Efficient simulation of multivariate non-stationary ground motions based on a virtual continuous process and EOLE

Abstract

Simulation of multivariate non-stationary ground motions (MNSGM) is of paramount importance to seismic reliability evaluation of large-span structures, e.g., bridge and dome structures. In this paper, the expansion optimal linear estimation (EOLE) method is extended to the simulation of MNSGM with high efficiency. A virtual continuous process is proposed to connect the multivariate ground motions to formulate a 1D−1V process. In that regard, the main work of this study is to obtain the expanded covariance/correlation matrix for the virtual 1D−1V process including the auto- and cross-correlation information, which will be determined by using inverse Fourier transform from the corresponding auto- and cross-evolutionary power spectrum density (EPSD) functions. Then, the EOLE method is applied to generate the 1D−1V virtual continuous process by decomposing the expanded covariance/correlation matrix. Finally, the MNSGM can be easily obtained by splitting the 1D−1V virtual continuous process correspondingly. The most attractive feature of the proposed method is that it only needs to decompose the covariance/correlation matrix once, which effectively circumvents the computational challenge of classic spectral representation method (SRM) for simulating MNSGM. Besides, two types of modulation functions for non-stationarity, i.e., the time- and time–frequency-modulations are considered. Two examples, involving the simulation of two types of MNSGM are presented to verify the effectiveness of this approach.