Design of intelligent neuro-structures optimized with Levenberg–Marquardt and Bayesian distribution for dynamical analysis of Caputo–Fabrizio fractional electric circuit models

Electrical engineering models utilize interconnected circuits that consist of charged particles to enable the simulation and study of electric devices and systems, taking advantage of effective electron transfer across a completed circuit. Electric circuits involving the Caputo-Fabrizio (CF) fractio...

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Veröffentlicht in:Engineering applications of artificial intelligence Jg. 160; S. 111920
Hauptverfasser: Kausar, Aneela, Chang, Chuan-Yu, Naz, Sidra, Raja, Muhammad Asif Zahoor, Khan, Rooh Ullah, Safiullah, Muhammad, Naz, Saeeda
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 27.11.2025
Schlagworte:
Bayesian regularization
Caputo-Fabrizio fractal operator
Convergence stability test
Electric circuits
Levenberg–Marquardt
Neural networks
Wilcoxon signed-Rank test
Electric circuits
Neural networks
Caputo-Fabrizio fractal operator
Bayesian regularization
Levenberg–Marquardt
Wilcoxon signed-Rank test
Convergence stability test
ISSN:0952-1976
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Zusammenfassung:Electrical engineering models utilize interconnected circuits that consist of charged particles to enable the simulation and study of electric devices and systems, taking advantage of effective electron transfer across a completed circuit. Electric circuits involving the Caputo-Fabrizio (CF) fractional derivative have been precisely modeled recently by known solutions, efficiently capturing the system's response. The paper talks about the application of electrical circuit models for analyzing fractional stiff differential equations in an effort to explore different properties of the fractal Resistor-Capacitor (RC) and Resistor-Inductor (RL) circuits. The study employs artificial intelligence-based neurocomputing techniques and backpropagation networks for the purposes of increasing the knowledge on fractal circuit models. The Bayesian Regularization backpropagated neural networks (BR-BNNs) and Levenberg–Marquardt backpropagated neural networks (LM-BNNs) are utilized as efficient procedure for the training. The mathematical equations of CF-fractional RC and RL circuits were implemented to generate synthetic reference datasets and these information's were then used as a target for execution of LM-BNNs and BR-BNNs to find approximate solutions for the models. To validate and compare the accuracy of BR-BNNs and LM-BNNs in solving CF-fractional electric circuit models, the convergence curves on iterative adaptation of mean squared error (MSE) are employed. Results show that BR-BNNs yields MSE of approximately 10−12 to 10−13 and absolute error within the range of 10−6 to 10−8, which providing strong evidence for the effectiveness of BR-BNNs approach than that of LM-BNNs algorithm. To further validate and endorse precision of the results, a performance evaluation via absolute error, statistical instance distribution in error histogram, regression analysis, convergence stability test, and Wilcoxon signed-rank test were exploited for CF-fractional electric circuit models that shows the statistical adequacy. •Application of neuro-computational paradigm via BR-BNNs and LM-BNNs for numerical fractional CF-electric circuit models is efficaciously presented.•Governing equations of CF fractional RC and RL models are utilized to compile the datasets for BR-BNNs and LM-BNNs and get approximate solutions.•The results indicate a reliable alternate framework to solve the system with reasonable precision and stability of CF electric circuit models.•To further confirm the accuracy of methodology, comparative studies on learning curves, error histograms, and regression index are exploited.
ISSN:0952-1976
DOI:10.1016/j.engappai.2025.111920