地震动反应谱拟合过程中小波基函数的选取

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

基于目标功率谱,本文从定量角度提出一种地震动反应谱拟合过程中小波基函数的选取方法.首先通过修正不同小波基函数所对应的小波系数来拟合地震动反应谱;然后设定总体误差绝对值和误差均方差这两个定量指标来描述各拟合波功率谱与目标功率谱的差异,借助数理统计的独立权数原理,求得不同小波基函数所对应的定量指标的综合评价值;最后对比综合评价值,得到拟合精度最高、误差离散最小的最优小波基.应用该方法,选取8种常见的小波基函数进行实例分析.结果表明,该方法得到的最优拟合波与原信号差异不大,拟合波反应谱、功率谱与目标反应谱、功率谱均吻合得较好,从而验证了该方法的正确性.

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.