经验模态分解及其雷达信号处理
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摘要
为了准确估计信号的瞬时频率,可用经验模态分解(EMD)将信号分解成有限个窄带信号。该方法因具有很强的自适应性及处理非平稳信号的能力而引起广泛关注,已在众多工程领域得到应用。但EMD是基于经验的方法,数值仿真和试验研究仍是分析EMD算法的主要方法。本文总结了EMD算法存在的问题,并指出深入挖掘支持该方法的理论基础是消除制约EMD算法进一步发展和应用推广的关键。针对所存在的问题,从改进筛分停止准则、抑制端点效应、改进包络生成方法和解决模态混叠问题等诸方面阐述了改进EMD算法的研究进展。综述了EMD在雷达信号处理领域的应用。最后分析指出了进一步研究EMD的几个主要方向。
In order to better estimate the instantaneous frequency of signals,the empirical mode decomposition (EMD) algorithm,proposed by Huang et al.,is used to break multi-component signals into several narrow subbands. EMD is an adaptive method and can be used to analyze nonstationary signals,so it has been widely applied to many engineering fields. However,EMD is still considered as an empirical method because it lacks a rigorous mathematical foundation,and its analysis depends largely on numerical simulations and experimental investigations. In this paper,related problems of the EMD algorithm are discussed,including its theoretical foundation and its applications. Some modified EMD algorithms are considered to overcome problems,such as stopping criterion,end effect,envelope of signals and mode aliasing. The applications of EMD to the processing of radar signals are reviewed. Some directions for further research on the EMD algorithm are suggested.
In order to better estimate the instantaneous frequency of signals,the empirical mode decomposition (EMD) algorithm,proposed by Huang et al.,is used to break multi-component signals into several narrow subbands. EMD is an adaptive method and can be used to analyze nonstationary signals,so it has been widely applied to many engineering fields. However,EMD is still considered as an empirical method because it lacks a rigorous mathematical foundation,and its analysis depends largely on numerical simulations and experimental investigations. In this paper,related problems of the EMD algorithm are discussed,including its theoretical foundation and its applications. Some modified EMD algorithms are considered to overcome problems,such as stopping criterion,end effect,envelope of signals and mode aliasing. The applications of EMD to the processing of radar signals are reviewed. Some directions for further research on the EMD algorithm are suggested.
引文
[1]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[J].Proc Roy Soc London A,1998,454:903-995.
[2]胡劲松,杨世锡.基于自相关的旋转机械振动信号EMD分解方法研究[J].机械强度,2007,29(3):376-379.Hu Jingsong,Yang Shixi.Journal of Mechanical Strength,2007,29(3):376-379.
[3]于德介,陈淼峰,程军圣,等.一种基于经验模式分解与支持向量机的转子故障诊断方法[J].中国电机工程学报,2006,26(16):162-167.Yu Dejie,Chen Miaofeng,Cheng Junsheng,et al.Proceedings of the CSEE,2006,26(16):162-167.
[4]Liu S L,Zhao H F,Wang H,et al.Application of improved EMD algorithm for the fault diagnosis of reciprocating pump valves with spring failure[C]//Int Symp Signal Process Its Appl(ISSPA).NJ:IEEE,2007:1-4.
[5]曹晖,曹永红.HH变换在地震动信号分析中的应用[J].重庆大学学报,2008,31(8):922-927.Cao Hui,Cao Yonghong.Journal of Chongqing University,2008,31(8):922-927.
[6]张榆锋,丁坤,章克信,等.超声多普勒管壁搏动和血流信号的分离研究[J].中国生物医学工程学报,2007,26(5):641-646.Zhang Yufeng,Ding Kun,Zhang Kexin,et al.Chinese Journal of Biomedical Engineering,2007,26(5):641-646.
[7]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究[J].振动与冲击,2006,25(3):40-44.Zhong Youming,Qin Shuren.Journal of Vibration and Shock,2006,25(3):40-44.
[8]Deléchelle E,Lemoine J,Niang O.Empirical mode decomposition:An analytical approach for sifting process[J].IEEE Signal Process Lett,2005,12(11):764-767.
[9]Diop E H S,Alexandre R,Boudraa A O.A PDE characterization of the intrinsic mode function[C]//Proc IEEE Int Conf Acoust,Speech Signal Process(ICASSP),2009:3429-3432.
[10]Hong H,Wang X L,Tao Z Y.Local integral mean-based sifting for empirical mode decomposition[J].IEEE Signal Process Lett,2009,16(10):841-844.
[11]Meignen S,Perrier V.A new formulation for empirical mode decompo-sition based on contrained optimization[J].IEEE Signal Process Lett,2007,12(14):932-935.
