过渡内蕴模态函数对经验模态分解去噪结果的影响研究及改进算法
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摘要
经验模态分解(Empirical Mode Decomposition,EMD)是一种具有较大应用潜力的去噪算法.目前,该算法存在的一个较大问题是过渡内蕴模态函数(Intrinsic Mode Function,IMF)中混叠噪声不能有效处理.过渡内蕴模态函数中混叠噪声不易剔除,限制了该算法的应用.本文针对此问题,通过研究过渡IMF的特点,首次提出一种有效去除过渡IMF中混叠噪声的方法.该方法首先对原信号进行一次EMD处理,得到包含过渡IMF的初步去噪结果,并将其与合适的余弦信号结合,改变其包络分布,然后对其结果再次进行EMD处理,仿真实验表明该方法在保留有效信号的同时,可以有效的去除过渡IMF中混叠的噪声,并将该方法用于实际地震资料随机噪声压制,处理效果令人满意.
The Empirical Mode Decomposition is a good method of do-noising which has great application potential.The existing do-noising methods based on EMD(Empirical Mode Decomposition) cannot effectively deal with the transition IMF(Intrinsic Mode Function) from the EMD of the original signal.Because of the noise aliasing in the transition IMF cannot be easily removed,the application of EMD in do-noising is limited.To solve this problem this paper studied the influence of transition IMF on EMD do-noising result,and proposes a method to remove the noise aliasing in the transition IMF.The envelope structure of inchoate do-noising results processed by single EMD would be changed with an opportune cosine signals,then the signal received is decomposed again by EMD and the noise aliasing in the transition IMF is remored.The do-noising results of analog signal show that it can effectively keep the useful signal and remove the noise aliasing in the transition IMF.Using this method to do-noise the actual seismic signal,it can suppress random noise and improve the SNR(signal to noise ratio) of seismic signal.
The Empirical Mode Decomposition is a good method of do-noising which has great application potential.The existing do-noising methods based on EMD(Empirical Mode Decomposition) cannot effectively deal with the transition IMF(Intrinsic Mode Function) from the EMD of the original signal.Because of the noise aliasing in the transition IMF cannot be easily removed,the application of EMD in do-noising is limited.To solve this problem this paper studied the influence of transition IMF on EMD do-noising result,and proposes a method to remove the noise aliasing in the transition IMF.The envelope structure of inchoate do-noising results processed by single EMD would be changed with an opportune cosine signals,then the signal received is decomposed again by EMD and the noise aliasing in the transition IMF is remored.The do-noising results of analog signal show that it can effectively keep the useful signal and remove the noise aliasing in the transition IMF.Using this method to do-noise the actual seismic signal,it can suppress random noise and improve the SNR(signal to noise ratio) of seismic signal.
引文
[1]Huang N E.The empirical mode decomposition and theHilbert spectrum for nonlinear and nonstationary time seriesanalysis.Proc.R.Soc.Lond A.1998,454(4):903-995.
[2]Boudraa O A,Cexus C J.EMD-Based Signal Filtering.IEEE Transactions on Instrumentation and Measurement,2007,56(6):2196-2202.
[3]陈凯.基于经验模式分解的去噪方法.石油地球物理勘探,2009,44(5):603-608.Chen K.A new denoising method based on Empirical ModeDecomposition(EMD).Oil Geophysical Prospecting,2009,44(5):603-608.
[4]Huang N E,Shen Z,Long R S.A new view of nonlinearwater waves:The Hilbert spectrum.Annu Rev.FluidMech,1999,31:417-457.
[5]杨光亮,朱元清,于海英.基于HHT的地震信号自动去噪算.大地测量与地球动力学,2010,30(3):39-42.Yang G L,Zhu Y Q,Yu H Y.Automatic de-noisingalgorithm of earthquake signal based on HHT decomposition.Journal of Geodesy and Geodynamics,2010,30(3):39-42.
[6]Kizhner S,Flatley T S,Huang N E,et al.On the Hilbert-Huang Transform Data Processing System Development.IEEE Aerospace Conference Proceedings,2004,3:1961-1979.
[7]Daubechies I,Lu J F,Wu H T.Synchrosqueezed wavelettransforms:An empirical mode decomposition-like tool.Applied and Computational Harmonic Analysis,2011,30:243-261.
