Simulation of non-stationary and non-Gaussian random processes by 3rd-order Spectral Representation Method: Theory and POD implementation

Abstract

This paper introduces the $3^{rd}$-order Spectral Representation Method for simulation of non-stationary and non-Gaussian stochastic processes. The proposed method extends the classical $2^{nd}$-order Spectral Representation Method to expand the stochastic process from an evolutionary bispectrum and an evolutionary power spectrum, thus matching the process completely up to third-order. A Proper Orthogonal Decomposition (POD) approach is further proposed to enable an efficient FFT-based implementation that reduces computational cost significantly. Two examples are presented, including the simulation of a fully non-stationary seismic ground motion process, highlighting the accuracy and efficacy of the proposed method.