Denoising Method Based on Singular Spectrum Analysis and Its Applications in Calculation of Maximal Liapunov Exponent

LIU Yuan-feng; ZHAO Mei

Volume 26 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(2): 163-168

LIU Yuan-feng, ZHAO Mei. Denoising Method Based on Singular Spectrum Analysis and Its Applications in Calculation of Maximal Liapunov Exponent[J]. Applied Mathematics and Mechanics, 2005, 26(2): 163-168.

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Denoising Method Based on Singular Spectrum Analysis and Its Applications in Calculation of Maximal Liapunov Exponent

LIU Yuan-feng^1,2,
ZHAO Mei¹

1.
State Key Laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai 200030, P. R. China;

Received Date: 2003-05-23
Rev Recd Date: 2004-09-14
Publish Date: 2005-02-15

Abstract

Abstract

An algorithm based on the data-adaptive filtering characteristics of singular spectrum analy sis (SSA) is proposed to denoise chaotic data.Firstly,the empirical orthogonal functions (EOFs) and principal components (PCs) of the signal were calculated,reconstruct the signal using the EOFs and PCs,and choose the optimal reconstructing order based on sigular spectrum to obtain the denoised signal.The noise of the signal can influence the calculating precision of maximal Liapunov exponents.The proposed denoising algorithm was applied to the maximal Liapunov exponents calculations of two chaotic system,Henon map and Logistic map.Some numerical results show that this denoising algo rithm could improve the calculating precision of maximal Liapunov exponent.
- singular spectrum analysis,
- denoising,
- maximal Liapunov exponent,
- chaotic system

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References

[1]	Broomhead D S，King G P.Extracting qualitative dynamics from experimental data[J].Physica D,1986,20(2/3):217—236. doi: 10.1016/0167-2789(86)90031-X
[2]	Vautard R，Ghil M.Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series[J].Physica D,1989,35(3):395—424. doi: 10.1016/0167-2789(89)90077-8
[3]	Vautard R,Yiou P，Ghil M.Singular-spectrum analysis: a toolkit for short, noisy chaotic signals[J].Physica D,1992,58(1/4): 95—126. doi: 10.1016/0167-2789(92)90103-T
[4]	Wolf A,Swift J B,Swinney H L，et al.Determining Liapunov exponents from a time series[J].Physica D,1985,16(3):285—297. doi: 10.1016/0167-2789(85)90011-9
[5]	Kantz H，Schreiber T.Nonlinear Time Series Analysis[M].New York： Cambridge University Press, 1997.
[6]	Rosenstein Michael T,Collins James J,De Luca Carlo J.A practical method for calculating largest Liapunov exponents from small data sets[J].Physica D,1993,65(1/2):117—133. doi: 10.1016/0167-2789(93)90009-P
[7]	Kantz Holger.A robust method to estimate the maximal Liapunov exponent of a time series[J].Physics Letters A,1994,185(1):77—87. doi: 10.1016/0375-9601(94)90991-1