Applying dual-tree complex discrete wavelet transform and gamma modulating function for simulation of ground motions

Abstract

The aim of this paper is to develop a stochastic-parametric model for the generation of synthetic ground motions (GMs) which are in accordance with a real GM. In the proposed model, the dual-tree complex discrete wavelet transform (DT-CDWT) is applied to real GMs to decompose them into several frequency bands. Then, the gamma modulating function (GMF) is used to simulate the wavelet coefficients of each level. Consequently, synthetic wavelet coefficients are generated using extracted model parameters and then synthetic GM is extracted by applying the inverse DT-CDWT to synthetic wavelet coefficients. This model simulates the time–frequency distribution of both wide-frequency and narrow-frequency bandwidth GMs. Besides being less time consuming, it simulates several dominant frequency peaks at any moment in the time duration of GM, because each frequency band is separately simulated by the gamma function. Moreover, the inelastic response spectra of synthetic GMs generated by the proposed model are a good estimate of target ones. Using the random sign generator in the proposed model, it is possible to generate any number of synthetic GMs in accordance with a recorded one. Because of these advantages, the proposed model is suitable for using in performance-based earthquake engineering.