Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis

doi:10.1088/1674-1056/22/3/030504

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.

Keywords: nonlinear time series detrended fluctuation analysis Lempel–Ziv complexity correlation coefficient

Received: 18 July 2012
Revised: 28 August 2012
Accepted manuscript online:

PACS:

05.45.-a

(Nonlinear dynamics and chaos)

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

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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Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis

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