Improve the Envelope of EMD with Piecewise Linear Fractal Interpolation

Abstract:

Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing non-stationary signals as sums of zero-mean amplitude modulation frequency modulation components. The traditional EMD algorithm adopts the cubic spline interpolation as an effective tool processing non-stationary signal, but it cannot effectively extract the characteristic frequencies from a highly non-stationary signal, and the overshoots and the undershoots may become a common phenomenon during the decomposition process. In order to solve the problem, we presents the piecewise linear fractal interpolation as the spline interpolating. Finally, we will use the simulation signal to verify the effectiveness of the improved EMD.

• Periodical: Key Engineering Materials (Volumes 439-440)
• Pages: 390-395
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.439-440.390
• Online since: June 2010
• Authors: Zhi Ping Fan, Tian Sheng Hong, Zhi Zhuan Liu, Zheng Zhe Jing
• Keywords: Empirical Mode Decomposition (EMD), Envelope Algorithm, Non-Stationary Signal, Piecewise Linear Fractal Interpolation, Sifting Process

References

[1] N. E. Huang et. al.: The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond. A, vol. 454, pp.903-995, Mar. (1998).

DOI: 10.1098/rspa.1998.0193

[2] Huang NE, Shen Z, Long S R, et al: A new view of nonlinear waves: The Hilbert spectrum, Annual Review of Fluid Mechanics, 417-457 (1999).

DOI: 10.1146/annurev.fluid.31.1.417

[3] M. Bamsley, Fractah Eveywbere: Academic Press, Inc., London.

[4] K. Semion, P. Thomas, Flatley, etc: On the Hilbert-Huang Transform Data Processing System Development. IEEE Aerospace Conference Proceedings, pp.1961-1979, (2004).

[5] C. Moler: Numerical Computing with Matlab. Society for Industrial and Applied Mathematics, (2004).

[6] Long Si sheng, Zhang Tie long, Long Feng. The causes and solutions for fitting overshoot and endpoint flying wing in Hilbert-Huang Transformation. ACTA SEISMOLO GICA SINICA Vol. 27, No. 5, 561-568.

[7] N. E Huang, Z. Shen and S.R. Long et al, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proceeding of Royal Society London, Series A. Vol. 454, 903-995, (1998).

DOI: 10.1098/rspa.1998.0193

[8] Huang NE, Wu M, Long S R, et al. A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proc. R. Soc, Lond. 2003, A 459: 2317-2345.

DOI: 10.1098/rspa.2003.1123

[9] P. Flandrin, Some aspects of Huang's empirical mode decomposition, from interpretation to applications, presented at the Int. Conf. Computational Harmonic Analysis (Invited Talk), Nashville, TN, (2004).

[10] M. Datig and T. Schlurmann, Performance and limitations of the Hilberthuang transformation (HHT) with an application to irregular water waves, , Ocean Engineering, Vol. 31, pp.1783-1834, (2004).

DOI: 10.1016/j.oceaneng.2004.03.007

[11] LIU Hui-Ting , NI Zhi- Wei, Clustering Method of Time Series Based on EM D and K-means Algorithm , PR & AI, VOL. 22, P803-808, (2009).

[12] WANG Ting , YANG Shen-yuan , LI Bing-bing, A New Method for End Effect of EMD, JOURNAL OF HARBIN UNIVERSI TY 0F SCIENCE AND TECHNOIDGY, VOL . 14, P23-26, (2009).