基于聚类经验模态分解(EEMD)的汶川M_S8.0强震动记录时频特性分析
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摘要
在2008年5月12日汶川MS8.0地震中,四川数字强震台网共获取了133组三分向加速度记录.本文选取了一些不同断层距的台站所获取的强震动记录进行了处理和分析.在数据处理中,采用基于聚类经验模态分解(EEMD)提取信号时频特性的方法,有效获得了信号能量的时频分布,提取了中心频率、Hilbert能量、最大振幅对应的时频等特性,并与傅里叶变换、小波变换进行了对比研究.研究结果表明,对非线性的强震记录采用聚类经验模态分解(EEMD)能抑制经验模态分解(EMD)中存在的模态混叠问题;与傅里叶变换和小波变换相比发现,HHT边际谱在低频处幅值高于傅里叶谱;与小波变换受到所选取的母波强烈影响不同,HHT直接从强震记录中分离出固有模态函数(IMF),更能反映出原始数据的固有特性,Hilbert谱反映出大部分能量都集中在一定的时间和频率范围内,而小波谱的能量却在频率范围内分布较为广泛.因此,基于EEMD的HHT在客观性和分辨率方面都具有明显的优越性,能提取到更多强震加速度记录的时频特性.
During 12 May 2008 Wenchuan MS8.0 earthquake,Sichuan strong motion network obtained 133 sets of 3-componet acceleration records.This paper processed and analyzed some of the records with different station distance from the fault.Using a clustering algorithm based on the ensemble empirical mode decomposition(EEMD),this paper effectively extracted the time-frequency distribution of the signal energy,its central frequency,Hilbert energy and the time-frequency characteristics corresponding to the maximum amplitudes,and made a comparative study of EEMD method with Fourier transform and wavelet transform(WT) analysis.This study obtained the following results:For non-linear strong motion records,EEMD can be used to suppress the mode mixing effect existing in empirical mode decomposition(EMD) decomposition;in comparison with Fourier transform and wavelet transform the Hilbert-Huang transform(HHT) marginal spectrum amplitude is larger than the low frequency Fourier spectrum amplitude;different from strong influence of the selected parent wave on WT,HHT can directly isolate inherent mode function(IMF) from the strong motion record,representing inherent characteristics of the original data;Hilbert amplitude spectrum exhibits the concentration of most energy in a certain time and frequency range,while wavelet spectral energy distribute in a wide frequency range.Therefore,the HHT based on EEMD has obvious advantages in terms of its objectivity and high resolution,being able to extract more time-frequency characteristics of seismic acceleration records.
During 12 May 2008 Wenchuan MS8.0 earthquake,Sichuan strong motion network obtained 133 sets of 3-componet acceleration records.This paper processed and analyzed some of the records with different station distance from the fault.Using a clustering algorithm based on the ensemble empirical mode decomposition(EEMD),this paper effectively extracted the time-frequency distribution of the signal energy,its central frequency,Hilbert energy and the time-frequency characteristics corresponding to the maximum amplitudes,and made a comparative study of EEMD method with Fourier transform and wavelet transform(WT) analysis.This study obtained the following results:For non-linear strong motion records,EEMD can be used to suppress the mode mixing effect existing in empirical mode decomposition(EMD) decomposition;in comparison with Fourier transform and wavelet transform the Hilbert-Huang transform(HHT) marginal spectrum amplitude is larger than the low frequency Fourier spectrum amplitude;different from strong influence of the selected parent wave on WT,HHT can directly isolate inherent mode function(IMF) from the strong motion record,representing inherent characteristics of the original data;Hilbert amplitude spectrum exhibits the concentration of most energy in a certain time and frequency range,while wavelet spectral energy distribute in a wide frequency range.Therefore,the HHT based on EEMD has obvious advantages in terms of its objectivity and high resolution,being able to extract more time-frequency characteristics of seismic acceleration records.
引文
段生全,贺振华,黄德济.2005.HHT方法及其在地震信号处理中的应用[J].成都理工大学学报:自然科学版,32(4):396--400.
