FFT-Based Simulation of Multi-Variate Nonstationary Random Processes

Abstract

A technique based on the fast Fourier transform (FFT) is developed to simulate a multivariate nonstationary Gaussian random process with a prescribed evolutionary spectral description. The utilization of the FFT algorithm has been made possible by a stochastic decomposition technique. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time-dependent weights which are simulated by the FFT algorithm. A general procedure is presented to express the spectral characteristics of the multivariate uni-dimensional process in terms of the desired expansion. The effectiveness of the proposed technique is demonstrated by means of three examples with different evolutionary spectral characteristics derived from past earthquake events. The closeness between the target and the corresponding estimated correlation structure suggests that the simulated time series reflect the prescribed probabilistic characteristics extremely well. The simulation approach is computationally efficient, particularly for simulating large numbers of multiple-correlated nonstationary random processes.