Simulation of nonstationary processes based on Hilbert spectrum and random phase

Abstract

Simulation of nonstationary processes has become an indispensable tool in engineering. A new method of simulation of nonstationary random processes is presented based on the orthogonal HHT spectra of sample observations. It takes advantage of orthogonal EMD, the instantaneous frequency, amplitude of the Hilbert transform and independent random phase angle, thus overcoming difficulties in the estimation of the frequency modulation and interdependence of frequency and amplitude modulation functions faced by most currently available methods. The new method extract and preserve the true physical features of the process. The examples of earthquake ground motion and subway vibration, as e low frequency and high frequency nonstationary processesses, were simulated in the paper. The time history of sample, Fourier amplitude spectrum of sample and response spectra of sample compare well with those of the records. The methods has great potential for engineering applications when dealing with nonstationary, nonlinear random peocesses.