[12]Azzaoui N,Snoussi H,Duchêne J.An enhanced empirical mode decomposition without sifting[C]//15th Workshop on Statistical Signal Processing.NJ:IEEE,2009:796-799.
[13]Rilling G,Flandrin P.One or two frequencies?The empirical mode decomposition answers[J].IEEE Trans Signal Process,2008,56(1):85-95.
[14]Chen Q H,Huang N,Riemenschneider S,et al.A B-spline approach for empirical mode decomposition[J].Advances in Computational Mathematics,2006,24:171-195.
[15]Wu S H,Liu Z S,Liu B Y.Enhancement of lidar backscatters signal-to-noise ratio using empirical mode decomposition method[J].Optics Communications,2006,267(1):137-144.
[16]Wu Z H,Huang N E.A study of the characteristics of white noise using the empirical mode decomposition method[J].Proc Roy Soc London A,2004,460:1597-1611.
[17]Cheng J S,Yu D J,Yang Y.Research on the intrinsic mode function(IMF)criterion in EMD method[J].Mech Syst Signal Process,2006,20:817-824.
[18]Xuan B,Xie Q W,Peng S L.EMD sifting based on bandwidth[J].IEEE Signal Process Lett,2007,14(8):537-540.
[19]于哲峰,杨智春.经验模分解中的间歇性控制方法改进及分解精度控制[J].机械科学与技术,2007,26(5):635-637.Yu Zhefeng,Yang Zhichun.Mechanical Science and Technology for Aerospace Engineering,2007,26(5):635-637.
[20]李雪耀,邹晓杰,张汝波,等.谱熵和主成分分析用于EMD分解研究[J].哈尔滨工程大学学报,2009,30(7):797-802.Li Xueyao,Zou Xiaojie,Zhang Rubo,et al.Journal of Harbin Engineering University,2009,30(7):797-802.
[21]胡爱军,安连锁,唐贵基.Hilbert-Huang变换端点效应处理新方法[J].机械工程学报,2008,44(4):154-158.Hu Aijun,An Liansuo,Tang Guiji.Chinese Journal of MechanicalEngineering,2008,44(4):154-158.
[22]胡维平,莫家玲,龚英姬,等.经验模态分解中多种边界处理方法的比较研究[J].电子与信息学报,2007,29(6):1394-1398.Hu Weiping,Mo Jialing,Gong Yingji,et al.Journal of Electronics&Information Technology,2007,29(6):1394-1398.
[23]王秋生,段丹辉.经验模态分解的边界效应处理技术[J].计算机测量与控制,2006,14(12):1673-1675.Wang Qiusheng,Duan Danhui.Computer Measurement&Control,2006,14(12):1673-1675.
[24]Kopsinis Y,McLaughlin S.Investigation and performance enhancement of the empirical mode decomposition method based on a heuristic search optimization approach[J].IEEE Trans Signal Process,2008,56(1):1-13.
[25]Hawley S D,Atlas L E,Chizeck H J.Some properties of an empirical mode type signal decomposition algorithm[J].IEEE Signal Process Lett,2010,17(1):24-27.
[26]Yang Y L,Deng J H,Tang W C,et al.Nonuniform extrema resampling and empirical mode decomposition[J].Chinese Journal of Electronics,2009,18(4):759-762.
[27]Huang N E,Shen Z,Long S R.A new view of nonlinear water waves:The Hilbert spectrum[J].Annu Rev Fluid Mech,1999,31:417-457.
[28]Deering R,Kaiser J F.The use of a masking signal to improve empirical mode decomposition[C]//Proc IEEE Int Conf Acoust,Speech Signal Process(ICASSP).NJ:IEEE,2005:485-488.
[29]Wu Z,Huang N E.Ensemble empirical mode decomposition:A noise-assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
[30]Gao Y C,Ge G T,Sheng Z Y,et al.Analysis and solution to the mode mixing phenomenon in EMD[C]//Congress Image Signal Process(CISP).NJ:IEEE,2008:223-227.
[31]盖广洪.经验模态分解的一种改进算法[J].西安交通大学学报,2004,38(11):1199-1202.Gai Guanghong.Journal of Xi'an Jiao Tong University,2004,38(11):1199-1202.
[32]李雪耀,黄永平,张汝波.一种基于支持向量回归机的经验模态分解方法[J].哈尔滨工程大学学报,2007,28(7):779-784.Li Xueyao,Huang Yongping,Zhang Rubo.Journal of Harbin Engineering University,2007,28(7):779-784.
[33]Cai C J,Liu W X,Fu J S,et al.A new approach for ground moving target indication in foliage environment[J].Signal Process,2006,86(1):84-97.
[34]Lai C P,Ruan Q,Narayanan R M.Hilbert-Huang transform(HHT)analysis of human activities using through-wall noise radar[C]//Int Symp Signal Syst Electron(ISSSE).NJ:IEEE,2007:115-118.
