Response analysis of non-Gaussian randomly excited systems via minimum cross entropy method

Abstract

A method based on the minimum cross entropy principle is presented for obtaining approximately the response distributions of nonlinear systems subjected to non-Gaussian random excitation. The response distributions are determined according to the minimization of the cross entropy (or the Kullback-Leibler divergence measure) between an a priori probability density and the estimated probability density under the constraints for the statistical moments of the response. The a priori probability distribution approximates the exact response distribution. In this paper, as the constraint conditions, the moment equations and the normalized condition of the probability density are used, and three types of a priori distributions are given by taking account of the bandwidth ratio between the excitation and the system. In order to demonstrate the validity of the method, a Duffing oscillator subjected to non-Gaussian excitation is analyzed by using the proposed procedure. Bimodal and gamma distributions are used for the excitation distribution. These distributions are highly non-Gaussian, and are different from each other. We compare the analytical results with the results obtained by Monte Carlo simulation and the maximum entropy method. It is shown that the proposed method yields the better approximate solutions than that obtained through the maximum entropy method. The numerical examples indicate the effectiveness of the a priori distribution described in this paper.