Simulation of ergodic multivariate stochastic processes: An enhanced spectral representation method

Abstract

The spectral representation method (SRM) has been extensively used in the simulation of multivariate stationary Gaussian stochastic processes. In this study, an enhanced SRM for the simulation of ergodic multivariate stochastic processes is developed. Through shifting a frequency increment, the enhanced SRM offers a faster convergence rate of probabilistic characteristics in comparison with conventional SRM. The computational efficiency is enhanced as the Cholesky decomposition is only required at single-indexed frequencies. Additionally, a two-dimensional fast Fourier transform (FFT) algorithm is proposed to expedite simultaneously estimation of the double summation of cosine functions in both frequency and space dimensions. Accordingly, compared to the traditional FFT-based SRM, in which FFT is only used for the summation in the frequency dimension, the simulation efficiency is further enhanced significantly. The numerical example concerning the simulation of wind velocity field demonstrates that the proposed method offers a faster convergence rate and a higher level of efficiency.