Machine learning aided stochastic structural free vibration analysis for functionally graded bar-type structures

Abstract

Abstract This paper presents a machine learning aided stochastic free vibration analysis for functionally graded (FG) bar-type structures through finite element method (FEM). The considered system uncertainties including the constituent material properties, the dimensions of structural members, and the degree of the gradation of the FGM are incorporated. A novel kernel-based machine learning technique, namely the extended support vector regression (X-SVR), is presented to estimate the governing relationship between the uncertain system parameters and the structural natural frequencies. Subsequently, by applying the Monte-Carlo Simulation (MCS) through the established regression model, various types of statistical characteristics (i.e., mean, standard deviation, probability density function or PDF, and cumulative distribution function or CDF) of structural natural frequencies can be effectively established. Four numerical examples including test functions and practically stimulated engineering structures are thoroughly investigated herein to demonstrate the accuracy, applicability, and computational efficiency of the proposed approach.