改进HHT算法在地震动特性分析中的应用研究
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摘要
本文首次提出了HFBG-EMD的HHT改进算法,将滑动平均3次B样条求均值方法与改进的滤波终止条件相结合,大大减小了传统的EMD分解滤波次数,并提高了HHT的原有精度。对用该方法求出的各阶IMF函数进行瞬时频率变换后发现,它对减小各阶IMF瞬时频率的带宽和提高地震动主频特性的作用比较显著。此外,本文还采用了先在原始地震信号中加入高频正弦谐波再进行分解的方法,有效消除了传统方法中一直难以克服的IMF模态混叠及瞬时频率畸变现象。
An improved algorithm HFBG-EMD is firstly brought up,which serves to adopt the method of means envelop form moving average three-order B-spline and modified G. Rilling filtering criteria,greatly reducing the filtering numbers in the EMD process and improving the precision of HHT. After an instantaneous frequency conversion of these IMF functions,which are obtained by this method,it was discovered that this method can be used to improve the dominant frequency characteristic and decrease the bandwidth of IMF instantaneous frequency. On the other hand,a high frequency harmonic wave is added into the original seismic signal,which can effectively eliminate the modal aliasing and the instantaneous frequency distortion of IMFs.
An improved algorithm HFBG-EMD is firstly brought up,which serves to adopt the method of means envelop form moving average three-order B-spline and modified G. Rilling filtering criteria,greatly reducing the filtering numbers in the EMD process and improving the precision of HHT. After an instantaneous frequency conversion of these IMF functions,which are obtained by this method,it was discovered that this method can be used to improve the dominant frequency characteristic and decrease the bandwidth of IMF instantaneous frequency. On the other hand,a high frequency harmonic wave is added into the original seismic signal,which can effectively eliminate the modal aliasing and the instantaneous frequency distortion of IMFs.
引文
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[13]Huang N E,Wu M,Long S R,et al.A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[C]∥Proceeding of Royal Society London A,2003,459:2317-2345.
[14]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报,2001,31(6):805-814.ZHAO Jinping.Study on the effects of abnormal events to empirical mode decomposition method and the removal method for abnormal signal[J].Journal of Ocean University of Qingdao,2001,31(6):805-814.(in Chinese)
[15]Peng Z K,Tse P W,Chu F L.A comparisi-on study of improved Hilbert-Huang transform and wavelet transform:application to fault diagnosis for rolling bearing[J].Mechanical Systems and Signal Processing,2005,19:974-988.
[16]Chang C C,Sun Z,Poon C W,et al.Multi-component signal decomposition techniques for structural health monitoring[C]∥Proceed-ings on Smart Structures and Materials.San Diego,USA:[s.n.],2005:873-888.
[2]Zhang X D,Bao Z.Non-stationary signal analysis and processing[M].Beijing:National Defense Industry Publisher,1998.(in Chinese)
[3]Morlet J,Arens E,Fourgeau E,et al.wave propagation and sampling theory-part 2:sampling theory and complex waves[J].Geophysics,1982,47(2):222-236.
[4]Qin Shuren,Chen Zhikui,Tang Baoping,et al.research of wavelet transform instrument system for signal analysis[J].Chinese Journal of Mechanical Engineering,2000,4(13):114-121.
[5]杨培杰,印兴耀,张广智.希尔伯特-黄变换地震信号时频分析与属性提取[J].地球物理学进展,2007,22(5):1585-1590.YANG Peijie,YIN Xingyao,ZHANG Guangzhi.Seismic signal time-frequency analysis and attributes extraction based on HHT[J].Progress in Geophysics,2007,22(5):1585-1590.(in Chinese)
[6]Huang N E,Shen Z,Long S R,et al.The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis[C]∥Proc.Roy.Soc.London A,1998,454:903-995.
[7]Bradley Matthew Battista,Camelia Knapp,Tom Mc Gee,et al.Application of the empirical mode decomposition and Hilbert-Huang transform to seismic reflection data[J].Geophysics,2007,72(2):29-37.
[8]公茂盛,谢礼立.HHT方法在地震工程中的应用之初步探讨[J].世界地震工程,2003,19(3):39-43.GONG Maosheng,XIE Lili.Discussion on the application of HHT method to earthquake engineering[J].World Earthquake Engineering,2003,19(3):39-43.(in Chinese)
[9]吴琛,周瑞忠.Hilbert—Huang变换在提取地震信号动力特性中的应用[J].地震工程与工程振动,2006,26(5):41-46.WU Chen,ZHOU Ruizhong.Application of Hilbert-Huang transform in extracting dynamic properties of seismic signals[J].Earthquake Engineering and Engineering Dynamics,2006,26(5):41-46.(in Chinese)
[10]Chen Q H,Huang N E,Riemens-Chneider S,XU Y S.A B spline approach for empiricalmode decompositions[J].Advances in Computational Mathematics,2006(24):171-195.
[11]Rilling G,Flandrin P,Goncal-Ves P.On empirical mode decomposition and its algorithms[C]∥IEEE2 EURASIP Workshop on Nonlinear Signal and Image Processing,Grado(I),June 9-11,2003.
[12]郑天翔,杨力华.经验模式分解算法的探讨和改进[J].中山大学学报:自然科学版,2007,46(1):1-6.ZHENG Tianxiang,YANG Lihua.Discussion and Improvement on empirical mode decomposition algorithm[J].Journal of Zhongshan University:Natural Science Edition,2007,46(1):1-6.(in Chinese)
[13]Huang N E,Wu M,Long S R,et al.A confidence limit for the empirical mode decomposition and Hilbert spectral analysis[C]∥Proceeding of Royal Society London A,2003,459:2317-2345.
[14]赵进平.异常事件对EMD方法的影响及其解决方法研究[J].青岛海洋大学学报,2001,31(6):805-814.ZHAO Jinping.Study on the effects of abnormal events to empirical mode decomposition method and the removal method for abnormal signal[J].Journal of Ocean University of Qingdao,2001,31(6):805-814.(in Chinese)
[15]Peng Z K,Tse P W,Chu F L.A comparisi-on study of improved Hilbert-Huang transform and wavelet transform:application to fault diagnosis for rolling bearing[J].Mechanical Systems and Signal Processing,2005,19:974-988.
[16]Chang C C,Sun Z,Poon C W,et al.Multi-component signal decomposition techniques for structural health monitoring[C]∥Proceed-ings on Smart Structures and Materials.San Diego,USA:[s.n.],2005:873-888.
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