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Three-dimensional causal complementary complexity: a new measure for time series complexity analysis

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Abstract

The empirical mode decomposition (EMD) energy entropy plane is an effective tool for analysing the complexity of time series, but mode mixing caused by EMD affects the accuracy of experimental results. To overcome this shortcoming, we propose a new complexity-entropy causal plane named the complete ensemble EMD with adaptive noise analysis (CEEMDAN) energy entropy plane, which is a combination of CEEMDAN energy entropy and the statistical complexity metric. Among the existing methods of entropy planes, no method has been proposed that can reflect the randomness and complexity of time series from both the internal mode of time series and the original signal. To further improve its signal classification ability and time series complexity analysis skills, we introduce dispersion entropy into the CEEMDAN energy entropy plane as a complementary feature and propose three-dimensional causal complementary complexity so that this representation space expands from two-dimensional to three-dimensional. Simulation experiments show that the proposed three-dimensional causal complementary complexity can better distinguish different states of the logistic map. In addition, real-world experiments show that the proposed three-dimensional causal complementary complexity has better performance in ship signal classification and bearing fault diagnosis.

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Data availability

The datasets analysed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This work was supported by the Natural Science Foundation of Shaanxi Province (No. 2022JM-337), National Natural Science Foundation of China (No.61871318) and Xi'an University of Technology Excellent Seed Fund (No. 252082220).

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Authors and Affiliations

  1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Yuxing Li, Shangbin Jiao, Yin Zhu & Yujun Li

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  1. Yuxing Li
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  2. Shangbin Jiao
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  3. Yin Zhu
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  4. Yujun Li
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Correspondence to Yuxing Li.

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Li, Y., Jiao, S., Zhu, Y. et al. Three-dimensional causal complementary complexity: a new measure for time series complexity analysis. Nonlinear Dyn 111, 17299–17316 (2023). https://doi.org/10.1007/s11071-023-08776-1

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  • DOI: https://doi.org/10.1007/s11071-023-08776-1

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