Time–Frequency Spectral Representation Models to Simulate Nonstationary Processes and Their Use to Generate Ground Motions

Abstract

In the present study, two new models are proposed to model nonstationary stochastic processes with time-frequency-dependent spectra and coherence. The models are developed based on the discrete orthonormal S-transform and are enhanced by using the time-frequency representation from the S-transform. One of the models is shown to be usable in carrying out the conditional simulation. A parallel is drawn between the proposed models and those based on the spectral representation method using the ordinary Fourier analysis to facilitate an understanding of the proposed models. Unlike the use of the evolutionary spectral theory, no amplitude modulation or frequency modulation functions need to be assigned and identified for the proposed models because they are included explicitly in the time-frequency spectra. Moreover, the use of the S-transform and discrete orthonormal S-transform provides a familiar time-frequency spectral representation rather than the timescale representation obtained from the wavelet transform. The exposition and use of the models are focused on the simulation of ground motions at single and multiple support, although the models can be equally applicable to nonstationary processes, such as the winds and waves. The adequacy of the simulated ground motion records is assessed in terms of the time-frequency spectral representation and response spectrum. Numerical examples, including conditionally simulate ground motions, are also given.