[35]Zhang J,Srirama P K,Mazumder M K.E-SPART analyzer for mars mission:A new approach in signal processing and sampling[J].IEEE Trans Ind Appl,2007,43(4):1084-1090.
[36]Yue H Y,Guo H D,Han C M,et al.A SAR interferogram filter based on the empirical mode decomposition method[C]//Proc IEEE Int Geosci and Remote Sens Symp(IGARSS).NJ:IEEE,2001:2061-2063.
[37]Zhou F,Xing M D,Bai X R,et al.Narrow-band interference suppression for SAR based on complex empirical mode decomposition[J].IEEE Geosci Remote Sens Lett,2009,6(3):423-427.
[38]Han C M,Guo H D,Wang C L,et al.A new multiscale edge detection technique[C]//Proc IEEE Int Geosci and Remote Sens Symp(IGARSS).NJ:IEEE,2002:3402-3404.
[39]Bai X R,Xing M D,Zhou F,et al.Imaging of micromotion targets with rotating parts based on empirical mode decomposition[J].IEEE Trans Geosci Remote Sens,2008,46(11):3514-3523.
[2]胡劲松,杨世锡.基于自相关的旋转机械振动信号EMD分解方法研究[J].机械强度,2007,29(3):376-379.Hu Jingsong,Yang Shixi.Journal of Mechanical Strength,2007,29(3):376-379.
[3]于德介,陈淼峰,程军圣,等.一种基于经验模式分解与支持向量机的转子故障诊断方法[J].中国电机工程学报,2006,26(16):162-167.Yu Dejie,Chen Miaofeng,Cheng Junsheng,et al.Proceedings of the CSEE,2006,26(16):162-167.
[4]Liu S L,Zhao H F,Wang H,et al.Application of improved EMD algorithm for the fault diagnosis of reciprocating pump valves with spring failure[C]//Int Symp Signal Process Its Appl(ISSPA).NJ:IEEE,2007:1-4.
[5]曹晖,曹永红.HH变换在地震动信号分析中的应用[J].重庆大学学报,2008,31(8):922-927.Cao Hui,Cao Yonghong.Journal of Chongqing University,2008,31(8):922-927.
[6]张榆锋,丁坤,章克信,等.超声多普勒管壁搏动和血流信号的分离研究[J].中国生物医学工程学报,2007,26(5):641-646.Zhang Yufeng,Ding Kun,Zhang Kexin,et al.Chinese Journal of Biomedical Engineering,2007,26(5):641-646.
[7]钟佑明,秦树人.希尔伯特-黄变换的统一理论依据研究[J].振动与冲击,2006,25(3):40-44.Zhong Youming,Qin Shuren.Journal of Vibration and Shock,2006,25(3):40-44.
[8]Deléchelle E,Lemoine J,Niang O.Empirical mode decomposition:An analytical approach for sifting process[J].IEEE Signal Process Lett,2005,12(11):764-767.
[9]Diop E H S,Alexandre R,Boudraa A O.A PDE characterization of the intrinsic mode function[C]//Proc IEEE Int Conf Acoust,Speech Signal Process(ICASSP),2009:3429-3432.
[10]Hong H,Wang X L,Tao Z Y.Local integral mean-based sifting for empirical mode decomposition[J].IEEE Signal Process Lett,2009,16(10):841-844.
[11]Meignen S,Perrier V.A new formulation for empirical mode decompo-sition based on contrained optimization[J].IEEE Signal Process Lett,2007,12(14):932-935.
[12]Azzaoui N,Snoussi H,Duchêne J.An enhanced empirical mode decomposition without sifting[C]//15th Workshop on Statistical Signal Processing.NJ:IEEE,2009:796-799.
[13]Rilling G,Flandrin P.One or two frequencies?The empirical mode decomposition answers[J].IEEE Trans Signal Process,2008,56(1):85-95.
[14]Chen Q H,Huang N,Riemenschneider S,et al.A B-spline approach for empirical mode decomposition[J].Advances in Computational Mathematics,2006,24:171-195.
[15]Wu S H,Liu Z S,Liu B Y.Enhancement of lidar backscatters signal-to-noise ratio using empirical mode decomposition method[J].Optics Communications,2006,267(1):137-144.
[16]Wu Z H,Huang N E.A study of the characteristics of white noise using the empirical mode decomposition method[J].Proc Roy Soc London A,2004,460:1597-1611.
[17]Cheng J S,Yu D J,Yang Y.Research on the intrinsic mode function(IMF)criterion in EMD method[J].Mech Syst Signal Process,2006,20:817-824.
[18]Xuan B,Xie Q W,Peng S L.EMD sifting based on bandwidth[J].IEEE Signal Process Lett,2007,14(8):537-540.