[8]Mendez M O,Corthout J,Huffel S Van,et al.Automaticscreening of obstructive sleep apnea from the ECG based onempirical mode decomposition and wavelet analysis.PhysiologicalMeasurement,2010,21:273-289.
[9]Peng Z K,Peter W T,Chu F L.An improved Hilbert-Huang transform and its application in vibration signalanalysis.Journal of Sound and Vibration,2005,286:187-205.
[10]Naveed R and Danilo P M.Empirical Mode Decomposition forTrivariate Signals.IEEE Transactions on Signal Processing,2010,3(58):1059-1068.
[11]Saurabh P,Madhuchhanda M.Empirical mode decompositionbased ECG enhancement and QRS detection.Computers inBiology and Medicine,2011,42:83-92.
[12]Macelloni L,Battista M B,Knapp C C.Optimal filteringhigh-resolution seismic reflection data using a weighted-modeempirical mode decomposition operator.Journal of AppliedGeophysics,2011,75:603-614.
[13]Zhang Z J,Wang G J,Harris J M.Multi-componentwavefield simulation in viscous extensively dilatancy anisotropicmedia.Phys Earth planet Inter,1999,114:25-28
[14]Zhang Z J,Lin Y H,Liu E R.Large static correction using ahybrid optimization method in complex terrain:someexperience learnt from China.Journal of Seismic Exploration.2005,13(4):337-352.
[15]Battista M B,Knapp C,McGee T,et al.Application of theempirical mode decomposition and Hilbert-Huang transformto seismic reflection data.Geophysics,2007,72(2):29-37.
[16]Kaslovsky N D,Meyer G F.Noise Corruption of empiricalmode decomposition and its effect on instantaneous frequency.Adaptive Data Analysis,2010,2(3):373-396.
[17]段生全,贺振华,黄德济.HHT方法及其在地震信号处理中的应用.成都理工大学学报(自然科学版),2005,32(4):396-400.Duan S Q,He Z H,Huang D J.Application of the Hilbert-Huang transform to the analysis of seismic signal,2005,32(4):396-400.
[18]徐可君,秦海勤,江龙平.基于EMD和HHT的航空发动机转子-机匣振动信号分析.振动与冲击,2011,30(7):237-240.Xu K J,Qin H Q,Jiang L P.Rotor-case vibration signalanalysis of an aero engine based on EMD and HHT.Journalof Vibration and Shock,2011,30(7):237-240.
[19]谭善文,秦树人,汤宝平.Hilbert-Huang变换的滤波特性及其应用.重庆大学学报,2004,2(27):9-12.Tan S W,Qin S R,Tang B P.The Filtering Character ofHilbert-Huang Transform and Its Application.Journal ofChongqing University,2004,2(27):237-240.
[20]白大为,底青云,王光杰.Hilbert-Huang变换与ELF信号处理.地球物理学进展,2009,24(3):1032-1038.Bai D W,Di Q Y,Wang G J.Hilbert-Huang transformationand ELF signal processing.Progress in Geophys.(in Chinese),2009,24(3):1032-1038.
[21]林玉荣,王强.基于一维经验模态分解的图像细节提取方法.吉林大学学报(工学版),2011,41(6):1766-1770.Lin Y R,Wang Q.Extracting details from images based on1-EMD.Journal of Jilin University(Engineering andTechnology Edition),2011,41(6):1766-1770.
[22]刘庆敏,杨午阳,田连玉等.基于经验模态分解的地震相分析技术.石油地球物理勘探,2010,45(supp1):145-149.Liu Q M,Yang W Y,Tian L Y,et al.Seismic facies analysistechnique based on the Empirical Mode Decomposition.OilGeophysical Prospecting,2010,45(supp1):145-149.
[23]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.地球物理学进展,2007,22(5):1585-1590.Yang P J,Yin X Y,Zhang G Z.Seismic signal time-frequency analysis and attributes extraction based on HHT.Progress in Geophysics.(in Chinese),2007,22(5):1585～1590.
[24]王宏禹.信号处理相关理论综合与统一法.北京:国防工业出版社,2005:208-209,217-221.Wang H Y.Synthesis and unification method in correlation theoryof signal processing.Beijing:National Defence Industry Press,2005:208-209,217-221.
