基于自适应序贯相似性检测波形匹配延拓的EMD端点效应抑制
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摘要
针对经验模态分解过程中信号两端出现的严重失真问题,在波形匹配延拓的基础上,提出了一种基于自适应序贯相似性检测波形匹配延拓的端点效应抑制方法。该算法引入基于精度的截止阈值,使算法有了很好的直观性和快速性。再通过对折自适应调节阈值,进一步减少遍历所需时间。通过对模拟信号和实际工程信号分别进行仿真分析,结果表明该算法能够有效的抑制在经验模态分解过程中出现的端点效应问题,改善分解效果。
Aiming at the crucial problem of ending effect which can lead to waveform distortion for double signals in the decomposition process of Empirical Mode Decomposition( EMD),a novel method for restraining the ending effect was proposed based on the self-adaptive sequential similarity detection of waveform matching extending. In the method,the introduction of cut-off precision threshold makes the algorithm intuitive and fast. And the folded self-adaptive threshold adjustment further reduces the time used for traversal. A simulation and analysis were carried out on analog signals and practical engineering signals,respectively. The results indicate that the algorithm proposed is able to effectively restrain the ending effect in the decomposition process of EMD and improves the overall decomposition efficacy.
Aiming at the crucial problem of ending effect which can lead to waveform distortion for double signals in the decomposition process of Empirical Mode Decomposition( EMD),a novel method for restraining the ending effect was proposed based on the self-adaptive sequential similarity detection of waveform matching extending. In the method,the introduction of cut-off precision threshold makes the algorithm intuitive and fast. And the folded self-adaptive threshold adjustment further reduces the time used for traversal. A simulation and analysis were carried out on analog signals and practical engineering signals,respectively. The results indicate that the algorithm proposed is able to effectively restrain the ending effect in the decomposition process of EMD and improves the overall decomposition efficacy.
引文
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[5]杨庆,陈桂明,薛冬林.基于最小平方距离相关的EMD改进算法及应用[J].振动与冲击,2011,30(6):62-66.YANY Qing,CHEN Guiming,XUE Donglin.Improved method for empirical mode decomposition based on SSDA and its application[J].Journal of Vibration and Shock,2011,30(6):62-66.
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[7]李钊,周晓军,徐云.基于均生函数周期叠加外推法的EMD端点问题的研究[J].振动与冲击,2013,32(15):138-143.LI Zhao,ZHOU Xiaojun,XU Yun.End effect treatment for EMD based on the period superposition extrapolation of mean generating function[J].Journal of Vibration and Shock,2013,32(15):138-143.
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[9]贺智,王强,沈毅,等.希尔伯特-黄变换端点效应抑制算法综述[J].软件,2011,32(10):1-7.HE Zhi,WANG Qiang,SHENG Yi,et al.Survey on end effects mitigation of Hilbert-Huang transform[J].Software,2011,32(10):1-7.
[10]WU Q,SHERMAN D R.Boundary extension and stop criteria for empirical mode decomposition[J].Advances in Adaptive Data Analysis,2010,2(2):159-169.
[11]朱金龙,邱晓辉.正交多项式拟合在EMD算法端点问题中的应用[J].计算机工程与应用,2004,42(23):72-74.ZHU Jinlong,QIU Xiaohui.Dealing with the end issue of EMD based on orthogonal polynomial[J].Computer Engineering&Applications,2006,42(23):72-74.
[12]程军圣,于德介,杨宇.Hilbert-Huang变换端点效应问题的探讨[J].振动与冲击,2005,24(6):40-47.CHENG Junsheng,YU Dejie,YANG Yu.Discussion of the end effects in Hilbert-Huang transform[J].Journal of Vibration and Shock,2005,24(6):40-47.
[13]DENG Y J,WANG W,QIAN C,et al.Boundaryprocessing-technique in MED method and Hilbert transform[J].Chinese Science Bulletin,2001,46(1):1-8.
[14]CHENG J S,YU D J,YANG Y,et al.Application of support vector regression machines to the processing of end effects of Hilbert-Huang[J].Mechanical System and Signal Processing,2007,21(3):1197-1211.
