Fuzzy permutation entropy derived from a novel distance between segments of time series

Zelin Zhang; Zhengtao Xiang; Yufeng Chen; Jinyu Xu; Zelin Zhang; Zhengtao Xiang; Yufeng Chen; Jinyu Xu

doi:10.3934/math.2020402

AIMS Mathematics

2020, Volume 5, Issue 6: 6244-6260. doi: 10.3934/math.2020402

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Research article

Fuzzy permutation entropy derived from a novel distance between segments of time series

1.
School of Science, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, China
2.
School of Electrical and Information Engineering, Hubei University of Automotive Technology, 167 Chechengxi Road, Shiyan 442002, China

Received: 11 June 2020 Accepted: 27 July 2020 Published: 05 August 2020
MSC : 94A17

As effective tools for time series analyzing, a variety of information entropies have been widely applied in engineering, economic, biomedicine and other fields. In this paper, we define a new distance between finite sequence based on inversion and derive a new entropy, Fuzzy Permutation Entropy(FPE). A comparison of recognition performance for WGN, 1/f noise, periodical, or chaotic sequence and sine waves shows that FPE is valid on distinguishing deterministic signals from stochastic signals. Further contrast studying versus FE and PE shows that FPE is more sensitive to the alteration of the complexity of time series and more effective on separating different signals. Moreover, FPE is used to explore the distinction of the complexity of various traffic flows via the time headways which is simulated from the improved brake light rule model. We hope it is conducive to design Intelligent Transportation Management System.
- information entropy,
- fuzzy entropy,
- permutation entropy,
- multiscale entropy,
- traffic flow
Citation: Zelin Zhang, Zhengtao Xiang, Yufeng Chen, Jinyu Xu. Fuzzy permutation entropy derived from a novel distance between segments of time series[J]. AIMS Mathematics, 2020, 5(6): 6244-6260. doi: 10.3934/math.2020402

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Abstract

As effective tools for time series analyzing, a variety of information entropies have been widely applied in engineering, economic, biomedicine and other fields. In this paper, we define a new distance between finite sequence based on inversion and derive a new entropy, Fuzzy Permutation Entropy(FPE). A comparison of recognition performance for WGN, 1/f noise, periodical, or chaotic sequence and sine waves shows that FPE is valid on distinguishing deterministic signals from stochastic signals. Further contrast studying versus FE and PE shows that FPE is more sensitive to the alteration of the complexity of time series and more effective on separating different signals. Moreover, FPE is used to explore the distinction of the complexity of various traffic flows via the time headways which is simulated from the improved brake light rule model. We hope it is conducive to design Intelligent Transportation Management System.

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