李大虎,何强,邵昌盛,石金虎,刘保金,顾勤平.2010.综合地球物理勘探在青川县城区活动断层探测中的应用[J].成都理工大学学报:自然科学版,32(4):396--400.
李大虎,何强,李才明,屈进红.2011.MATLAB与C++混合编程实现航磁异常提取的小波分析方法研究[J].地震研究,34(2):121--126.
李杰,刘希强,李红,毛玉华,郑树田.2005.利用小波变换方法分析形变观测资料的正常背景变化特征[J].地震学报,27(1):33--41.
李琪,林云芳,曾小苹.2006.应用小波变换提取张北地震的震磁效应[J].地球物理学报,49(3):855--863.
李小军,周正华,于海英,温瑞智.2008.汶川8.0级地震强震动观测及记录初步分析[G]∥汶川地震建筑震害调查与灾后重建分析报吿.北京:中国建筑工业出版社:1--8.
李小军.2009.汶川8.0级地震余震流动台站未校正加速度记录[M].北京:地震出版社:106--113,273--282.
罗奇峰,石春香.2003.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报:自然科学版,31(6):637--640.
石春香,罗奇峰.2003.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,25(4):398--405.
武安绪,吴培稚,兰从欣,徐平,林向东.2005.Hilbret-Huang变换与地震信号的时频分析[J].中国地震,21(2):207--215.
于海英,王栋,杨永强,解全才,江汶乡,周宝峰.2009.汶川8.0级地震强震动加速度记录的初步分析[J].地震工程与工程振动,29(1):1--13.
张立,傅容珊,周挚,山秀明,梁虹,全海燕.2007.基于HHT提取重力固体潮的地震前兆信息[J].地震学报,29(2):222--226.
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Daubechies I.1988.Orthonormal base of compactly supported wavelet[J].Communication on Pure and Applied Mathematics,41(3):909--966.
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Flandrin P R.2004.Empirical mode decomposition as a filterbank[J].IEEE Signal Process Lett,11(2):112--114.
Huang N E,Zheng S,Long S R,Wu M C,Shih H H,Zhang Q,Yen N C,Tung C C,Liu H H.1998.The empiricalmode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis[C]∥Proe R SocLond,A454:903--995.
Huang N E,Zheng S,Steven R L.1999.A new view of nonlinear water waves:The Hilbert spectrum[J].Annu RevFluid Mech,31(1):417--457.
Huang N E,Wu M C,Long S R,Shen S S P,Qu W,Per G,Fan K.2003.A confidence limit for the empirical mode decomposition and hilbert spectral analysis[C]∥Proc R Soc Lond,A459:2317--2345.
Huang N E,Wu Z H.2008.A review on Hilbert-Huang transform:Method and its applications to geophysical studies[J].Reviews of Geophysics,46,RG2006,doi:10.1029/2007RG000228.
Mallat S G.1989.A theory for multiresolution signal decomposition:The wavelet representation[J].IEEE Transactionson Pattern Analysis and Machine Intelligence,11(7):674--693.
Morlet J,Arens G,Fourgeau E,Glard D.1982.Wave propagation and sampling theory[J].Geophysics,47(1):203-211.
Rilling G,Flandrin P,Goncalyes P.2003.On empirical mode decomposition and its algorithms[C]∥IEEE-EURASIPWorkshop on Nonlinear Signal and Image Processing(NSIP2003),Grado(I),June2003:8--11.
Wu Z H,Huang N E.2004.A study of the characteristics of white noise using the empirical mode decomposition method[J].Proc R Soc Land A,460(2046):1597--1611.
Wu Z H,Huang N E.2005.Ensemble Empirical Mode Decomposition-A Noise-Assisted Data Analysis Method[R].Calverton:Center for Ocean-Land-Atmosphere Studies:1--41.
Wu Z H,Huang N E.2009.Ensemble empirical mode decomposition:A noise assisted data analysis method[J].Advances in Adaptive Data Analysis,1(1):1--41.
李大虎,何强,邵昌盛,石金虎,刘保金,顾勤平.2010.综合地球物理勘探在青川县城区活动断层探测中的应用[J].成都理工大学学报:自然科学版,32(4):396--400.
