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

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

doi:10.3390/e23121685

Open AccessArticle

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

by

Naveed Ahmad Khan

¹

,

Fahad Sameer Alshammari

^2,*

,

Carlos Andrés Tavera Romero

³

and

Muhammad Sulaiman

^1,*

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

^*

Authors to whom correspondence should be addressed.

Entropy 2021, 23(12), 1685; https://doi.org/10.3390/e23121685

Submission received: 22 September 2021 / Revised: 18 November 2021 / Accepted: 9 December 2021 / Published: 15 December 2021

(This article belongs to the Special Issue Artificial Intelligence and Computational Issues in Engineering Applications)

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

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MDPI and ACS Style

Khan, N.A.; Alshammari, F.S.; Romero, C.A.T.; Sulaiman, M. Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique. Entropy 2021, 23, 1685. https://doi.org/10.3390/e23121685

AMA Style

Khan NA, Alshammari FS, Romero CAT, Sulaiman M. Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique. Entropy. 2021; 23(12):1685. https://doi.org/10.3390/e23121685

Chicago/Turabian Style

Khan, Naveed Ahmad, Fahad Sameer Alshammari, Carlos Andrés Tavera Romero, and Muhammad Sulaiman. 2021. "Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique" Entropy 23, no. 12: 1685. https://doi.org/10.3390/e23121685

APA Style

Khan, N. A., Alshammari, F. S., Romero, C. A. T., & Sulaiman, M. (2021). Study of Nonlinear Models of Oscillatory Systems by Applying an Intelligent Computational Technique. Entropy, 23(12), 1685. https://doi.org/10.3390/e23121685

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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

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