Simulation of fully nonstationary random processes using generalized harmonic wavelets

Abstract

Simulation of nonstationary random processes plays an important role to probabilistic response analysis of structures and systems under stochastic excitations via Monte Carlo methods. Based on the evolutionary spectral representation theory, this article proposes a novel approach to simulate one-dimensional nonstationary random processes by using generalized harmonic wavelet (GHW). According to the explicit relationship between the evolutionary power spectral density (EPSD) and GHW coefficients, the samples of a random process can be generated by superposing GHWs with stochastic phase angles. The attractive features of the proposed approach are (1) the sample time histories obtained by the proposed method can accurately match the target EPSD and reflect the evolutionary probabilistic characteristics of the random process, (2) the number of GHWs used in the simulation is fixed due to the constraint relationship between the frequency and time resolutions of GHWs, and (3) the proposed method has better computational efficiency than the classical spectrum representation method (SRM). To demonstrate the accuracy and efficiency of the proposed GHW-based approach, three case studies involving the generation of time history samples from a given EPSD model, the simulation of an actual earthquake record, and a comparison between the proposed method and the SRM are presented respectively.