Simulation of Multivariate Nonstationary Random Processes by FFT

Abstract

The fast Fourier transform (FFT) technique is utilized to simulate a multivariate nonstationary Gaussian random process with prescribed evolutionary spectral description. A stochastic decomposition technique facilitates utilization of the FFT algorithm. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time‐dependent weights that are simulated by the FFT algorithm. The desired evolutionary spectral characteristics of the multivariate unidimensional process may be prescribed in a closed form or a set of numerical values at discrete frequencies. 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.