Efficient simulation method of fully nonstationary stochastic vector processes via generalized harmonic wavelet.

• A GHW-based method to simulate fully nonstationary stochastic vector processes is proposed. • This method improves the computing efficiency of vector process simulation by reducing the numbers of random variables. • The relationship between the cross spectrum matrix and the GHW coefficients of vector process is derived. Currently, the most common approach to simulate stochastic vector processes for structural dynamic reliability analysis is the Spectral Representation Method (SRM), characterized by a superposition of amplitude-modulated trigonometric functions with random phase angles. However, to represent the vector processes completely, the SRM requires the sampling of a large number of independent random variables, that may cause a large amount of computational cost for the time history sample generation and structural reliability calculation. To reduce the number of random variables, this paper presents a method based on the generalized harmonic wavelet (GHW) to simulate fully nonstationary stochastic vector processes. First, the relationship between the GHW coefficients and the evolutionary cross spectrum matrix of the stochastic vector process is derived. Then, based on the inverse GHW transform, a general simulation formula by superposing GHWs is proposed. The corresponding simplified method which requires less independent random variables is also presented. At last, a numerical case study is provided to emphasize the efficiency of the proposed method. The result indicates that, due to the localization of the energy distribution of the GHW in the time–frequency domain, the proposed method could generate the stochastic vector process samples using less components and is more efficient than the SRM. This method has high potential for application in the Monte Carlo simulation of spatially variable seismic ground motions or wind velocities for structural dynamic reliability analysis. [ABSTRACT FROM AUTHOR]