The seismic ground motions are nonstationary stochastic processes and vary from site to site. The time histories of synthetic ground motions are used for nonlinear inelastic structural dynamic analysis since the historical records are limit or unavailable for a particular scenario seismic event. This is especially the case for structures with multiple supports. The characteristics of the nonstationary stochastic ground motions depend on the earthquake magnitude, fault mechanism, source-to-site distance, and local site conditions. The characteristics could be represented by time-frequency (dependent) power spectral density (TFPSD) and coherence functions. The assessment of such power spectral density and coherence functions are presented by using historical records and the S-transform – a Fourier transform with time localized and frequency-dependent windows – is carried out. New models of the TFPSD function and coherence function are presented. Also, new time-frequency spectral representation methods (TFSRMs) to simulate nonstationary stochastic processes are proposed. The TFSRM is developed by taking the advantages of the orthonormal basis functions in the discrete orthogonal S-transform (DOST) and the refined time-frequency representation obtained by using the S-transform. TFSRM can be used to simulate ground motions at a single site or multiple sites. They can also be used to simulate seismic ground motions conditioned on observed ground motions. TFSRM can cope with the time-varying lagged coherence function; this is not the case with the well-known spectral representation method (SRM).
Similar to the SRM, the direct use of TFSRM leads to Gaussian processes (stationary or nonstationary). However, there is indicates that the seismic ground motions may not be Gaussian. A new iterative power and amplitude correction algorithm is proposed to simulate nonstationary non-Gaussian stochastic processes. This procedure is successfully implemented and illustrated by numerical examples
