Assessment of Wavelet-based Representation Techniques for the Characterization of Stochastic Processes Modelling Pulse-like Strong Ground Motions

Recently, the Meyer wavelet packets transform (MWPT), the harmonic wavelet transform (HWT), and the S-transform have been used to process recorded earthquake induced strong ground motions (GMs) in various earthquake engineering and engineering seismology applications. In this paper, the potential of these three wavelet-based time-frequency representation (TFR) techniques to identify and to characterize low-frequency pulse-like content in GMs is assessed. This is achieved by processing ensembles of simulated non-stationary time-histories with known energy content upon appropriately fine-tuning the considered TFRs. Next, the ensemble average wavelet transform is used to characterize the energy distribution of the time-histories on the time-frequency plane, within a Monte-Carlo analysis framework. Specifically, the considered time-histories are realizations of sums of uncorrelated uniformly modulated stochastic processes characterized by analytically known evolutionary power spectra (EPSDs). These EPSDs are judicially defined to model the frequency content of pulse-like GMs. Pertinent numerical results considering EPSDs compatible with the elastic design spectrum of the current European (EC8) aseismic code provisions are included, in which pre-specified pulse-type frequency content is introduced by adding low-frequency "patches of energy". The reported numerical data indicate that the HWT provides for smoother estimates of the considered EPSDs than the MWPT. Further, the S-transform is more accurate than both the HWT and the MWPT in identifying the time location and central frequency of the low frequency components contained in the considered artificial pulse-like accelerograms. Overall, this study sheds light into the challenges of detecting low frequency content “corrupted” by higher frequency components in artificial signals modelling pulse-like accelerograms in an effort to inform best practices in the application of TFR techniques to characterize low frequency pulses in recorded GMs.