Investigation of fractional models of damping material by a neuroevolutionary approach. (November 2020)

• Record Type: Journal Article
• Authors: Waseem, Waseem; Sulaiman, M.; Aljohani, Abdulah Jeza
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Fractional calculus -- Damping materials -- Viscoelastic dynamical systems -- Unsupervised machine learning -- Fractional order Darwinian particle swarm optimizer -- Bagley and Torvik model -- Artificial neural networks; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110198
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: This research paper deals with a problem related to the damped materials involved in structural dynamics. The problem considered in this paper involves a fractional-order damping coefficient in the form of fractional derivatives to present a better mathematical model of the vibration systems. We have suggested 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 involving unknown decision weights. These weights are determined with the help of Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm by setting a fitness function for each case. 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.