A candidate method for prediction of the non-stationary response of strongly nonlinear systems under wide-band noise excitation

Abstract

This paper expands the application of the RBFNN method to the prediction of non-stationary responses in strongly nonlinear systems subjected to wide-band noises (WBNs) excitation. Specifically, the SAM is initially employed to deduce the averaged Fokker–Planck–Kolmogorov (FPK) equation. The non-stationary responses of the energy of the system under WBNs are modeled as a one-dimensional Markov diffusion process. This yields a one-dimensional FPK equation that governs the NSRs of the system subject to WBNs. Subsequently, solving the corresponding FPK equation and obtaining the system’s NSRs are accomplished with the RBFNN method. Furthermore, four indicative cases exposed to WBNs are studied to verify the proposed scheme. Comparisons with simulations demonstrate the accuracy and efficiency of the developed technique.