Evaluating the performance of different mother wavelet functions for down-sampling of earthquake records

Abstract

Application of discrete wavelet transform for down-sampling earthquake records has been started since 2002. Although the mother wavelet function plays an important role in the accuracy of wavelet transform, there is no study to investigate the effect of this function on dynamic analysis error. In addition, most studies have used a limited number of earthquake records for down-sampling application of wavelet transform. Therefore, in this paper, a comprehensive study is performed on 36 different mother wavelet functions and 100 earthquake records. The linear and nonlinear response spectra of the main records and their down-sampled ones have been used to evaluate the performance of different mother wavelet functions. Approximate waves are obtained for three levels using wavelet transform. Also, dynamic analyses are done for 101 single-degree-of-freedom systems (with a period between 0 and 5 s) and 5 behavior coefficients consisting of more than 7 million analyses. Results show that the Daubechies family of wavelet functions used in previous studies for down-sampling earthquake records often cause errors greater than 15%. But the Biorthogonal wavelet functions which have not been used for down-sampling before, have an error of less than 2.5% and are the best wavelet functions for down-sampling earthquake records. In addition, a method called wavelet functions combination is presented to ensure minimum errors at different levels of down-sampling. In the next step, to evaluate the effect of the wavelet function on the accuracy of dynamic analysis of real structures, 3, 9, and 20 story structures are analyzed using the IDA method and finally, an irregular structure is also analyzed. The results obtained from the nonlinear analysis of these structures show that Biorthogonal wavelet functions can reduce the wavelet error from 27% to 6%.