutions, and mathematical interpretations of derived symbolic formulas. For benchmarking purposes, MLP-A, MLP-B, and MLP-C models are developed based on the architectures of their KAN counterparts. A comparative analysis between KAN and MLP frameworks is conducted to assess differences in modeling performance, with particular focus on the impact of network depth, width, and parameter configurations. Theoretical analyses, grounded in the Kolmogorov–Arnold representation theorem and Cybenko’s theorem, explain KANs’ ability to approximate complex functions with fewer nodes. The experimental results demonstrate that KANs exhibit two key advantages: (1) superior accuracy with fewer parameters compared to traditional MLPs, and (2) the ability to generate white-box mathematical expressions. Thus, this work bridges the gap between empirical models and black-box machine learning in manufacturing applications. KANs uniquely combine the adaptability of data-driven methods with the interpretability of physics-based models, offering actionable insights for researchers and practitioners. Full article

A solid oxide fuel cell (SOFC) is an electrochemical energy conversion device that provides higher thermoelectric efficiency than traditional cogeneration systems. Current research in this field highlights a variety of mathematical models. These models are based on complex physicochemical and electrochemical reactions, enabling accurate simulation and optimal control of fuel cells. However, these models require substantial computational resources, leading to high processing times. White box and gray box models are unable to achieve real-time optimization of control parameters. A potential solution involves using data-driven machine learning (ML) black-box models. This study examines three ML models: artificial neural network (ANN), random forest (RF), and extreme gradient boosting (XGB). The training dataset consisted of experimental results from SOFC laboratory experiments, comprising 32,843 records with 47 control parameters. The study evaluated the effectiveness of input matrix dimensionality reduction using the following feature importance evaluation methods: mean decrease in impurity (MDI), permutation importance (PI), principal component analysis (PCA), and Shapley additive explanations (SHAP). The application of ML models revealed a complex nonlinear relationship between the SOFC output voltage and the control parameters of the system. The default XGB model achieved the optimal balance between accuracy (MSE = 0.9940) and training speed (τ = 0.173 s/it), with performance capabilities that enable real-time enhancement of SOFC thermoelectric characteristics during system operation. Full article

Cancer is a complex disease, responsible for a significant portion of global deaths. The increasing prioritisation of know-why over know-how approaches in biological research has favoured the rising use of both white- and black-box mathematical techniques for cancer modelling, seeking to better grasp the multi-scale mechanistic workings of its complex phenomena (such as tumour-immune interactions, drug resistance, tumour growth and diffusion, etc.). In light of this wide-ranging use of mathematics in cancer modelling, the unique memory and non-local properties of Fractional Calculus (FC) have been sought after in the last decade to replace ordinary differentiation in the hypothesising of FC’s superior modelling of complex oncological phenomena, which has been shown to possess an accumulated knowledge of its past states. As such, this review aims to present a thorough and structured survey about the main guiding trends and modelling categories in cancer research, emphasising in the field of oncology FC’s increasing employment in mathematical modelling as a whole. The most pivotal research questions, challenges and future perspectives are also outlined. Full article

Explainable machine learning is an emerging new domain fundamental for trustworthy real-world applications. A lack of trust and understanding are the main drawbacks of deep learning models when applied to real-world decision systems and prediction tasks. Such models are considered as black boxes because they are unable to explain the reasons for their predictions in human terms; thus, they cannot be universally trusted. In critical real-world applications, such as in medical, legal, and financial ones, an explanation of machine learning (ML) model decisions is considered crucially significant and mandatory in order to acquire trust and avoid fatal ML bugs, which could disturb human safety, rights, and health. Nevertheless, explainable models are more than often less accurate; thus, it is essential to invent new methodologies for creating interpretable predictors that are almost as accurate as black-box ones. In this work, we propose a novel explainable feature extraction and prediction framework applied to 3D image recognition. In particular, we propose a new set of explainable features based on mathematical and geometric concepts, such as lines, vertices, contours, and the area size of objects. These features are calculated based on the extracted contours of every 3D input image slice. In order to validate the efficiency of the proposed approach, we apply it to a critical real-world application: pneumonia detection based on CT 3D images. In our experimental results, the proposed white-box prediction framework manages to achieve a performance similar to or marginally better than state-of-the-art 3D-CNN black-box models. Considering the fact that the proposed approach is explainable, such a performance is particularly significant. Full article

