Response distribution of nonlinear systems subjected to non-Gaussian random excitation using Gaussian mixture model

Abstract

The method using Gaussian mixture model and moment equations is developed to obtain the probability density of the stationary response of a nonlinear system subjected to non-Gaussian random excitation. The excitation is characterized by the probability density function and the power spectrum. In this paper, the stationary response distribution of the system is approximated by the Gaussian mixture model, which is expressed by the weighted sum of several Gaussian distributions with the different parameters. The parameters in the model are determined according to the moment equations for the response and the excitation. The proposed method is applied to a Duffing oscillator subjected to non-Gaussian excitation with the gamma distribution and the power spectral density characterized by the bandwidth parameter. The analytical results of the stationary response distributions are compared with simulation results. The results show this method is valid for the highly skewed excitation with a wide range of the bandwidth parameter. The influences of the shape of the distribution and the bandwidth of the excitation on the response distributions are also investigated.