非平稳地震地面运动局部谱密度正交化HHT估计
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摘要
基于采用能反映时频非平稳特性的时变谱密度(局部谱密度)来描述地震地面运动的必要性,给出了利用正交HHT(Hilbert-Huang Transform)估计地震地面运动局部谱密度的方法.具体算例表明:与多重过滤和短时傅立叶变换相对比,利用正交HHT法来估计局部谱密度,速度更快,精度更高;与传统HHT方法相比,正交HHT法避免了能量泄露,有更普遍的适用性.因此,它是一种高效的局部谱密度估计方法.同时,用得到的局部谱密度对三条地震波的能量进行研究,总结了地震波样本能量的分布和变化情况.
It is necessary to describe earthquake ground motion with local spectral density,which is time-dependent and can reflect the non-stationary characteristics.The paper presents a method to estimate local spectral density by adopting the Hilbert-Hung Transform(HHT).A comparative study is conducted on the results of traditional HHT,Multifilter and STFT with some numerical examples.Comparison results show that the orthogonal HHT has great advantages on local spectral density estimation due to its higher precision and faster speed over the Multifilter and STFT.With the orthogonal HHT method,leakage of energy can be avoided.The local spectral density derived in this paper is also adopted to study the energy of three earthquake records.A significant conclusion is drawn on the energy distribution and its variation.
It is necessary to describe earthquake ground motion with local spectral density,which is time-dependent and can reflect the non-stationary characteristics.The paper presents a method to estimate local spectral density by adopting the Hilbert-Hung Transform(HHT).A comparative study is conducted on the results of traditional HHT,Multifilter and STFT with some numerical examples.Comparison results show that the orthogonal HHT has great advantages on local spectral density estimation due to its higher precision and faster speed over the Multifilter and STFT.With the orthogonal HHT method,leakage of energy can be avoided.The local spectral density derived in this paper is also adopted to study the energy of three earthquake records.A significant conclusion is drawn on the energy distribution and its variation.
引文
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[3]胡灿阳,陈清军.基于HHT法的地震地面运动局部谱密度估计[J].振动与冲击,2007,26(10):126.HU Canyang,CHEN Qingjun.Estimation of local spectral densi-ty of earthquake ground motion based on HHT theory[J].Jour-nal of Vibration and Shock,2007,26(10):126.
[4]罗奇峰,石春香.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,2003,31(6):637.LUO Qifeng,SHI Chunxiang.Hilbert-Huang transform and sev-eral problems in its calculation method[J].Journal of Tongji Uni-versity:Natural Science,2003,31(6):637.
[5]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.ZHAO Jinping.Study on the effects of abnormal events to empir-ical mode decomposition method and removal method for abnor-mal signal[J].Journal of Ocean University of Qingdao,2001,31(6):805.
[6]楼梦麟,黄天立.正交化经验模式分解方法[J].同济大学学报:自然科学版,2007,35(3):293.LOU Menglin,HUANG Tianli.The orthogonal empirical modedecomposition[J].Journal of Tongji University:Natural Science,2007,35(3):293.
[7]Mark W D.Spectral analysis of the convolution and filtering ofnon-stationary stochastic processes[J].J Sound and Vibration,1970,(11):19.
[8]Kameda,Hiroyuki.Evolutionary spectra of seismogram by multi-filter[J].J Engng Mech,ASCE,1975,101(6):787.
[9]Husid R L.Analisis de terremotos:analisis general[J].Revista delID1EM,Santiago Chile,1969,8(1):21.
[10]大崎顺彦.地震动的谱分析入门[M].吕敏申,谢礼立,译.北京:地震出版社,1980.Ohsaki Y.Spectrum analysis of seismic motion[M].Translatedby LV Minshen,XIE Lili.Bejing:Seismic Press,1980.
[2]Leon Cohen.Time-frequency analysis:theory and applications[M].Englewood Cliffs:Prentice Hall,1995.
[3]胡灿阳,陈清军.基于HHT法的地震地面运动局部谱密度估计[J].振动与冲击,2007,26(10):126.HU Canyang,CHEN Qingjun.Estimation of local spectral densi-ty of earthquake ground motion based on HHT theory[J].Jour-nal of Vibration and Shock,2007,26(10):126.
[4]罗奇峰,石春香.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,2003,31(6):637.LUO Qifeng,SHI Chunxiang.Hilbert-Huang transform and sev-eral problems in its calculation method[J].Journal of Tongji Uni-versity:Natural Science,2003,31(6):637.
[5]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.ZHAO Jinping.Study on the effects of abnormal events to empir-ical mode decomposition method and removal method for abnor-mal signal[J].Journal of Ocean University of Qingdao,2001,31(6):805.
[6]楼梦麟,黄天立.正交化经验模式分解方法[J].同济大学学报:自然科学版,2007,35(3):293.LOU Menglin,HUANG Tianli.The orthogonal empirical modedecomposition[J].Journal of Tongji University:Natural Science,2007,35(3):293.
[7]Mark W D.Spectral analysis of the convolution and filtering ofnon-stationary stochastic processes[J].J Sound and Vibration,1970,(11):19.
[8]Kameda,Hiroyuki.Evolutionary spectra of seismogram by multi-filter[J].J Engng Mech,ASCE,1975,101(6):787.
[9]Husid R L.Analisis de terremotos:analisis general[J].Revista delID1EM,Santiago Chile,1969,8(1):21.
[10]大崎顺彦.地震动的谱分析入门[M].吕敏申,谢礼立,译.北京:地震出版社,1980.Ohsaki Y.Spectrum analysis of seismic motion[M].Translatedby LV Minshen,XIE Lili.Bejing:Seismic Press,1980.
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