Process method for end effects of HHT based on data/ extrema symmetrical extension and its application

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (22) : 178-184.

Chen Wu 1,2, Hong Xiang1,2 , Xipeng Du1,2

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Abstract

End effects produce in EMD decomposition because the endpoint is not extreme point and the requirements of spline interpolation could not be met. And then End effects produce in Hilbert transform due to the convolution calculation and the energy leakage of Fourier transform. In this paper, a data/ extrema symmetrical extension method is proposed. Using end data symmetrical extension, the end swings result from EMD and Hilbert transform can be released to the outside of the data. Through extrema symmetrical extension, the shape of the cubic spline envelope curve is further controlled and the envelope curve of the original data is more accurate. The simulation demonstrates the effectiveness of the method. When this method is applied to the structural dynamic non-linear characteristics analysis, clear physical meaning and two non-linear mechanical characteristics including "frequency band extension" and "main frequency drift" can be described accurately.

Key words

Hilbert-Huang transforms / end data / extrema / symmetrical extension / non-linear mechanical characteristics

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Chen Wu 1,2, Hong Xiang1,2,Xipeng Du1,2. Process method for end effects of HHT based on data/ extrema symmetrical extension and its application[J]. Journal of Vibration and Shock, 2017, 36(22): 178-184

References

[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.R.Soc.Lond., 1998, A454:903~995.
[2] 吴祚菊,张建经,王志佳,吴兴序.改进HHT算法在地震动特性分析中的应用研究[J].地震工程与工程振动, 2015,35(2): 86-93
Wu Zuoju, Zhang Jianjing, Wang Zhijia, Wu Xingxu. Research on seismic instantaneous frequency characteris¬tics based on modified HHT algorithm [J]. Earthquake Engineering and Engineering Dynamics, 2015, 35(2):86-93. (in Chinese)
[3] 韩建平,李林,王洪涛, 钱炯. 基于Hilbert-Huang变换和随机减量技术的模态参数识别[J] 世界地震工程,2011, 27(1):72-77
Han Jianping,Li Lin,Wang Hongtao,Qian Jiong. Modal parameter identification based on Hilbert-Huang transform and random decrement technique [J]. World Earthquake Engineering, 2011, 27(1):72-77. (in Chinese)
[4] Yi-Li Tseng, Pin-Yu Ko, and Fu-Shan Jaw.Detection of the third and fourth heart sounds using Hilbert-Huang transform[J] BioMedical Engineering Online,2012(1):1-8.
[5] Yaguo Lei ,Jing Lin, Zhengjia He, Ming J. Zuo. A review on empirical mode decomposition in fault diagnosis of rotating machinery [J]. Mechanical Systems and Signal Processing, 2013, 35(1–2):108–126.
[6] 杨光亮,朱元清,于海英.基于HHT的地震信号自动去噪方法[J] 大地测量与地球动力学,2010,30(3):39-42
Yang Guangliang, Zhu Yuanqing, Yuhaiying.Automatic de-nosing algorithm of earthquake signal based on HHT decomposition[J].Journal of Geodesy and Geodynamics, 2010,30(3):39-42(in Chinese)
[7] Ioannidis, K. Andreadis, I. A Digital Image Stabilization Method Based on the Hilbert–Huang Transform [J]. IEEE Transaction on Instrumentation and Measurement, 2012,61(9):2446-2457
[8] Huang N.E., Wu M.,Long S.R.,et al. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis [J]. Proc.R.Soc.Lind.,2003, A459:2317-2345.
[9] 舒忠平, 杨智春.抑制经验模分解边缘效应的极值点对称延拓法[J]. 西北工业大学学报,2006,24(5):639-643
Shu Zhongping , Yang Zhichun. A Better Method for Effectively Suppressing End Effect of Empirical Mode Decomposition (EMD)[J]. Journal of Northwestern Polytechnical University, 2006, 24(5):639-643(in Chinese)
[10] 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
Shen Lu, Zhou Xiaojun, Zhang Zhigang, et al. Boundary- extension method in Hilbert-Huang transform[J].Journal of Vibration and Shock, 2009,28(8):168-171（in Chinese）
[11] 王学敏,黄方林. EMD端点效应抑制的一种实用方法[J]. 振动.测试与诊断. 2012(3): 493-497.
Wang Xuemin, Huang Fanglin. Practical Method to Restrain the End Effect of EMD [J]. Journal of Vibration, Measurement & Diagnosis. 2012(3): 493-497.(in Chinese)
[12] 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, 40(16): 84-86, 100.
Liu Huiting, Zhang Min, Cheng Jiaxing. Dealing with the End Iusse of EMD Based on Polynomial Fitting Algorithm [J]. Computer Engineering and Applications. 2004, 40(16): 84-86, 100. (in Chinese)

[13] Huang N.E. Empirical mode decomposition apparatus, method and article of manufacture for analysing biologi¬cal signals and performing curve fitting: United states, 6381559[P].2002-02-04.
[14] 黄大吉,赵进平,苏纪兰. 希尔伯特-黄变换的端点延拓[J]. 海洋学报(中文版). 2003(01): 1-11.
Huang Daji, Zhao Jinping, Su Jilan. Practical implementa¬tion of Hilbert-Huang transform algorithm [J]. Acta. Oceanologica Sinica, 2003,25(1):1-11.(in Chinese)
[15] 邓拥军,王伟,钱成春,等. EMD方法及Hilbert 变换中边界问题的处理[ J].科学通报, 2001, 46( 3): 257-263.
Deng Yongjun, Wang Wei, Qian Chengchun, etc. Manage-ment of boundary problem in EMD and HHT [ J]. Chinese Science Bulletin, 2001, 46( 3): 257-263. (in Chinese)
[16] 窦东阳,赵英凯.利用ARIM A改进HHT端点效应的方法[ J].振动、测试与诊断, 2010, 30( 3): 249-253.
Dou Dongyang , Zhao Ying kai. Method of improving ending effect of Hilbert-Huang transform using auto-regressive integrated moving average model [J]. Journal of Vibration, Measurement & Diagnosis, 2010, 30(3): 249-253. (in Chinese)
[17] 李雪耀,张汝波,王武.基于支持向量回归机的HHT边界效应处理[J].智能系统学报,2007,2(3):39-44
Li Xueyao,Zhang Rubo, Wangwu. End effects processing in HHT based on support vector regression machines [J]. CAAI Transaction on Intelligent Systems, 2007,2(3):39-44. (in Chinese)
[18] 吴琛,周瑞忠. 基于Hilbert谱的结构动力响应非线性特征分析[J].振动与冲击,2013.7,32(14):70-76
Wu Chen, Zhou Ruizhong. Nonlinear behavior analysis of structural dynamic response based on Hilbert spectrum [J]. Journal of vibration and shock,2013.7,32(14):70-76.(in Chinese)