Stochastic modeling and simulation of ground motions using complex discrete wavelet transform and Gaussian mixture model

Abstract The aim of this research is to develop a stochastic model for generating synthetic ground motions in accordance with a recorded ground motion. In this model, Complex discrete wavelet transform is used to extract wavelet coefficients of a ground motion, and the Gaussian mixture distribution to capture the statistical behavior and simulate these coefficients. Synthetic ground motion is generated by applying inverse wavelet transform to synthetic wavelet coefficients that are extracted based on the fitted Gaussian mixture models and a random sign generator. This model is able to generate an ensemble of synthetic ground motions with temporal and spectral nonstationary characteristics similar to those of the recorded ground motion. In contrast to the previous models, the Gaussian mixture model is able to simulate several dominant frequency peaks at each time, multiple peaks in the temporal amplitude of ground motions, and near-fault ground motions containing several pulses. Also, the Gaussian mixture model provides good estimates of the energy distribution and the inelastic response spectrum of recorded ground motions. Besides these capabilities, the proposed model demands much less computational effort than the previous models.