A spectral-based Monte Carlo algorithm for generating samples of nonstationary Gaussian processes

Abstract

A Monte Carlo algorithm is developed for generating samples of arbitrary real-valued nonstationary Gaussian processes. The algorithm is based on representations of these processes by finite sums of harmonics with dependent Gaussian coefficients, in contract to similar representations available for stationary Gaussian processes that have independent Gaussian coefficients. The proposed algorithm is based on an idea in [Grigoriu, J. Eng. Mech., ASCE 119: 328–343, 1993]. It is shown that the covariance matrix of the random coefficients in the representation proposed for nonstationary Gaussian processes can be obtained simply from ordinates of the generalized spectral densities of these processes. Two numerical examples are presented to illustrate the application of the proposed algorithm and assess its performance. The examples are a stationary Gaussian process and a nonstationary Gaussian process obtained from a stationary process by distorting its time scale.