Simulation of stationary ground motion processes: hybrid orthogonal expansion-random function approach

Referring to the orthogonal expansion of stochastic processes, a hybrid orthogonal expansion-random function approach was proposed. Firstly, the stochastic process was expanded as a linear combination of normalized orthogonal basis functions and standard orthogonal random variables. Using the definition of random function, these standard orthogonal random variables in the expanded formula were then denoted by the orthogonal function form of a basic random variable. Through investigating three different forms of orthogonal random functions, the original stochastic process can be readily functioned by a single basic random variable. Compared to the existing representative schemes of stochastic process such as the classic Karhunen-Loeve decomposition and the pure orthogonal expansion, the proposed approach can accurately capture the second-order statistics using only a basic random variable, which bypasses the essential challenge in solving the Fredholm integral equation. A numerical example with power spectral density function of stationary ground motion was investigated to demonstrate the effectiveness and advantages of the hybrid approach.