基于离散谐小波变换的地震波时变谱估计及非平稳地震波人工合成  

Time-varying spectrum estimation and artificial non-stationary ground motion simulation via dyadic harmonic wavelet transform

作　　者：樊剑[1,2] 吕超[1] 张辉[1] 

机构地区：[1]华中科技大学土木工程与力学学院,中国武汉430074 [2]华中科技大学控制结构湖北省重点实验室,中国武汉430074

出　　处：《地震学报》2009年第3期333-341,共9页Acta Seismologica Sinica

基　　金：国家自然科学基金项目(50778079)资助

摘　　要：采用在频域内具有极好紧支性和盒形特性的谐小波作为母小波,推导了基于离散谐小波变换的地震波时变谱,并给出了不同尺度下能量随时间变化的包络函数的近似解析表达式.文中以Northridge地震波为例分析了时频分布特征.研究发现,对于自振频率为f的结构,其地震反应与输入地震波的时变谱在f处的时域最大值(即maxt∈Tp[p(f,t)])以及地震波在f频率点附近的信号分量在时域内的能量集中程度有很大的关系;与db4小波基相比,利用谐小波作为母小波的小波变换,其频域具有较好的分辨率,但时域分辨率却较差.最后提出了两种基于离散谐小波逆变换的人工非平稳地震波仿真方法.Explicit mathematical expression of time-varying spectrum of non-stationary ground motion is derived by using the harmonic wavelet transform. The choice of harmonic wavelet is made because it is defined by a simple explicit for- mula and they are exactly boxlike representation in frequency domain. The time-frequency characteristic of seismic wave of Northridge earthquake is ana- lyzed through numerical examples. It is showed that the seismic response of the structure with natural frequency f is remarkably related to the time domain maximum of time-varying spectrum of input ground motion and the energy concentration degree of the signal component at the scale corresponding to the frequency. The frequency domain resolution is better and the time domain resolution is worse by using the harmonic wavelet than by using the db4 wavelet, but the explicit formula of time-frequency spectrum can be obtained by using the harmonic wavelet. Finally, the method of generating artificial non-stationary ground motion is presented based on dyadic harmonic wavelet.

关 键 词：谐小波变换 时变谱 非平稳地震波 

分 类 号：TN912.3[电子电信—通信与信息系统] TP391.41[电子电信—信息与通信工程]