Advertisement

Applied Mathematics and Mechanics

, Volume 26, Issue 2, pp 179–184 | Cite as

Denoising method based on singular spectrum analysis and its applications in calculation of maximal liapunov exponent

  • Liu Yuan-feng
  • Zhao Mei
Article

Abstract

An algorithm based on the data-adaptive filtering characteristics of singular spectrum analysis (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 algorithm could improve the calculating precision of maximal Liapunov exponent.

Key words

singular spectrum analysis denoising maximal Liapunov exponent chaotic system 

Chinese Library Classification

O411 

2000 Mathematics Subject Classification

37D45 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Broomhead D S, King G P. Extracting qualitative dynamics from experimental data[J].Physica D, 1986,20(2/3):217–236.MATHMathSciNetCrossRefGoogle Scholar
  2. [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.MATHMathSciNetCrossRefGoogle Scholar
  3. [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.CrossRefGoogle Scholar
  4. [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.MATHMathSciNetCrossRefGoogle Scholar
  5. [5]
    Kantz H, Schreiber T.Nonlinear Time Series Analysis[M] Cambridge University Press, New York, 1997.Google Scholar
  6. [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.MathSciNetCrossRefGoogle Scholar
  7. [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.CrossRefGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2005

Authors and Affiliations

  • Liu Yuan-feng
    • 1
    • 2
  • Zhao Mei
    • 1
  1. 1.State Key Laboratory of Vibration, Shock and NoiseShanghai Jiaotong UniversityShanghaiP.R. China
  2. 2.Guangdong Kelon Electrical Holdings Co. Ltd.GuangdongP.R.China

Personalised recommendations