【摘要】 利用短时傅里叶变换(STFT)、Wigner-Ville分布、连续小波变换、S变换以及变复窗口的S变换等现代时频分析技术对地震波进行时变谱估计。推导了基于连续小波变换的小波能量谱的具体表达式,并把近年来提出的变复窗口S变换应用到地震波的时频分析。通过研究表明对于均匀调制非平稳地震波,通过适当选择窗口的长度,利用STFT估计时变谱可得到较好的效果,小波变换与S变换以及变复窗口S变换的估计值在高频段存在能量泄漏现象;各方法估计的时变谱时间边缘函数与目标函数均符合较好;而频率边缘函数,Wigner-Ville分布与目标函数符合得最好,STFT次之,小波变换、S变换以及复窗S变换在高频段存在一定误差。对于频率非平稳性较强的地震波,通过适当地调节窗口参数,利用变复窗口S变换可得到地震波在时频域内有较好分辨率的时变谱;连续小波变换虽然在高频段存在能量泄漏现象,但其在时间域内有较好的分辨率。更多还原

【Abstract】 The Problems of estimating the time-varying spectrum of earthquake ground motions estimation using STFT, Wigner-Ville distribution, continuous wavelet transform, S-transform and improved S-transform with a complex window are addressed. Mathematical expression of wavelet energy spectrum based on continuous wavelet transform was derived. Numerical results show that estimating the time-varying spectrum of separable non-stationary ground motion via STFT is effective provided the width of window is chosen properly, however,wavelet transform,S-transform and improved S-transform will lead to energy overlapping in high frequency range. The improved S-transform is found to be most effective to estimate the time-varying spectrum of ground motion with high non-stationariness in frequency by adjusting the parameter of time window.The continuous wavelet transform has effective time-domain resolution even though the energy overlapping in high frequency range.更多还原