Mathematical and Computational Applications

23 pages, 10781 KiB

Open AccessArticle

Secure Communication of Electric Drive System Using Chaotic Systems Base on Disturbance Observer and Fuzzy Brain Emotional Learning Neural Network

by Huyen Chau Phan Thi, Nhat Quang Dang and Van Nam Giap

Math. Comput. Appl. 2025, 30(4), 73; https://doi.org/10.3390/mca30040073 (registering DOI) - 14 Jul 2025

Abstract

This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness [...] Read more.

This paper presents a novel wireless control framework for electric drive systems by employing a fuzzy brain emotional learning neural network (FBELNN) controller in conjunction with a Disturbance Observer (DO). The communication scheme uses chaotic system dynamics to ensure data confidentiality and robustness against disturbance in wireless environments. To be applied to embedded microprocessors, the continuous-time chaotic system is discretized using the Grunwald–Letnikov approximation. To avoid the loss of generality of chaotic behavior, Lyapunov exponents are computed to validate the preservation of chaos in the discrete-time domain. The FBELNN controller is then developed to synchronize two non-identical chaotic systems under different initial conditions, enabling secure data encryption and decryption. Additionally, the DOB is introduced to estimate and mitigate the effects of bounded uncertainties and external disturbances, enhancing the system’s resilience to stealthy attacks. The proposed control structure is experimentally implemented on a wireless communication system utilizing ESP32 microcontrollers (Espressif Systems, Shanghai, China) based on the ESP-NOW protocol. Both control and feedback signals of the electric drive system are encrypted using chaotic states, and real-time decryption at the receiver confirms system integrity. Experimental results verify the effectiveness of the proposed method in achieving robust synchronization, accurate signal recovery, and a reliable wireless control system. The combination of FBELNN and DOB demonstrates significant potential for real-time, low-cost, and secure applications in smart electric drive systems and industrial automation. Full article

(This article belongs to the Special Issue Applied Optimization in Automatic Control and Systems Engineering)

21 pages, 7862 KiB

Open AccessArticle

Physics-Informed Neural Network for Nonlinear Bending Analysis of Nano-Beams: A Systematic Hyperparameter Optimization

by Saba Sadat Mirsadeghi Esfahani, Ali Fallah and Mohammad Mohammadi Aghdam

Math. Comput. Appl. 2025, 30(4), 72; https://doi.org/10.3390/mca30040072 (registering DOI) - 14 Jul 2025

Abstract

This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton’s principle, incorporating nonlocal strain gradient theory, and based on Euler–Bernoulli beam theory. In [...] Read more.

This paper investigates the nonlinear bending analysis of nano-beams using the physics-informed neural network (PINN) method. The nonlinear governing equations for the bending of size-dependent nano-beams are derived from Hamilton’s principle, incorporating nonlocal strain gradient theory, and based on Euler–Bernoulli beam theory. In the PINN method, the solution is approximated by a deep neural network, with network parameters determined by minimizing a loss function that consists of the governing equation and boundary conditions. Despite numerous reports demonstrating the applicability of the PINN method for solving various engineering problems, tuning the network hyperparameters remains challenging. In this study, a systematic approach is employed to fine-tune the hyperparameters using hyperparameter optimization (HPO) via Gaussian process-based Bayesian optimization. Comparison of the PINN results with available reference solutions shows that the PINN, with the optimized parameters, produces results with high accuracy. Finally, the impacts of boundary conditions, different loads, and the influence of nonlocal strain gradient parameters on the bending behavior of nano-beams are investigated. Full article

(This article belongs to the Special Issue Advances in Computational and Applied Mechanics (SACAM))

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20 pages, 981 KiB

Open AccessArticle

Permeability Prediction Using Vision Transformers

by Cenk Temizel, Uchenna Odi, Kehao Li, Lei Liu, Salih Tutun and Javier Santos

Math. Comput. Appl. 2025, 30(4), 71; https://doi.org/10.3390/mca30040071 - 8 Jul 2025

Viewed by 246

Abstract

Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural [...] Read more.