李大虎,何强,李才明,屈进红.2011.MATLAB与C++混合编程实现航磁异常提取的小波分析方法研究[J].地震研究,34(2):121--126.
李杰,刘希强,李红,毛玉华,郑树田.2005.利用小波变换方法分析形变观测资料的正常背景变化特征[J].地震学报,27(1):33--41.
李琪,林云芳,曾小苹.2006.应用小波变换提取张北地震的震磁效应[J].地球物理学报,49(3):855--863.
李小军,周正华,于海英,温瑞智.2008.汶川8.0级地震强震动观测及记录初步分析[G]∥汶川地震建筑震害调查与灾后重建分析报吿.北京:中国建筑工业出版社:1--8.
李小军.2009.汶川8.0级地震余震流动台站未校正加速度记录[M].北京:地震出版社:106--113,273--282.
罗奇峰,石春香.2003.Hilbert-Huang变换理论及其计算中的问题[J].同济大学学报:自然科学版,31(6):637--640.
石春香,罗奇峰.2003.时程信号的Hilbert-Huang变换与小波分析[J].地震学报,25(4):398--405.
武安绪,吴培稚,兰从欣,徐平,林向东.2005.Hilbret-Huang变换与地震信号的时频分析[J].中国地震,21(2):207--215.
于海英,王栋,杨永强,解全才,江汶乡,周宝峰.2009.汶川8.0级地震强震动加速度记录的初步分析[J].地震工程与工程振动,29(1):1--13.
张立,傅容珊,周挚,山秀明,梁虹,全海燕.2007.基于HHT提取重力固体潮的地震前兆信息[J].地震学报,29(2):222--226.
Caulfield H J,Szu H H.1992.Parallel discrete and continuous wavelet transforms[J].Optical Eng,31(9):1831839.
Daubechies I.1988.Orthonormal base of compactly supported wavelet[J].Communication on Pure and Applied Mathematics,41(3):909--966.
Daubechies I.1990.The wavelet transform,time frequency localization and signal analysis[J].IEEE Tansactions on Information Theory,65(5):961--1006.
Flandrin P R.2004.Empirical mode decomposition as a filterbank[J].IEEE Signal Process Lett,11(2):112--114.
Huang N E,Zheng S,Long S R,Wu M C,Shih H H,Zhang Q,Yen N C,Tung C C,Liu H H.1998.The empiricalmode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis[C]∥Proe R SocLond,A454:903--995.
Huang N E,Zheng S,Steven R L.1999.A new view of nonlinear water waves:The Hilbert spectrum[J].Annu RevFluid Mech,31(1):417--457.
Huang N E,Wu M C,Long S R,Shen S S P,Qu W,Per G,Fan K.2003.A confidence limit for the empirical mode decomposition and hilbert spectral analysis[C]∥Proc R Soc Lond,A459:2317--2345.
Huang N E,Wu Z H.2008.A review on Hilbert-Huang transform:Method and its applications to geophysical studies[J].Reviews of Geophysics,46,RG2006,doi:10.1029/2007RG000228.
Mallat S G.1989.A theory for multiresolution signal decomposition:The wavelet representation[J].IEEE Transactionson Pattern Analysis and Machine Intelligence,11(7):674--693.
Morlet J,Arens G,Fourgeau E,Glard D.1982.Wave propagation and sampling theory[J].Geophysics,47(1):203-211.
Rilling G,Flandrin P,Goncalyes P.2003.On empirical mode decomposition and its algorithms[C]∥IEEE-EURASIPWorkshop on Nonlinear Signal and Image Processing(NSIP2003),Grado(I),June2003:8--11.
Wu Z H,Huang N E.2004.A study of the characteristics of white noise using the empirical mode decomposition method[J].Proc R Soc Land A,460(2046):1597--1611.
Wu Z H,Huang N E.2005.Ensemble Empirical Mode Decomposition-A Noise-Assisted Data Analysis Method[R].Calverton:Center for Ocean-Land-Atmosphere Studies:1--41.
Wu Z H,Huang N E.2009.Ensemble empirical mode decomposition:A noise assisted data analysis method[J].Advances in Adaptive Data Analysis,1(1):1--41.
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