Statistical bilinearization in stochastic nonlinear dynamics

A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system is approximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this Volterra series. The parameters of the bilinear system are determined by minimizing the difference between the original system and the bilinear system in a statistical sense. Application to a piece-wise linear system illustrates the effectiveness of this approach in approximating truly nonlinear, stochastic response phenomena in both the statistical moments and the power spectral density of the response of this system in case of a white noise excitation.