Transient probabilistic analysis of nonlinear systems excited by correlated external and parametric Gaussian white noise

This paper explores using the exponential-polynomial-closure (EPC) method to analyze the transient probabilistic solutions to nonlinear stochastic oscillators excited by correlated external and parametric Gaussian white noise. The probabilistic solution to the transient responses of the nonlinear oscillator is governed by the Fokker–Planck–Kolmogorov (FPK) equation, in which the solution is denoted as an exponentially polynomial function with time-variant coefficients. These coefficients can be solved numerically by introducing a proper weighted function and making the projection of the residual error vanish. Meanwhile, three numerical examples are presented to verify the effectiveness and efficiency of the EPC method for analyzing the nonlinear oscillators through the comparisons with the Monte Carlo simulation (MCS) method. Moreover, the influence of the correlation coefficient between the excitations of external and parametric Gaussian white noise is investigated.