Correlation between detrended fluctuation analysis and the Lempel–Ziv complexity in nonlinear time series analysis |
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| Authors: | Tang You-Fu Liu Shu-Lin Jiang Rui-Hong Liu Ying-Hui |
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| Institution: | 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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| Keywords: | nonlinear time series detrended fluctuation analysis Lempel&ndash Ziv complexity correlation coefficient |
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