基于标准化自协方差相关函数的EMD改进算法
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摘要
针对经验模态分解中存在的端点效应问题,提出了一种基于标准化自协方差相关窗函数的改进算法。利用标准化自协方差相关函数作为判定准则,在原信号内部寻找与端点处波形最相似,幅值差异最小的一段波形,用此段波形代替产生端点效应的包络线进行迭代。为有效降低分解误差,对延拓后的信号加窗函数,再进行经验模态分解。通过仿真和工程试验结果表明该算法可以有效地抑制端点效应,具有较高的分解精度,与其他几种常见算法相比具有算法简单、易于实现的特点。
In order to solve the problem of end effect in EMD,a standardized covariance window function improved algorithm is proposed.A standardized self-covariance correlation function is used for the similarity criterion of the internal signal to find the endpoint waveform which is the smallest amplitude difference waveforms for data extension,instead of this segmentation waveform to produce the end effect to iterate the envelope.In order to reduce the decomposition error,the analyzed signal is preprocessed by multiplying with the defined window,and the EMD method is used to analyze the preprocessed signal.Simulation and experimental results show that the algorithm can effectively restrain the end effect.The algorithm is simple and easy to implement compared with several other common algorithm.
In order to solve the problem of end effect in EMD,a standardized covariance window function improved algorithm is proposed.A standardized self-covariance correlation function is used for the similarity criterion of the internal signal to find the endpoint waveform which is the smallest amplitude difference waveforms for data extension,instead of this segmentation waveform to produce the end effect to iterate the envelope.In order to reduce the decomposition error,the analyzed signal is preprocessed by multiplying with the defined window,and the EMD method is used to analyze the preprocessed signal.Simulation and experimental results show that the algorithm can effectively restrain the end effect.The algorithm is simple and easy to implement compared with several other common algorithm.
引文
[1]Huang N E,Shen Z,Long S R,et al.The empirical mode de-composition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[J].Proceedings of the RoyalSociety A,1998,454:903-995.
[2]沈路,周晓军,张志刚,等.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击,2009,28(8):168-171.
[3]Zhang Qingjie,Zhu Huayong,Shen Lincheng.A new methodfor mitigation of end effect in empirical mode decomposition[C]//2010 2nd International Asia Conference on Informaticsin Control,Automation and Robotics.[s.l.]:[s.n.],2010:400-403.
[4]Rilling G,Flandrin P,Goncalves P.On Empirical Mode De-composition and Its Algorithms[C]//IEEE-Eurasip Work-shop on Nonlinear Signal and Image Processing.[s.l.]:[s.n.],2003.
[5]祈克玉,施坤林,霍鹏飞,等.EMD端点效应处理在转子摩擦故障诊断中的应用[J].振动测试与诊断,2010,30(5):492-495.
[6]Huang N E.Empirical mode decomposition apparatus,methodand article of manufacture for analyzing biological signals andperfoming curve fitting[P].United States Patent,2002.
[7]王婷,杨莘元,李冰冰.一种改善EMD端点效应的新方法[J].哈尔滨理工大学学报,2009,14(5):23-26.
[8]胡爱军,安连锁,廖贵基.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.
[9]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004(16):84-86.
[10]Cheng Junsheng,Yu Dejie,Yang Yu.A fault diagnosis ap-proach for roller bearings based on EMD method and AR mod-el[J].Mechanical Systems and Signal Processing,2006,20(2):350-362.
[11]任达千,吴昭同,严拱标.EMD端点效应的评价指标及抑制端点效应的窗函数法[J].制造业自动化,2007,29(1):21-24.
[2]沈路,周晓军,张志刚,等.Hilbert-Huang变换中的一种端点延拓方法[J].振动与冲击,2009,28(8):168-171.
[3]Zhang Qingjie,Zhu Huayong,Shen Lincheng.A new methodfor mitigation of end effect in empirical mode decomposition[C]//2010 2nd International Asia Conference on Informaticsin Control,Automation and Robotics.[s.l.]:[s.n.],2010:400-403.
[4]Rilling G,Flandrin P,Goncalves P.On Empirical Mode De-composition and Its Algorithms[C]//IEEE-Eurasip Work-shop on Nonlinear Signal and Image Processing.[s.l.]:[s.n.],2003.
[5]祈克玉,施坤林,霍鹏飞,等.EMD端点效应处理在转子摩擦故障诊断中的应用[J].振动测试与诊断,2010,30(5):492-495.
[6]Huang N E.Empirical mode decomposition apparatus,methodand article of manufacture for analyzing biological signals andperfoming curve fitting[P].United States Patent,2002.
[7]王婷,杨莘元,李冰冰.一种改善EMD端点效应的新方法[J].哈尔滨理工大学学报,2009,14(5):23-26.
[8]胡爱军,安连锁,廖贵基.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.
[9]刘慧婷,张旻,程家兴.基于多项式拟合算法的EMD端点问题的处理[J].计算机工程与应用,2004(16):84-86.
[10]Cheng Junsheng,Yu Dejie,Yang Yu.A fault diagnosis ap-proach for roller bearings based on EMD method and AR mod-el[J].Mechanical Systems and Signal Processing,2006,20(2):350-362.
[11]任达千,吴昭同,严拱标.EMD端点效应的评价指标及抑制端点效应的窗函数法[J].制造业自动化,2007,29(1):21-24.