[19]于哲峰,杨智春.经验模分解中的间歇性控制方法改进及分解精度控制[J].机械科学与技术,2007,26(5):635-637.Yu Zhefeng,Yang Zhichun.Mechanical Science and Technology for Aerospace Engineering,2007,26(5):635-637.
[20]李雪耀,邹晓杰,张汝波,等.谱熵和主成分分析用于EMD分解研究[J].哈尔滨工程大学学报,2009,30(7):797-802.Li Xueyao,Zou Xiaojie,Zhang Rubo,et al.Journal of Harbin Engineering University,2009,30(7):797-802.
[21]胡爱军,安连锁,唐贵基.Hilbert-Huang变换端点效应处理新方法[J].机械工程学报,2008,44(4):154-158.Hu Aijun,An Liansuo,Tang Guiji.Chinese Journal of MechanicalEngineering,2008,44(4):154-158.
[22]胡维平,莫家玲,龚英姬,等.经验模态分解中多种边界处理方法的比较研究[J].电子与信息学报,2007,29(6):1394-1398.Hu Weiping,Mo Jialing,Gong Yingji,et al.Journal of Electronics&Information Technology,2007,29(6):1394-1398.
[23]王秋生,段丹辉.经验模态分解的边界效应处理技术[J].计算机测量与控制,2006,14(12):1673-1675.Wang Qiusheng,Duan Danhui.Computer Measurement&Control,2006,14(12):1673-1675.
[24]Kopsinis Y,McLaughlin S.Investigation and performance enhancement of the empirical mode decomposition method based on a heuristic search optimization approach[J].IEEE Trans Signal Process,2008,56(1):1-13.
[25]Hawley S D,Atlas L E,Chizeck H J.Some properties of an empirical mode type signal decomposition algorithm[J].IEEE Signal Process Lett,2010,17(1):24-27.
[26]Yang Y L,Deng J H,Tang W C,et al.Nonuniform extrema resampling and empirical mode decomposition[J].Chinese Journal of Electronics,2009,18(4):759-762.
[27]Huang N E,Shen Z,Long S R.A new view of nonlinear water waves:The Hilbert spectrum[J].Annu Rev Fluid Mech,1999,31:417-457.
[28]Deering R,Kaiser J F.The use of a masking signal to improve empirical mode decomposition[C]//Proc IEEE Int Conf Acoust,Speech Signal Process(ICASSP).NJ:IEEE,2005:485-488.
[29]Wu Z,Huang N E.Ensemble empirical mode decomposition:A noise-assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
[30]Gao Y C,Ge G T,Sheng Z Y,et al.Analysis and solution to the mode mixing phenomenon in EMD[C]//Congress Image Signal Process(CISP).NJ:IEEE,2008:223-227.
[31]盖广洪.经验模态分解的一种改进算法[J].西安交通大学学报,2004,38(11):1199-1202.Gai Guanghong.Journal of Xi'an Jiao Tong University,2004,38(11):1199-1202.
[32]李雪耀,黄永平,张汝波.一种基于支持向量回归机的经验模态分解方法[J].哈尔滨工程大学学报,2007,28(7):779-784.Li Xueyao,Huang Yongping,Zhang Rubo.Journal of Harbin Engineering University,2007,28(7):779-784.
[33]Cai C J,Liu W X,Fu J S,et al.A new approach for ground moving target indication in foliage environment[J].Signal Process,2006,86(1):84-97.
[34]Lai C P,Ruan Q,Narayanan R M.Hilbert-Huang transform(HHT)analysis of human activities using through-wall noise radar[C]//Int Symp Signal Syst Electron(ISSSE).NJ:IEEE,2007:115-118.
[35]Zhang J,Srirama P K,Mazumder M K.E-SPART analyzer for mars mission:A new approach in signal processing and sampling[J].IEEE Trans Ind Appl,2007,43(4):1084-1090.
[36]Yue H Y,Guo H D,Han C M,et al.A SAR interferogram filter based on the empirical mode decomposition method[C]//Proc IEEE Int Geosci and Remote Sens Symp(IGARSS).NJ:IEEE,2001:2061-2063.
[37]Zhou F,Xing M D,Bai X R,et al.Narrow-band interference suppression for SAR based on complex empirical mode decomposition[J].IEEE Geosci Remote Sens Lett,2009,6(3):423-427.
[38]Han C M,Guo H D,Wang C L,et al.A new multiscale edge detection technique[C]//Proc IEEE Int Geosci and Remote Sens Symp(IGARSS).NJ:IEEE,2002:3402-3404.
[39]Bai X R,Xing M D,Zhou F,et al.Imaging of micromotion targets with rotating parts based on empirical mode decomposition[J].IEEE Trans Geosci Remote Sens,2008,46(11):3514-3523.
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