An accurate fuel consumption prediction model is the basis for ship navigation status analysis, energy conservation, and emission reduction. In this study, we develop a black-box model based on machine learning and a white-box model based on mathematical methods to predict ship fuel consumption rates. We also apply the Kwon formula as a data preprocessing cleaning method for the black-box model that can eliminate the data generated during the acceleration and deceleration process. The ship model test data and the regression methods are employed to evaluate the accuracy of the models. Furthermore, we use the predicted correlation between fuel consumption rates and speed under simulated conditions for model performance validation. We also discuss applying the data-cleaning method in the preprocessing of the black-box model. The results demonstrate that this method is feasible and can support the performance of the fuel consumption model in a broad and dense distribution of noise data in data collected from real ships. We improved the error to 4% of the white-box model and the $R^2$ to 0.9977 and 0.9922 of the XGBoost and RF models, respectively. After applying the Kwon cleaning method, the value of $R^2$ also can reach 0.9954, which can provide decision support for the operation of shipping companies. Full article

Today, a lot of research on autonomous driving technology is being conducted, and various vehicles with autonomous driving functions, such as ACC (adaptive cruise control) are being released. The autonomous vehicle recognizes obstacles ahead by the fusion of data from various sensors, such as lidar and radar sensors, including camera sensors. As the number of vehicles equipped with such autonomous driving functions increases, securing safety and reliability is a big issue. Recently, Mobileye proposed the RSS (responsibility-sensitive safety) model, which is a white box mathematical model, to secure the safety of autonomous vehicles and clarify responsibility in the case of an accident. In this paper, a method of applying the RSS model to a variable focus function camera that can cover the recognition range of a lidar sensor and a radar sensor with a single camera sensor is considered. The variables of the RSS model suitable for the variable focus function camera were defined, the variable values were determined, and the safe distances for each velocity were derived by applying the determined variable values. In addition, as a result of considering the time required to obtain the data, and the time required to change the focal length of the camera, it was confirmed that the response time obtained using the derived safe distance was a valid result. Full article

One of the most common problems in science is to investigate a function describing a system. When the estimate is made based on a classical mathematical model (white-box), the function is obtained throughout solving a differential equation. Alternatively, the prediction can be made by an artificial neural network (black-box) based on trends found in past data. Both approaches have their advantages and disadvantages. Mathematical models were seen as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. Simultaneously, the approximation of neural networks can reproduce the solution exceptionally well if fed sufficient data. The difference is that an artificial neural network requires big data to build its accurate approximation, whereas a typical mathematical model needs several data points to estimate an empirical constant. Therefore, the common problem that developers meet is the inaccuracy of mathematical models and artificial neural networks. Another common challenge is the mathematical models’ computational complexity or lack of data for a sufficient precision of the artificial neural networks. Here we analyze a grey-box solution in which an artificial neural network predicts just a part of the mathematical model, and its weights are adjusted based on the mathematical model’s output using the evolutionary approach to avoid overfitting. The performance of the grey-box model is statistically compared to a Dense Neural Network on benchmarking functions. With the use of Shaffer procedure, it was shown that the grey-box approach performs exceptionally well when the overall complexity of a problem is properly distributed with the mathematical model and the Artificial Neural Network. The obtained calculation results indicate that such an approach could increase precision and limit the dataset required for learning. To show the applicability of the presented approach, it was employed in modeling of the electrochemical reaction in the Solid Oxide Fuel Cell’s anode. Implementation of a grey-box model improved the prediction in comparison to the typically used methodology. Full article

Agro-industrial wastes suitable for economical and high mass production of novel Trichoderma species under solid-state fermentation were identified by optimizing the culture conditions using a mathematical model and evaluating the viability of the formulated bio-product. Fourteen inexpensive, locally available, organic substrates and cereals were examined using a one-factor-at-a-time experiment. The fungus colonized nearly all substrates after 21 days of incubation, although the degree of colonization and conidiation varied among the substrates. A mixture of wheat bran and white rice (2:1 w/w) was found to support maximum growth of T. asperellum AU131 (3.2 × 10⁷ spores/g dry substrate) and T. longibrachiatum AU158 (3.5 × 10⁷ spores/g dry substrate). Using a fractional factorial design, the most significant growth factors influencing biomass production were found to be temperature, moisture content, inoculum concentration, and incubation period (p ≤ 0.05). Analysis of variance of a Box–Behnken design showed that the regression model was highly significant (p ≤ 0.05) with F-values of 10.38 (P = 0.0027, T. asperellum AU131) and 12.01 (p < 0.0017, T. longibrachiatum AU158). Under optimal conditions, maximum conidia yield of log₁₀ (8.6) (T. asperellum AU131) and log₁₀(9.18) (T. longibrachiatum) were obtained. For wettable powder Trichoderma species formulations, it was possible to maintain conidial viability at room temperature (25 °C) for eight months at concentrations above 10⁶ CFU/g. Full article

