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EMD based refined composite multiscale entropy analysis of complex signals

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  • Wang, Jing
  • Shang, Pengjian
  • Xia, Jianan
  • Shi, Wenbin

Abstract

Multiscale entropy (MSE) is an effective method to measure the complexity of signals from complex systems, which has been applied to various fields successfully. However, MSE may yield an inaccurate estimate of entropy and induce undefined entropy as the coarse-graining procedure reduces the length of data considerably at large scales. Refined composite multiscale entropy (RCMSE) is then developed to solve this problem. However, trends superimposed in signals may significantly affect the complexity measurement. Thus we introduce an empirical mode decomposition based RCMSE, called EMD–RCMSE to first eliminate such effects of trends and then measure the complexity of signals. It is validated from simulated signals and has good estimation. In addition, this method is also applied to study the complexity of traffic signals and we obtain some interesting results: (1) Traffic signals are more complex than the results showing from RCMSE/MSE; (2) Weekday and weekend patterns (different combination of trends) greatly affect the results; (3) Complexity indices change with time at each day, due to the degree of human activities.

Suggested Citation

  • Wang, Jing & Shang, Pengjian & Xia, Jianan & Shi, Wenbin, 2015. "EMD based refined composite multiscale entropy analysis of complex signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 583-593.
    • Handle: RePEc:eee:phsmap:v:421:y:2015:i:c:p:583-593
    DOI: 10.1016/j.physa.2014.12.001
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    References listed on IDEAS

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    1. Ansorge, Rainer, 1990. "What does the entropy condition mean in traffic flow theory?," Transportation Research Part B: Methodological, Elsevier, vol. 24(2), pages 133-143, April.
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    3. Xia, Jianan & Shang, Pengjian & Wang, Jing & Shi, Wenbin, 2014. "Classifying of financial time series based on multiscale entropy and multiscale time irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 151-158.
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    Citations

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    Cited by:

    1. Yin, Yi & Shang, Pengjian & Feng, Guochen, 2016. "Modified multiscale cross-sample entropy for complex time series," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 98-110.
    2. Wang, Shujia & Yang, Zhuojin & Zheng, Xin & Ma, Zhuang, 2024. "Analysis of complex time series based on EEMD energy entropy plane," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Tian, Hu & Zheng, Xiaolong & Zeng, Daniel Danjun, 2019. "Analyzing the dynamic sectoral influence in Chinese and American stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    4. Zhang, Ningning & Lin, Aijing & Ma, Hui & Shang, Pengjian & Yang, Pengbo, 2018. "Weighted multivariate composite multiscale sample entropy analysis for the complexity of nonlinear times series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 595-607.
    5. Brechtl, Jamieson & Xie, Xie & Liaw, Peter K. & Zinkle, Steven J., 2018. "Complexity modeling and analysis of chaos and other fluctuating phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 166-175.
    6. Xu, Meng & Shang, Pengjian, 2018. "Analysis of financial time series using multiscale entropy based on skewness and kurtosis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 1543-1550.
    7. Xia, Jianan & Shang, Pengjian & Lu, Dan & Yin, Yi, 2016. "A comprehensive segmentation analysis of crude oil market based on time irreversibility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 104-114.
    8. Fan, Qingju, 2016. "Asymmetric multiscale detrended fluctuation analysis of California electricity spot price," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 252-260.
    9. Xiong, Hui & Shang, Pengjian & Bian, Songhan, 2017. "Detecting intrinsic dynamics of traffic flow with recurrence analysis and empirical mode decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 70-84.
    10. Liu, Yunxiao & Lin, Youfang & Wang, Jing & Shang, Pengjian, 2018. "Refined generalized multiscale entropy analysis for physiological signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 975-985.

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