RBFNN for Calculating the Stationary Response of SDOF Nonlinear Systems Excited by Poisson White Noise

Abstract

Random perturbations in nature described by non-Gaussian excitation models are far more widely applied and development prospects than that of Gaussian excitation models in practice. However, the stochastic dynamics research of non-Gaussian excitation is still not very mature. In this work, radial-basis-function-neural-network (RBFNN) is applied for calculating the stationary response of single-degree-of-freedom (SDOF) nonlinear system excited by Poisson white noise. Specifically, the trial probability-density-function (PDF) solution of reduced generalized-Fokker–Plank–Kolmogorov (GFPK) equation is constructed by a suitable number of Gaussian basis functions (GBFs) with a fixed set of means and standard deviations. Subsequently, an approximate squared error of the GFPK equation in a finite domain is considered. Together with the normalization condition, the approximate squared error can be minimized by establishing a Lagrangian function, and then the optimal weight coefficients associated with the approximate PDF solution are solved from a system of linear algebraic equations. For demonstrating the effectiveness of the proposed procedure, two specific examples are presented. The corresponding reduced GFPK equation is truncated with higher order for the strong non-Gaussian case. The precision of the analytical solution is verified against the Monte Carlo simulation (MCS) data. In addition, all the results indicate that RBFNN shows fairly high efficiency under the premise of ensuring high precision in the whole computational procedure.