Selection of wavelet basis function in the simulation of seismic response spectrum

Based on the target power spectrum, this paper proposed a method for selecting wavelet basis function in the simulation of seismic response spectrum from a quantitative point of view. Firstly, we revised the different wavelet coefficients that correspond to different wavelet basis functions to simulate the seismic response spectrum. And then we set two quantitative indices, i.e., overall error absolute values and mean square errors to describe the differences between the power spectrum of the simulated wave and the target power spectrum. Using the principle of independent weight in mathematical statistics, we obtained the comprehensive evaluation values of the quantitative indices that correspond to the different wavelet basis functions. Finally, from all of the comprehensive evaluation values, we got the optimal wavelet basis with highest simulation accuracy and minimum discreteness of error. Using this method, we selected eight kinds of common wavelet basis functions for instance analysis. The results show that the optimal simulated wave based on this method has slight difference from the original signal, and simulated wave response spectrum coincides well with the target response spectrum, the same as power spectrum, verifying the correctness of the method proposed in this paper.