Error Assessment for Spectral Representation Method in Random Field Simulation

Abstract

Random fields, such as the wind velocity field and the seismic ground motion field, are usually simulated by the spectral representation method (SRM). The SRM mainly relies on two methods: the random amplitudes method and the random phases method. However, the temporal statistics estimated from one SRM-simulated sample process differs from the target characteristics. Such differences can usually be assessed by the statistical errors, i. e., bias errors and stochastic errors. The closed-form solutions of statistical errors produced by random phases method have been given. This paper gives the closed-form solutions of statistical errors produced by the random phases methods and compares the statistical errors produced by both methods. The comparison of the stochastic errors of power spectral density functions produced by different methods demonstrates that (1) the random amplitudes method exhibits higher but more uniformly distributed stochastic errors than the random phases method; and (2) the stochastic errors produced by the random phases method are dependent on the decomposition method, whereas those produced by the random amplitudes method are not.