Accurate permeability predictions remain pivotal for understanding fluid flow in porous media, influencing crucial operations across petroleum engineering, hydrogeology, and related fields. Traditional approaches, while robust, often grapple with the inherent heterogeneity of reservoir rocks. With the advent of deep learning, convolutional neural networks (CNNs) have emerged as potent tools in image-based permeability estimation, capitalizing on micro-CT scans and digital rock imagery. This paper introduces a novel paradigm, employing vision transformers (ViTs)—a recent advancement in computer vision—for this crucial task. ViTs, which segment images into fixed-sized patches and process them through transformer architectures, present a promising alternative to CNNs. We present a methodology for implementing ViTs for permeability prediction, its results on diverse rock samples, and a comparison against conventional CNNs. The prediction results suggest that, with adequate training data, ViTs can match or surpass the predictive accuracy of CNNs, especially in rocks exhibiting significant heterogeneity. This study underscores the potential of ViTs as an innovative tool in permeability prediction, paving the way for further research and integration into mainstream reservoir characterization workflows. Full article

(This article belongs to the Special Issue Feature Papers in Mathematical and Computational Applications 2025)

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15 pages, 1033 KiB

Open AccessArticle

A Comparative Analysis of Numerical Methods for Mathematical Modelling of Intravascular Drug Concentrations Using a Two-Compartment Pharmacokinetic Model

by Kaniz Fatima, Basit Ali, Abdul Attayyab Khan, Sadique Ahmed, Abdelhamied Ashraf Ateya and Naveed Ahmad

Math. Comput. Appl. 2025, 30(4), 70; https://doi.org/10.3390/mca30040070 - 7 Jul 2025

Viewed by 95

Abstract

Pharmacokinetic modelling is extensively used in understanding drug behavior, distribution and optimizing dosing regimens. This study presents a two-compartment pharmacokinetic model developed using three numerical approaches that includes the Euler method, fourth-order Runge–Kutta method, and Adams–Bashforth–Moulton method. The model incorporates key parameters including [...] Read more.

Pharmacokinetic modelling is extensively used in understanding drug behavior, distribution and optimizing dosing regimens. This study presents a two-compartment pharmacokinetic model developed using three numerical approaches that includes the Euler method, fourth-order Runge–Kutta method, and Adams–Bashforth–Moulton method. The model incorporates key parameters including elimination, transfer rate constants, and compartment volumes. The numerical approaches are used to simulate the concentration of drug profiles, which are then compared to the exact solution. The results reveal that with an average error of 1.54%, the fourth-order Runge–Kutta technique provides optimized results compared to other methods when the overall average error is taken into account, which shows that the Runge–Kutta method is better in terms of accuracy and consistency for drug concentration estimates in the two-compartment model. This mathematical model may be used to optimize dosing procedures by providing a less complex method. Along with that, it also monitors therapeutic medication levels, which provides accurate analysis for drug distribution and elimination kinetics. Full article

(This article belongs to the Topic Numerical Methods for Partial Differential Equations)

23 pages, 1090 KiB

Open AccessArticle

Air Pollution, Socioeconomic Status, and Avoidable Hospitalizations: A Multifaceted Analysis

by Carlos Minutti-Martinez, Miguel F. Mata-Rivera, Magali Arellano-Vazquez, Boris Escalante-Ramírez and Jimena Olveres

Math. Comput. Appl. 2025, 30(4), 69; https://doi.org/10.3390/mca30040069 - 30 Jun 2025

Viewed by 405

Abstract

This study investigates the combined effects of air pollution and socioeconomic factors on disease incidence and severity, addressing gaps in prior research that often analyzed these factors separately. Using data from 86,170 hospitalizations in Mexico City (2015–2019), we employed multivariate statistical methods (PCA [...] Read more.

This study investigates the combined effects of air pollution and socioeconomic factors on disease incidence and severity, addressing gaps in prior research that often analyzed these factors separately. Using data from 86,170 hospitalizations in Mexico City (2015–2019), we employed multivariate statistical methods (PCA and factor analysis) to construct composite measures of social and economic status and grouped correlated pollutants. Logistic and negative binomial regression models assessed their associations with hospitalization risk and frequency. Results showed that economic status significantly influenced diabetes complications, while social factors affected prenatal care-related diseases and hypertension. The

{PM}_{10}

–

{PM}_{2.5}

–CO group increased the incidence of asthma, influenza, and epilepsy, whereas

{NO}_{2}

–

{NO}_{x}

impacted diabetes complication severity and influenza. Nonlinear effects and interactions (e.g., age and weight) were also identified, highlighting the need for integrated analyses in environmental health research. Full article