[15]王录雁,王强,鲁冬林,等.EMD自适应三角波延拓算法[J].振动与冲击,2014,33(4):94-99.WANG Luyan,WANG Qiang,LU Donglin,et al.A selfadaptive triangular waveform matching extension algorithm for EMD[J].Journal of Vibration and Shock,2014,33(4):94-99.
[2]HUANG N E,SHEN Z,LONG S R.A new view of water wave-The Hilbert spectrum[J].Ann.Rev.Flid Mech.,1993,31:417-457.
[3]RATO R T,ORTIGUEIRA M D,BATISTA A G.On the HHT,its problem,and some solution[J].Mechanical System and Signal Processing,2008,22(6):1374-1394.
[4]邵晨曦,王剑,范金锋,等.一种自适应的EMD端点延拓方法[J].电子学报,2007,35(10):1944-1948.SHAO Chenxi,WANG Jian,FAN Jinfeng,et al.A selfadaptive method dealing with the end issue of EMD[J].Acta Electronica Sinica,2007,35(10):1944-1948.
[5]杨庆,陈桂明,薛冬林.基于最小平方距离相关的EMD改进算法及应用[J].振动与冲击,2011,30(6):62-66.YANY Qing,CHEN Guiming,XUE Donglin.Improved method for empirical mode decomposition based on SSDA and its application[J].Journal of Vibration and Shock,2011,30(6):62-66.
[6]高强,段晨东,赵艳青,等.最大相关波形延拓的经验模式分解端点效应抑制方法[J].振动与冲击,2013,32(2):62-66.GAO Qiang,DUAN Chendong,ZHAO Yanqing,et al.Amaximal correlation waveform extension method for end effects reduction of empirical mode decomposition[J].Journal of Vibration and Shock,2013,32(2):62-66.
[7]李钊,周晓军,徐云.基于均生函数周期叠加外推法的EMD端点问题的研究[J].振动与冲击,2013,32(15):138-143.LI Zhao,ZHOU Xiaojun,XU Yun.End effect treatment for EMD based on the period superposition extrapolation of mean generating function[J].Journal of Vibration and Shock,2013,32(15):138-143.
[8]HUANG D J,ZHAO J P.Practical implementation of Hilbert-Huang transform algorithm[J].High Technology Letters,2002,8(3):40-47.
[9]贺智,王强,沈毅,等.希尔伯特-黄变换端点效应抑制算法综述[J].软件,2011,32(10):1-7.HE Zhi,WANG Qiang,SHENG Yi,et al.Survey on end effects mitigation of Hilbert-Huang transform[J].Software,2011,32(10):1-7.
[10]WU Q,SHERMAN D R.Boundary extension and stop criteria for empirical mode decomposition[J].Advances in Adaptive Data Analysis,2010,2(2):159-169.
[11]朱金龙,邱晓辉.正交多项式拟合在EMD算法端点问题中的应用[J].计算机工程与应用,2004,42(23):72-74.ZHU Jinlong,QIU Xiaohui.Dealing with the end issue of EMD based on orthogonal polynomial[J].Computer Engineering&Applications,2006,42(23):72-74.
[12]程军圣,于德介,杨宇.Hilbert-Huang变换端点效应问题的探讨[J].振动与冲击,2005,24(6):40-47.CHENG Junsheng,YU Dejie,YANG Yu.Discussion of the end effects in Hilbert-Huang transform[J].Journal of Vibration and Shock,2005,24(6):40-47.
[13]DENG Y J,WANG W,QIAN C,et al.Boundaryprocessing-technique in MED method and Hilbert transform[J].Chinese Science Bulletin,2001,46(1):1-8.
[14]CHENG J S,YU D J,YANG Y,et al.Application of support vector regression machines to the processing of end effects of Hilbert-Huang[J].Mechanical System and Signal Processing,2007,21(3):1197-1211.
[15]王录雁,王强,鲁冬林,等.EMD自适应三角波延拓算法[J].振动与冲击,2014,33(4):94-99.WANG Luyan,WANG Qiang,LU Donglin,et al.A selfadaptive triangular waveform matching extension algorithm for EMD[J].Journal of Vibration and Shock,2014,33(4):94-99.