Simulation of Multi-Variate Stationary and Nonstationary Random Processes: A Recent Development

Abstract

This paper present computationally efficient procedures to simulate multivariate stationary random processes for any desired time duration, and nonstationary processes consistent with prescribed evolutionary spectrum. The simulation of multi-variate stationary random processes is based on the simple convenience of conventional FFT-based simulation schemes, but without the drawback of large computer memory requirement that has in the part precluded the generation of long-duration time series utilizing the FFT-based approaches. Central to this technique is a simulation of a large number of time series segments by utilizing the FFT algorithm, which is followed by their synthesis by means of a digital filter to obtain the desired length of simulated time series. The effectiveness of this methodology is demonstrated by means of examples concerning the simulation of a multi-variate random wind field and the spatial variation of wave kinematics in a random sea. The simulation of multi-variate nonstationary random processes is also based on FFT algorithm. The utilization of FFT has been made possible by a stochastic decomposition technique. The decomposed spectral matrix is expanded into a weighted summation of basic functions and time-dependent weights which are simulated by FFT. The effectiveness of the proposed technique is demonstrated by means of examples of the past earthquake events. This approach is computationally very efficient in simulating a large set of nonstationary processes, such as ground motion, that are needed for ensemble averaging of the response time histories.