(This article belongs to the Special Issue New Trends in Computational Intelligence and Applications 2024)

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17 pages, 4466 KiB

Open AccessArticle

Extracting Flow Characteristics from Single and Multi-Point Time Series Through Correlation Analysis

by Anup Saha and Harish Subramani

Math. Comput. Appl. 2025, 30(4), 68; https://doi.org/10.3390/mca30040068 - 30 Jun 2025

Viewed by 207

Abstract

Strongly driven fluid and combustion systems typically contain a few, nonlinearly coupled, major flow constituents. It is necessary to identify the flow constituents in order to establish the underlying dynamics and to control these complex flows. Due to non-trivial boundary condition in realistic [...] Read more.

Strongly driven fluid and combustion systems typically contain a few, nonlinearly coupled, major flow constituents. It is necessary to identify the flow constituents in order to establish the underlying dynamics and to control these complex flows. Due to non-trivial boundary condition in realistic systems and long-range coupling, it is often difficult to construct accurate models of large-scale reacting systems. The question then arises if these flow constituents can be identified and controlled through analysis of experimental data. The difficulties in such analyses originate in the presence of high levels of noise and irregularities in the flow. A typical time series contains high-frequency noise as well as low-frequency features originating from the near translational invariance of the underlying fluid systems. We propose a pair of approaches to study such data. The first is the use of auto and cross correlation functions. Auto-correlation functions of the time series from a single transducer can be used effectively to demonstrate the low dimensionality of the flow. Second, we show that multi-point time series from appropriately placed transducers can be used to establish spatial characteristics of these flow constituents. The novelty of the approaches lies in the establishment of geometric and dynamic features of the primary flow constituents based on sensor data only, without the need of expensive imaging tools. These methods can potentially identify changes in flow behavior within complex propulsion systems, such as aircraft engines, by utilizing data collected from embedded transducers. Full article

(This article belongs to the Section Engineering)

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30 pages, 2494 KiB

Open AccessArticle

A Novel Framework for Mental Illness Detection Leveraging TOPSIS-ModCHI-Based Feature-Driven Randomized Neural Networks

by Santosh Kumar Behera and Rajashree Dash

Math. Comput. Appl. 2025, 30(4), 67; https://doi.org/10.3390/mca30040067 - 30 Jun 2025

Viewed by 244

Abstract

Mental illness has emerged as a significant global health crisis, inflicting immense suffering and causing a notable decrease in productivity. Identifying mental health disorders at an early stage allows healthcare professionals to implement more targeted and impactful interventions, leading to a significant improvement [...] Read more.

Mental illness has emerged as a significant global health crisis, inflicting immense suffering and causing a notable decrease in productivity. Identifying mental health disorders at an early stage allows healthcare professionals to implement more targeted and impactful interventions, leading to a significant improvement in the overall well-being of the patient. Recent advances in Artificial Intelligence (AI) have opened new avenues for analyzing medical records and behavioral data of patients to assist mental health professionals in their decision-making processes. In this study performance of four Randomized Neural Networks (RandNNs) such as Board Learning System (BLS), Random Vector Functional Link Network (RVFLN), Kernelized RVFLN (KRVFLN), and Extreme Learning Machine (ELM) are explored for detecting the type of mental illness a user may have by analyzing the random text of the user posted on social media. To improve the performance of the RandNNs during handling the text documents with unbalanced class distributions, a hybrid feature selection (FS) technique named as TOPSIS-ModCHI is suggested in the preprocessing stage of the classification framework. The effectiveness of the suggested FS with all the four randomized networks is assessed over the publicly available Reddit Mental Health Dataset after experimenting on two benchmark multiclass unbalanced datasets. From the experimental results, it is inferred that detecting the mental illness using BLS with TOPSIS-ModCHI produces the highest precision value of 0.92, recall value of 0.66, f-measure value of 0.77, and Hamming loss value of 0.06 as compared to ELM, RVFLN, and KRVFLN with a minimum feature size of 900. Overall, utilizing BLS for mental health analysis can offer a promising avenue toward improved interventions and a better understanding of mental health issues, aiding in decision-making processes. Full article

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Math. Comput. Appl., Volume 30, Issue 4 (August 2025) – 7 articles

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