High-Efficiency Simulation Method for Nonstationary and Non-Gaussian Stochastic Ground Motion

The actual ground motion is not only time-frequency nonstationary, but also shows the fat-tailed non-Gaussianity of marginal distribution. An efficient simulation method of nonstationary and non-Gaussian stochastic process is proposed. First, the cubic Hermite polynomial model (HPM) is extended to quartic and simplified quintic cases, the monotone transformation model of the autocorrelation function (ACF) and the corresponding applicable range are given, and linear moments (L-moments) are introduced to solve the unknown shape coefficients. Then, based on the higher-order HPM, a noniterative method for estimating the evolutionary power spectral density (EPSD) of the underlying Gaussian process is proposed. Finally, the spectral representation method (SRM) based on proper orthogonal decomposition (POD) is used so that the underlying Gaussian process can be obtained efficiently via a few fast Fourier transforms (FFTs), so as to translate into the target non-Gaussian process according to the established HPM. The numerical examples show the exceptional performance of the high-order HPM in non-Gaussian translation, while affirming the proposed method’s efficiency and accuracy in simulating fully nonstationary and non-Gaussian ground motion.