Investigation of fractional models of damping material by a neuroevolutionary approach

Waseem Waseem, M. Sulaiman and Abdulah Jeza Aljohani

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: This research paper deals with a problem related to the damped materials contained in structural dynamics. The problem dealt with here involves a fractional-order damping coefficient in the form of fractional derivatives that present a better mathematical model of the vibration systems. Fractional derivatives are widely used to characterize the viscoelastic features in structural designs. Unlike the integer order differentiation, fractional-order derivatives consider local as well as the global evolution of the system. Therefore, fractional differential equations can be indicated as a reasonable choice for modeling certain physical phenomena, and to present more accurate mathematical solutions to real-world applications than the ordinary differential equations. We have proposed a novel unsupervised machine learning procedure that first designs general solutions, with the help of Artificial Neural Networks (ANNs), for the fractional-order differential equation containing unknown decision weights. These weights are worked out with the help of Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm by setting a fitness function for each case. Results obtained from our simulations are better in the sense that they are overlapping with the analytical solutions available in the literature.

Keywords: Fractional calculus; Damping materials; Viscoelastic dynamical systems; Unsupervised machine learning; Fractional order Darwinian particle swarm optimizer; Bagley and Torvik model; Artificial neural networks (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305944

DOI: 10.1016/j.chaos.2020.110198

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