Black carbon (BC) is an important component of particulate matter (PM) in urban environments. BC is typically emitted from gas and diesel engines, coal-fired power plants, and other sources that burn fossil fuel. In contrast to PM, BC measurements are not always available on a large scale due to the operational cost and complexity of the instrumentation. Therefore, it is advantageous to develop a mathematical model for estimating the quantity of BC in the air, termed a BC proxy, to enable widening of spatial air pollution mapping. This article presents the development of BC proxies based on a Bayesian framework using measurements of PM concentrations and size distributions from 10 to 10,000 nm from a recent mobile air pollution study across several areas of Jordan. Bayesian methods using informative priors can naturally prevent over-fitting in the modelling process and the methods generate a confidence interval around the prediction, thus the estimated BC concentration can be directly quantified and assessed. In particular, two types of models are developed based on their transparency and interpretability, referred to as white-box and black-box models. The proposed methods are tested on extensive data sets obtained from the measurement campaign in Jordan. In this study, black-box models perform slightly better due to their model complexity. Nevertheless, the results demonstrate that the performance of both models does not differ significantly. In practice, white-box models are relatively more convenient to be deployed, the methods are well understood by scientists, and the models can be used to better understand key relationships. Full article

Rock mechanical properties play a key role in the optimization process of engineering practices in the oil and gas industry so that better field development decisions can be made. Estimation of these properties is central in well placement, drilling programs, and well completion design. The elastic behavior of rocks can be studied by determining two main parameters: Young’s modulus and Poisson’s ratio. Accurate determination of the Poisson’s ratio helps to estimate the in-situ horizontal stresses and in turn, avoid many critical problems which interrupt drilling operations, such as pipe sticking and wellbore instability issues. Accurate Poisson’s ratio values can be experimentally determined using retrieved core samples under simulated in-situ downhole conditions. However, this technique is time-consuming and economically ineffective, requiring the development of a more effective technique. This study has developed a new generalized model to estimate static Poisson’s ratio values of sandstone rocks using a supervised artificial neural network (ANN). The developed ANN model uses well log data such as bulk density and sonic log as the input parameters to target static Poisson’s ratio values as outputs. Subsequently, the developed ANN model was transformed into a more practical and easier to use white-box mode using an ANN-based empirical equation. Core data (692 data points) and their corresponding petrophysical data were used to train and test the ANN model. The self-adaptive differential evolution (SADE) algorithm was used to fine-tune the parameters of the ANN model to obtain the most accurate results in terms of the highest correlation coefficient (R) and the lowest mean absolute percentage error (MAPE). The results obtained from the optimized ANN model show an excellent agreement with the laboratory measured static Poisson’s ratio, confirming the high accuracy of the developed model. A comparison of the developed ANN-based empirical correlation with the previously developed approaches demonstrates the superiority of the developed correlation in predicting static Poisson’s ratio values with the highest R and the lowest MAPE. The developed correlation performs in a manner far superior to other approaches when validated against unseen field data. The developed ANN-based mathematical model can be used as a robust tool to estimate static Poisson’s ratio without the need to run the ANN model. Full article

This paper deals with the comparison of different methods which can be used for the prediction of the performance curves of pumps as turbines (PATs). The considered approaches are four, i.e., one physics-based simulation model (“white box” model), two “gray box” models, which integrate theory on turbomachines with specific data correlations, and one “black box” model. More in detail, the modeling approaches are: (1) a physics-based simulation model developed by the same authors, which includes the equations for estimating head, power, and efficiency and uses loss coefficients and specific parameters; (2) a model developed by Derakhshan and Nourbakhsh, which first predicts the best efficiency point of a PAT and then reconstructs their complete characteristic curves by means of two ad hoc equations; (3) the prediction model developed by Singh and Nestmann, which predicts the complete turbine characteristics based on pump shape and size; (4) an Evolutionary Polynomial Regression model, which represents a data-driven hybrid scheme which can be used for identifying the explicit mathematical relationship between PAT and pump curves. All approaches are applied to literature data, relying on both pump and PAT performance curves of head, power, and efficiency over the entire range of operation. The experimental data were provided by Derakhshan and Nourbakhsh for four different turbomachines, working in both pump and PAT mode with specific speed values in the range 1.53–5.82. This paper provides a quantitative assessment of the predictions made by means of the considered approaches and also analyzes consistency from a physical point of view. Advantages and drawbacks of each method are also analyzed and discussed. Full article