Simulation of Multivariate Random Processes: Hybrid DFT and Digital Filtering Approach

Abstract

A numerical simulation technique is presented that combines the advantages of the discrete Fourier transform (DFT) algorithm and a digital filtering scheme to generate continuous long-duration multivariate random processes. This approach offers the simple convenience of conventional fast Fourier transform (FFT) based simulation schemes; however, it does not suffer from the drawback of the large computer memory requirement that in the past has precluded the generation of long-duration time series utilizing FFT-based approaches. Central to this technique is a simulation of a large number of time series segments by utilizing the FFT algorithm, which are subsequently synthesized by means of a digital filter to provide the desired duration of simulated processes. This approach offers computational efficiency, convenience, and robustness. The computer code based on the present methodology does not require users to have experience in determining optimal model parameters, unlike the procedures based on parametric models. The effectiveness of this methodology is demonstrated by means of examples concerning the simulation of a multivariate random wind field and the spatial variation of wave kinematics in a random sea with prescribed spectral descriptions. The simulated data showed excellent agreement with the target spectral characteristics. The proposed technique has immediate applications to the simulation of real-time processes.