POD-based dimension reduction representation of stochastic ground motion fields

Abstract

In this paper, two kinds of proper orthogonal decomposition (POD) representations for simulating the non-stationary stochastic vector processes are derived based on the basic theory of POD, namely the orthogonal-random-variables-based POD representation and the random-phase-angles-based POD representation. It is clarified that the random-phase-angles-based scheme is a special case of the orthogonal-random-variables-based scheme, and the differences between them are analyzed from the number of elementary random variables and the constraint conditions. It is found that the randomness degree (the number of elementary random variables) of the non-stationary stochastic vector processes could be greatly reduced by introducing some appropriate constraint conditions. To this end, the efficient dimension reduction simulation of the non-stationary stochastic vector processes with just two elementary random variables is realized through introducing more rigorous constraints on the orthogonal random variables in the orthogonal-random-variables-based scheme. Also, the complete probability information of the stochastic processes is fully emerged. Through the numerical analysis of the ground motion stochastic field simulation, it is obtained that the relative errors of the mean and standard deviation, evolutionary power spectrum and coherence function of the non-stationary ground motion acceleration vector process are all in good agreement with the corresponding target values, which shows that the proposed method is effective and accurate. Meanwhile, in order to further verify the applicability of this method in terms of engineering characteristics upon ground motion, according to the five classes of the typical soil sites divided in “Seismic ground motion parameters zonation map of China”, 920 strong motion records are selected for comparing and analyzing the response spectrum and the Fourier amplitude spectrum of ground motion acceleration, respectively. The research shows that the simulation results of the proposed method have good consistency with the strong motion records, which lays a solid foundation for this proposed method applied in engineering applications.