On the simulation of stochastic processes by spectral representation

In this paper, a modification in the simulation formula for generating stationary stochastic processes, using the spectral representation method developed by Shinozuka, is presented. It is shown that with this modification, the ensemble and temporal autocorrelation function of the simulated stochastic process for fixed values of time lag τ converge to their target autocorrelation function much more quickly. If the sample function is synthesized with N frequencies, then the rate of the convergence is of the order 1/N4 instead of 1/N for the original simulation formula. However, for the whole simulation time T0, the convergences of the autocorrelation functions are not uniform for the time lag τ throughout the range from 0 to T0/2. It turns out that the proposed modified simulation formula is preferable for the time lag |τ| ⩽ T0/2π and the original simulation formula is preferable for the time lag T0/2π < |τ| ⩽ T0/2.