Modeling and Simulation of Nonstationary Processes Utilizing Wavelet and Hilbert Transforms

Abstract

An approach is proposed for modeling and simulating nonstationary earthquake ground motions that utilizes stationary wavelet and Hilbert transforms. The proposed model is based on the time-frequency representation of a process, which is essential for capturing the nonstationary characteristics of earthquake ground motions. Stationary wavelet transform is first utilized to decompose a sample of a multicomponent nonstationary random process into a set of monocomponent signals. These signals are subsequently transformed to analytic signals using the Hilbert transform, which yields the instantaneous amplitudes and frequencies. Without the customary assumption of piecewise stationarity or reliance on an assumed modulation function, this approach is able to simulate nonstationary random processes, such as earthquake ground motion, based on a sample realization of the process and its instantaneous features. The method is extended to the simulation of multivariate random processes utilizing the proper orthogonal decomposition. Example simulations of measured ground-motion records are presented to demonstrate the efficacy of the proposed scheme. Utilization of this method for simulation of gust fronts is also discussed, further emphasizing the utility of this new framework for the simulation of a host of nonstationary processes with their respective features.