基于现代时频分析技术的地震波时变谱估计
|
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。
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.
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.
引文
[1]Jun Iyama,Hitoshi Kuwamura.Application of wavelets to a-nalysis and simulation of earthquake motions[J].Earthquake Engineering and Structural Dynamics,1999,28:255—272.
[2]Biswajit Basu,Vinay K.Gupta.Seismic response of SDOF sys-tems by wavelet modeling of non-stationary processes[J].Journal of Engineering Mechanics,1998,124:1142—1150.
[3]Basu B,Gupta V K.Wavelet-based analysis of the non-sta-tionary response of a slipping foundation[J].Journal of Sound and Vibration,1999,222:547—563.
[4]Sushovan Mukherjee,Vinay K.Gupta.Wavelet-based charac-terization of design ground motions[J].Earthquake Engineer-ing and Structural Dynamics,2002:31,1173—1190.
[5]Kurtis Gurley,Ahsan Kareem.Application of wavelet trans-forms in earthquake,wind,and ocean engineering[J].Engi-neering Structures,1999,21:149—167.
[6]Spanos P D,Giuseppe Failla.Evolutionary spectra estimation using wavelets[J].Journal of Engineering Mechanics,2004,130:952—960.
[7]曹晖,赖明,白绍良.地震地面运动的局部谱密度描述及其估计方法[J].世界地震工程,2004,20(2):43—49.
[8]科恩.时频分析:理论与应用[M].白居宪译.西安:西安交通大学出版社,1997.
[9]彭玉华.小波变换与工程应用[M].北京:科学出版社,2003.
[10]Pinnegar C R.Time-frequency and time-time filtering with the S-transform and TT-transform[J].Digital Signal Process-ing,2005,15:604—620.
[11]Pinnegar C R,Mansinha L.Time-local Fourier analysis with a scalable,phase-modulated analyzing function:the S-trans-form with a complex window[J].Signal Processing.2004,84:1167—1176.
[2]Biswajit Basu,Vinay K.Gupta.Seismic response of SDOF sys-tems by wavelet modeling of non-stationary processes[J].Journal of Engineering Mechanics,1998,124:1142—1150.
[3]Basu B,Gupta V K.Wavelet-based analysis of the non-sta-tionary response of a slipping foundation[J].Journal of Sound and Vibration,1999,222:547—563.
[4]Sushovan Mukherjee,Vinay K.Gupta.Wavelet-based charac-terization of design ground motions[J].Earthquake Engineer-ing and Structural Dynamics,2002:31,1173—1190.
[5]Kurtis Gurley,Ahsan Kareem.Application of wavelet trans-forms in earthquake,wind,and ocean engineering[J].Engi-neering Structures,1999,21:149—167.
[6]Spanos P D,Giuseppe Failla.Evolutionary spectra estimation using wavelets[J].Journal of Engineering Mechanics,2004,130:952—960.
[7]曹晖,赖明,白绍良.地震地面运动的局部谱密度描述及其估计方法[J].世界地震工程,2004,20(2):43—49.
[8]科恩.时频分析:理论与应用[M].白居宪译.西安:西安交通大学出版社,1997.
[9]彭玉华.小波变换与工程应用[M].北京:科学出版社,2003.
[10]Pinnegar C R.Time-frequency and time-time filtering with the S-transform and TT-transform[J].Digital Signal Process-ing,2005,15:604—620.
[11]Pinnegar C R,Mansinha L.Time-local Fourier analysis with a scalable,phase-modulated analyzing function:the S-trans-form with a complex window[J].Signal Processing.2004,84:1167—1176.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心