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Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis |
Tang You-Fu (唐友福)a b, Liu Shu-Lin (刘树林)a, Jiang Rui-Hong (姜锐红)a, Liu Ying-Hui (刘颖慧)a |
a School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China;
b School of Mechanical Science and Engineering, Northeast Petroleum University, Daqing 163318, China |
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Abstract We focus on the study of the correlation between the detrended fluctuation analysis (DFA) and the Lempel–Ziv complexity (LZC) in nonlinear time series analysis in this paper. Typical dynamical systems including logistic map and Duffing model are investigated. Moreover, the influences of the Gaussian random noise on both DFA and LZC are analyzed. The results show a high correlation between DFA and LZC, which can quantify the non-stationarity and the nonlinearity of the time series, respectively. With the enhancement of the random component, the exponent α and the normalized complexity index C show increasing trends. In addition, C is found to be more sensitive to the fluctuation in the nonlinear time series than α. Finally, the correlation between DFA and LZC is applied to the feature extraction of vibration signals for a reciprocating compressor gas valve, and an effective fault diagnosis result is obtained.
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Received: 18 July 2012
Revised: 28 August 2012
Accepted manuscript online:
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PACS:
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05.45.-a
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(Nonlinear dynamics and chaos)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 51175316) and the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20103108110006). |
Corresponding Authors:
Liu Shu-Lin
E-mail: lsl346@shu.edu.cn
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Cite this article:
Tang You-Fu (唐友福), Liu Shu-Lin (刘树林), Jiang Rui-Hong (姜锐红), Liu Ying-Hui (刘颖慧) Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis 2013 Chin. Phys. B 22 030504
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[1] |
Huang N E, Shen Z and Long S R 1998 Proc. R. Soc. London, Ser. A 454 903
|
[2] |
Srinivasan K, Panickar P, Raman G, Kim B H and Williams D R 2009 J. Sound Vib. 323 910
|
[3] |
Dwivedi Y and Rao S S 2011 J. Time Ser. Anal. 32 68
|
[4] |
Andel J, Netuka I and Ranocha P 2007 Stat. 41 279
|
[5] |
Kalvoda T and Hwang Y R 2010 Sens. Actuators A 161 39
|
[6] |
Yuan Y, Li Y, Mandicb D P and Yang B J 2009 Chin. Phys. B 18 958
|
[7] |
Cong R, Liu S L and Ma R 2008 Acta Phys. Sin. 57 7487 (in Chinese)
|
[8] |
Wu T Y, Chen J C and Wang C 2012 Mech. Syst. Sig. Process 30 103
|
[9] |
Tang Y F, Liu S L, Lei N, Jiang R H and Liu Y H 2012 Acta Phys. Sin. 61 170504 (in Chinese)
|
[10] |
Xie F, Yang R and Zhang B 2012 Acta Phys. Sin. 61 110504 (in Chinese)
|
[11] |
Luo X L, Wang J and Han C X 2012 Chin. Phys. B 21 028701
|
[12] |
Peng C K, Buldyrev S V and Havlin S 1994 Phys. Rev. E 49 1685
|
[13] |
Zhu S S, Xu Z X, Yin K X and Xu Y L 2011 Chin. Phys. B 20 050503
|
[14] |
Zhou Y, Yu Z G and Leung Y 2011 Chin. Phys. B 20 090507
|
[15] |
Li S S, Lan J and Han B 2012 Chin. Phys. B 21 064601
|
[16] |
Burt T and Worrall F 2007 Hydrocarb Process 21 3529
|
[17] |
Peng C K, Havlin S, Stanley H E and Goldberger A L 1995 Chaos 5 82
|
[18] |
deMoura E P, Vieira A P, Irma M A S and Silva A A 2009 Mech. Syst. Sig. Process 23 682
|
[19] |
Daw C S, Finney C E A and Tracy E R 2003 Rev. Sci. Instrum. 74 915
|
[20] |
Hong H B and Liang M 2009 J. Sound Vib. 320 452
|
[21] |
Hou W, Feng G L and Dong W J 2005 Acta Phys. Sin. 54 3940 (in Chinese)
|
[22] |
Wang K, Guan X P, Ding X F and Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese)
|
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