[25]陈林,宋海斌.地震信号瞬时频率的估算.地球物理学报,2009,52(1):206-214.Chen L,Song H B.The estimation of instantaneous frequencyof seismic signal.Chinese J.Geophys.(in Chinese),2009,52(1):206-214.
[26]李月,林红波,杨宝俊等.强随机噪声条件下时窗类型局部线性化对TFPF技术的影响.地球物理学报,2009,52(7):1899-1906.Li Y,Lin H B,Yang B J,et al.The influence of limitedlinearization of time window on TFPT under the strong noisebackground.Chinese J.Geophys.(in Chinese),2009,52(7):1899-1906.
[27]鲁来玉,何正勤,丁志峰等.华北科学探测台阵背景噪声特征分析.地球物理学报,2009,52(10):2566-2572.Lu L Y,He Z Q,Ding Z F,et al.Investigation of ambientnoise source in North China array.Chinese J.Geophys.(inChinese),2009,52(10):2566.2572.
[28]Wu Z H,Huang N E.A study of the characteristics of whitenoise using the empirical mode decomposition method.Proc.R.Soc.Lond A.2004,454:1597-1611.
[29]Flandrin P,Rilling G,Goncalves P.Empirical ModeDecomposition as a Filter Bank.IEEE Signal ProcessingLetters,2003,10(20):1-4.
[30]孙晖.经验模态分解理论与应用研究[博士论文].浙江:浙江大学,2005.Sun H.Research on Empirical Mode Decomposition Theotyand Its Application[Ph.D.thesis].Zhejiang:ZhejiangUniversity,2005.
[2]Boudraa O A,Cexus C J.EMD-Based Signal Filtering.IEEE Transactions on Instrumentation and Measurement,2007,56(6):2196-2202.
[3]陈凯.基于经验模式分解的去噪方法.石油地球物理勘探,2009,44(5):603-608.Chen K.A new denoising method based on Empirical ModeDecomposition(EMD).Oil Geophysical Prospecting,2009,44(5):603-608.
[4]Huang N E,Shen Z,Long R S.A new view of nonlinearwater waves:The Hilbert spectrum.Annu Rev.FluidMech,1999,31:417-457.
[5]杨光亮,朱元清,于海英.基于HHT的地震信号自动去噪算.大地测量与地球动力学,2010,30(3):39-42.Yang G L,Zhu Y Q,Yu H Y.Automatic de-noisingalgorithm of earthquake signal based on HHT decomposition.Journal of Geodesy and Geodynamics,2010,30(3):39-42.
[6]Kizhner S,Flatley T S,Huang N E,et al.On the Hilbert-Huang Transform Data Processing System Development.IEEE Aerospace Conference Proceedings,2004,3:1961-1979.
[7]Daubechies I,Lu J F,Wu H T.Synchrosqueezed wavelettransforms:An empirical mode decomposition-like tool.Applied and Computational Harmonic Analysis,2011,30:243-261.
[8]Mendez M O,Corthout J,Huffel S Van,et al.Automaticscreening of obstructive sleep apnea from the ECG based onempirical mode decomposition and wavelet analysis.PhysiologicalMeasurement,2010,21:273-289.
[9]Peng Z K,Peter W T,Chu F L.An improved Hilbert-Huang transform and its application in vibration signalanalysis.Journal of Sound and Vibration,2005,286:187-205.
[10]Naveed R and Danilo P M.Empirical Mode Decomposition forTrivariate Signals.IEEE Transactions on Signal Processing,2010,3(58):1059-1068.
[11]Saurabh P,Madhuchhanda M.Empirical mode decompositionbased ECG enhancement and QRS detection.Computers inBiology and Medicine,2011,42:83-92.
[12]Macelloni L,Battista M B,Knapp C C.Optimal filteringhigh-resolution seismic reflection data using a weighted-modeempirical mode decomposition operator.Journal of AppliedGeophysics,2011,75:603-614.
[13]Zhang Z J,Wang G J,Harris J M.Multi-componentwavefield simulation in viscous extensively dilatancy anisotropicmedia.Phys Earth planet Inter,1999,114:25-28
[14]Zhang Z J,Lin Y H,Liu E R.Large static correction using ahybrid optimization method in complex terrain:someexperience learnt from China.Journal of Seismic Exploration.2005,13(4):337-352.
[15]Battista M B,Knapp C,McGee T,et al.Application of theempirical mode decomposition and Hilbert-Huang transformto seismic reflection data.Geophysics,2007,72(2):29-37.
