Seismic response evaluation of structures using discrete wavelet transform through linear analysis

In this article, the discrete wavelet transform (DWT) has been used to construct the wavelet response spectrum analysis (WRSA) of structures in the linear elastic zone. For this purpose, the elastic response spectra of different single degree of freedom (SDOF) systems are studied for different beam-to-column stiffness ratios. Initially, using the DWT, the records of nearand far-field earthquakes are decomposed into three levels. Finally, the linear response spectra of the SDOF systems are constructed subjected to the main and decomposed earthquakes. In the end, the error values for different levels of decompositions are computed using the considered error estimation criteria. The results show that using WRSA, the computational volume of time history analysis has reduced since the consuming time to perform the analysis has significantly reduced (e.g., it reduces the computational cost by almost 50% in the first decomposition level). In addition, the results indicate that the highest error values occur for the structures with a beam-to-column stiffness ratio equal to one. However, for the structures with ratios of greater than one, the values of error reduced. For the conventional structures where the ratio is less than one and the natural period is in the range of 0.5 s and 10 s, the error values are <10%. Results also revealed that, except for the structures with beam-to-column stiffness ratio equal to one, in all the other cases, the values of error for the structure subjected to the near-field earthquakes are less than those of the far-field ones. Furthermore, the results obtained from the SDOF system analysis were investigated for several multi-degree-of-freedom structures with a linear behavior.