Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique

Naveed Ahmad Khan; Fahad Sameer Alshammari; Carlos Andrés Tavera Romero; Muhammad Sulaiman

doi:10.3390/e23121685

Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique

Entropy (Basel). 2021 Dec 15;23(12):1685. doi: 10.3390/e23121685.

Authors

Naveed Ahmad Khan¹, Fahad Sameer Alshammari², Carlos Andrés Tavera Romero³, Muhammad Sulaiman¹

Affiliations

¹ Department of Mathematics, Abdul Wali Khan University Mardan, Khyber-Pakhtunkhwa 23200, Pakistan.
² Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia.
³ COMBA R&D Laboratory, Faculty of Engineering, Universidad Santiago de Cali, Cali 76001, Colombia.

Abstract

In this paper, we have analyzed the mathematical model of various nonlinear oscillators arising in different fields of engineering. Further, approximate solutions for different variations in oscillators are studied by using feedforward neural networks (NNs) based on the backpropagated Levenberg-Marquardt algorithm (BLMA). A data set for different problem scenarios for the supervised learning of BLMA has been generated by the Runge-Kutta method of order 4 (RK-4) with the "NDSolve" package in Mathematica. The worth of the approximate solution by NN-BLMA is attained by employing the processing of testing, training, and validation of the reference data set. For each model, convergence analysis, error histograms, regression analysis, and curve fitting are considered to study the robustness and accuracy of the design scheme.

Keywords: Levenberg–Marquardt algorithm; Runge–Kutta method; damping; large amplitude; mass attached to a stretched elastic wire; neural networks; nonlinear oscillator; soft computing.