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

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

中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30504-030504.doi: 10.1088/1674-1056/22/3/030504

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

唐友福^{a b}, 刘树林^a, 姜锐红^a, 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

收稿日期:2012-07-18 修回日期:2012-08-28 出版日期:2013-02-01 发布日期:2013-02-01
基金资助:
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).

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

Received:2012-07-18 Revised:2012-08-28 Online:2013-02-01 Published:2013-02-01
Contact: Liu Shu-Lin E-mail:lsl346@shu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: nonlinear time series, detrended fluctuation analysis, Lempel-Ziv complexity, correlation coefficient

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.

Key words: nonlinear time series, detrended fluctuation analysis, Lempel–Ziv complexity, correlation coefficient

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

唐友福, 刘树林, 姜锐红, 刘颖慧. Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis[J]. 中国物理B, 2013, 22(3): 30504-030504.

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[J]. Chin. Phys. B, 2013, 22(3): 30504-030504.

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

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

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