综合斜率和三次样条的EMD端点效应抑制方法

Abstract
Figure/Table
References (17)
Related Citation (15)

Download: PDF (2037 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract The end effect will influence the results of empirical mode decomposition (EMD) during the processing of intrinsic mode function (IMF) extraction. In this paper, a new end condition method combined with the idea of improved slope based method (ISBM) and cubic spline based method (CSBM) is proposed. The novelty of this new method lies in that the slope ratio is defined as the tendency of the signal, further to set the coordinates of the extended points combined with the tendency of the signal and its envelope, which can overcome the deficiency of CSBM when setting the values of the extended points. Four different analog signals, two signals from engineering applications, and three performance criteria, i.e., orthogonal index, mean square error and energy error, are selected to evaluate the new method compared with ISBM and CSBM. Experimental results indicate that, overall, the performance of the proposed method is better than that of CSBM and ISBM.
Key words: empirical mode decomposition; the end effect; slope; cubic spline; extension

Key words： empirical mode decomposition the end effect slope cubic spline extension

Received: 28 April 2021 Published: 28 July 2022

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	LIANG Liming1
	2
	WANG Maozhi1
	2
	XU Wenxi1
	2
	TAN Mengting1
	2
	ZHANG Mingyue1
	2
	WANG Shangkun1
	2

Cite this article:

LIANG Liming1,2,WANG Maozhi1, et al. Restriction of the end effect of EMD by utilizing slope and cubic spline based methods[J]. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(14): 70-76.

URL:

http://jvs.sjtu.edu.cn/EN/ OR http://jvs.sjtu.edu.cn/EN/Y2022/V41/I14/70

[1] Huang N E, Shen Z, Long S R, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1998, 454: 903-995.
[2] Huang N E, Wu M L, Qu W, et al. Applications of Hilbert-Huang transform to non-stationary financial time series analysis [J]. Applied Stochastic Models in Business and Industry, 2003, 19(3):245-268.
[3] Rilling G, Flandrin P, Goncalves P. On empirical mode decomposition and its algorithms [J]. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, NSIP-03, 2003, 1-5.
[4] 王红军, 付瑶. 基于多项式拟合的EMD端点效应处理方法研究[J] . 机械设计与制造, 2010, 10: 197-199.
Wang Hongjun, Fu Yao. Study of polynomial fitting technique for EMD end effect [J]. Machinery Design & Manufacture, 2010, 10: 197-199.
[5] Huang D J, Zhao J P, Su J L. Practical implementation of Hilbert-Huang Transform algorithm [J]. Acta Oceanologica Sinica, 2003, 22 (1): 1-14.
[6] Datig M, Schlurmann T. Performance and limitations of the Hilbert-Huang transformation (HHT) with an application to irregular water waves [J]. Ocean Engineering, 2004, 31: 1783–1834.
[7] Wu F J, Qu L S. An improved method for restraining the end effect in empirical mode decomposition and its applications to the fault diagnosis of large rotating machinery [J]. Journal of Sound and Vibration, 2008, 314: 586-602.
[8] Xu W X, Chen S H, Wang M Z, et al. Eliminating the end effect of empirical mode decomposition using a cubic spline based method [J]. Digital Signal Processing, 2021, 110: 102936.
[9] 蔡艳平, 李艾华, 石林锁, 等. EMD端点效应的改进型混沌延拓方法及其在机械故障诊断中的应用 [J]. 振动与冲击, 2011, 30(11): 46-52.
Cai Yanping, Li Aihua, Shi Linsuo, et al. Processing method for end effects of EMD based on improved chaos forecasting model and its application in machinery fault diagnosis [J]. Journal of Vibration and Shock, 2011, 30(11): 46-52.
[10] 杨剑锋, 石戈戈, 周天奇, 等. 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 [J]. 振动与冲击, 2018, 37(18): 121-125.
Yang Jianfeng, Shi Gege, Zhou Tianqi, et al. Waveform extension method based on similarity sequential detection for the end effects reduction of EMD [J]. Journal of Vibration and Shock, 2018, 37(18): 121-125.
[11] Li H Y, Qin X Y, Zhao D, et al. An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm [J]. Applied Mathematics and Computation., 2018, 332: 406-419.
[12] Li H Y, Li L, Zhao D. An improved EMD method with modified envelope algorithm based on C2 piecewise rational cubic spline interpolation for EMI signal decomposition [J]. Applied Mathematics and Computation, 2018, 335: 112-123.
[13] Huang N E. Introduction to the Hilbert–Huang transform and its related mathematical problems [J]. Hilbert-Huang transform and its applications, 2005, 5: 1-26.
[14] Tabrizi A A, Garibaldi L, Fasana A, et al. Automatic damage identification of roller bearings and effects of sifting stop criterion of IMFs [J]. Measurement, 2016, 93: 435-441.
[15] 薛毅. 数值分析与科学计算[M]. 科学出版社, 2011. 224-235.
Xue Yi. Numerical Analysis and Scientific Computation [M]. Science Press, 2011. 224-235.
[16] Yang L J, Yang Z H, Yang L H, et al. An improved envelope algorithm for eliminating undershoots [J]. Digital Signal Processing, 2013, 23(1): 401-411.
[17] Bearing Data Center Seeded Fault Test Data [EB/OL]. https://csegroups.case.edu/bearingdatacenter/pages/download-data-file. Accessed 2021.6.29.