Efficient ground motion conditional simulation method for nonstationary multivariate processes based on Kriging method and orthogonal discrete wavelet transform

Abstract

Conditional ground motion simulation methods preserve more physical features of actual ground motions than unconditional methods by including actual earthquake records. This study developed a conditional multivariate nonstationary process simulation method based on the combination of the Kriging method and the orthogonal discrete wavelet transform (DWT). The Kriging method is used to ensure the spectral coherences between simulations as prescribed and is extended to nonstationary random processes by applying it to the average power spectral density (APSD) of ground motions. The ground motions' DWT wavelet coefficients are assumed to be uniformly time-modulated stationary processes whose time-modulating functions are the envelopes of the seed record's wavelet coefficients. The APSD and the envelopes together outline the energy distribution of the random field in both the time and frequency domain features. The power spectral densities of the stationary random processes' DWT coefficients are derived and used to estimate the APSD of the ground motions' DWT coefficients. Approaches to realizing uniformly time-modulated stationary processes with prescribed APSDs and envelope functions are developed. Monte Carlo simulations were conducted to verify the new method's effectiveness. Results show that both the target APSD and coherences can be well approximated, but precise approximation cannot always be realized in the high-frequency range. The new approach possesses a simple structure, involves simple algorithms, and applies to time-independent spectral coherence models, making it an efficient method compared with existing methods.