Spectral representation-based dimension reduction for simulating multivariate non-stationary ground motions

A framework of spectral representation-based dimension reduction for simulating multivariate non-stationary stochastic ground motion processes is addressed in this paper. By means of introducing random functions serving as constraints correlating with the orthogonal random variables in the original spectral representation scheme, the high-dimensional randomness degree involved in the multivariate stochastic processes can thus be reduced substantially. To this aim, three random function forms considering the combination of trigonometric functions and orthogonal polynomials are constructed for simulation purpose. Accordingly, the accurate representation of the original stochastic processes is realized with merely three elementary random variables, overcoming the principal challenge of numerous random variables faced by the Monte Carlo simulation method. Also, the consistency of the statistics between the sample functions of stochastic ground motions and strong motion records is established with update of the ground motion model parameters in stochastic simulation techniques. Numerical investigations involving the comparisons with the Monte Carlo simulation method and the validation based on the strong motion records are presented to demonstrate the superiority and effectiveness of the proposed methodology in practical engineering applications.