Seismic Response of SDOF Systems by Wavelet Modeling of Nonstationary Processes

A wavelet-based random vibration theory is presented in this paper to predict the stochastic seismic response of a single-degree-of-freedom system. Functions of wavelet coefficients are used to model ground motions as nonstationary processes in terms of both amplitude and frequency nonstationarity. An orthogonal basis function has been proposed for this purpose. An input-output relationship is developed and closed form solutions are obtained for the output instantaneous power spectral density function and its moments. These moments are used to predict the response statistics of interest. The largest peak amplitude is predicted based on the existing first passage formulation, whereas the higher order peak amplitudes are estimated by using the order statistics approach for an “equivalent” stationary process. The proposed formulation has been validated through statistical simulation in the cases of two example motions and several single-degree-of-freedom oscillators.