Comparison of Different Methods of Wavelet and Wavelet Packet Transform in Processing Ground Motion Records

Future design procedures for civil structures, especially those to be protected from extreme and blast relatedloads, will need to account for temporal evolution of their frequency content. There are, however, several instanceswhere acceleration time histories are required as seismic input. For example, to determine the ultimate resistance andto identify modes of structures’ failure, a nonlinear time history analysis is needed. In other cases, acceleration timehistories are required for linear analyses. Many seismic codes require this type of analysis for buildings which haveirregularities. The process of time-frequency analysis made possible by the wavelet transform provides insight into thecharacter of transient signals through time-frequency maps of the time variant spectral decomposition that traditionalapproaches miss. In this paper an approach is examined and a new method for processing the ground motion which ismodeled as a non-stationary process (both in amplitude and frequency), is proposed. This method uses the best basissearch algorithm with wavelet packets. In this approach, the signal is expressed as a linear combination of timefrequencyatoms which are obtained by dilations of the analyzing functions, and are organized into dictionaries aswavelet packets. Several numerical examples are given to verify the developed models.