An efficient ergodic simulation of multivariate stochastic processes with spectral representation

Abstract

A simulation formula to generate stationary multivariate stochastic processes is derived from the Fourier–Stieltjes integral of spectral representation. It is proved that the proposed algorithm generates ergodic sample functions in the mean value and in the correlation when the sample length is equal to one period (the generated sample functions are periodic). The algorithm is very efficient computationally since it takes advantage of the fast Fourier transform technique. The simulation of longitudinal wind velocity fluctuations and the simulation of longitudinal and vertical wind fluctuating components on a bridge deck are performed. It has been noted that there are good agreements between the temporal and target auto-/cross-correlation functions of simulated wind velocities.