基于小波包方法的非平稳地震动模拟和设计谱拟合

Simulation of non-stationary ground motions and fitting of design spectrum based on wavelet packet method

提出了一种基于小波包分解和重构的模拟非平稳地震动并拟合设计谱的方法.该方法模拟出工程用地震动并调整频率分量,使其以一定的精度拟合设计谱.首先,利用5个参数生成了构成地震动加速度时程的小波包系数矩阵,并通过小波包重构获得加速度时程,该系数矩阵模拟了实际地震记录中频率随持时逐渐减小的特点.其次,将模拟的地震动利用小波包分解方法分解为具有高分辨率非重叠的小波包系数矩阵,然后根据设计谱调整频率分量.数值算例表明,该方法模拟的不同持时的加速度时程均能吻合同一设计谱,且迭代后仍然能保留地震动的非平稳特性.另外,该方法具有较稳定和较快的收敛过程,能在有限次调整迭代中实现较高的拟合精度.

A method to simulate the non-stationary ground motions and fit the design spectrum is proposed based on wavelet packet decomposition and reconstruction. The method simulates ground motions for engineering and adjusts its frequency components so that the response spectrum will fit the design spectrum. Firstly, the wavelet packet coefficient matrix for ground motion acceleration time history is generated using 5 parameters, which characterizes the frequency attenuation with duration in real recordings. The acceleration time history can be obtained by wavelet packet reconstruction. Then, by wavelet packet decomposition the simulated ground motion is decomposed into a desired number of wavelet packet coefficient matrices with high resolution and non-overlapping frequency contents, and then the frequency component is adjusted for matching the response spectrum of the simulated accelerogram with the acceleration time histories with specified design spectrum. Numerical example demonstrates that different durations simulated by the proposed method all fit the design spectrum. The accelerograms keep the non-stationarities of ground motion even after iteration. Moreover, the method is stable and fast for convergence, and can achieve high fitting accuracy in limited iteration times.