An Analysis of a Nonlinear System Excited by Combined Gaussian and Poisson White Noises Using Complex Fractional Moments

Abstract

An analytical method using complex fractional moments (CFM) is applied for nonlinear systems under combined Gaussian and Poisson white noises. The CFM is a new kind of statistical moment, which is defined by extending the order of moments to a complex number, and is related to a Mellin transform of a probability density function (PDF). In order to find the PDF of the response of the system, first, we derive the governing equations of the response CFMs by applying a Mellin transform to the generalized Fokker-Planck-Kolmogorov equation. Since the governing equations are linear, they can be solved analytically to get the CFMs. Finally, the inverse Mellin transform to the CFMs yields the response PDF. The effectiveness of the present method is demonstrated by comparing analytical and Monte Carlo simulation results. The influence of parameters of the system and the excitation upon the accuracy of the present method is also discussed.