[16]Kaslovsky N D,Meyer G F.Noise Corruption of empiricalmode decomposition and its effect on instantaneous frequency.Adaptive Data Analysis,2010,2(3):373-396.
[17]段生全,贺振华,黄德济.HHT方法及其在地震信号处理中的应用.成都理工大学学报(自然科学版),2005,32(4):396-400.Duan S Q,He Z H,Huang D J.Application of the Hilbert-Huang transform to the analysis of seismic signal,2005,32(4):396-400.
[18]徐可君,秦海勤,江龙平.基于EMD和HHT的航空发动机转子-机匣振动信号分析.振动与冲击,2011,30(7):237-240.Xu K J,Qin H Q,Jiang L P.Rotor-case vibration signalanalysis of an aero engine based on EMD and HHT.Journalof Vibration and Shock,2011,30(7):237-240.
[19]谭善文,秦树人,汤宝平.Hilbert-Huang变换的滤波特性及其应用.重庆大学学报,2004,2(27):9-12.Tan S W,Qin S R,Tang B P.The Filtering Character ofHilbert-Huang Transform and Its Application.Journal ofChongqing University,2004,2(27):237-240.
[20]白大为,底青云,王光杰.Hilbert-Huang变换与ELF信号处理.地球物理学进展,2009,24(3):1032-1038.Bai D W,Di Q Y,Wang G J.Hilbert-Huang transformationand ELF signal processing.Progress in Geophys.(in Chinese),2009,24(3):1032-1038.
[21]林玉荣,王强.基于一维经验模态分解的图像细节提取方法.吉林大学学报(工学版),2011,41(6):1766-1770.Lin Y R,Wang Q.Extracting details from images based on1-EMD.Journal of Jilin University(Engineering andTechnology Edition),2011,41(6):1766-1770.
[22]刘庆敏,杨午阳,田连玉等.基于经验模态分解的地震相分析技术.石油地球物理勘探,2010,45(supp1):145-149.Liu Q M,Yang W Y,Tian L Y,et al.Seismic facies analysistechnique based on the Empirical Mode Decomposition.OilGeophysical Prospecting,2010,45(supp1):145-149.
[23]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.地球物理学进展,2007,22(5):1585-1590.Yang P J,Yin X Y,Zhang G Z.Seismic signal time-frequency analysis and attributes extraction based on HHT.Progress in Geophysics.(in Chinese),2007,22(5):1585～1590.
[24]王宏禹.信号处理相关理论综合与统一法.北京:国防工业出版社,2005:208-209,217-221.Wang H Y.Synthesis and unification method in correlation theoryof signal processing.Beijing:National Defence Industry Press,2005:208-209,217-221.
[25]陈林,宋海斌.地震信号瞬时频率的估算.地球物理学报,2009,52(1):206-214.Chen L,Song H B.The estimation of instantaneous frequencyof seismic signal.Chinese J.Geophys.(in Chinese),2009,52(1):206-214.
[26]李月,林红波,杨宝俊等.强随机噪声条件下时窗类型局部线性化对TFPF技术的影响.地球物理学报,2009,52(7):1899-1906.Li Y,Lin H B,Yang B J,et al.The influence of limitedlinearization of time window on TFPT under the strong noisebackground.Chinese J.Geophys.(in Chinese),2009,52(7):1899-1906.
[27]鲁来玉,何正勤,丁志峰等.华北科学探测台阵背景噪声特征分析.地球物理学报,2009,52(10):2566-2572.Lu L Y,He Z Q,Ding Z F,et al.Investigation of ambientnoise source in North China array.Chinese J.Geophys.(inChinese),2009,52(10):2566.2572.
[28]Wu Z H,Huang N E.A study of the characteristics of whitenoise using the empirical mode decomposition method.Proc.R.Soc.Lond A.2004,454:1597-1611.
[29]Flandrin P,Rilling G,Goncalves P.Empirical ModeDecomposition as a Filter Bank.IEEE Signal ProcessingLetters,2003,10(20):1-4.
[30]孙晖.经验模态分解理论与应用研究[博士论文].浙江:浙江大学,2005.Sun H.Research on Empirical Mode Decomposition Theotyand Its Application[Ph.D.thesis].Zhejiang:ZhejiangUniversity,2005.
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