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Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection

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Abstract

This work proposes a novel method to construct weighted dynamic transfer network to map time series to complex networks. Firstly, we map time series into symbolic series by analyzing phase space characteristics. Then, we construct the complex network directly from the symbol sequence: symbol compositions correspond to network nodes, and the network edges are the temporal succession between nodes. Meanwhile, a novel method, spectral entropy, is proposed to quantify the local smoothness of complex networks. These two methods are demonstrated by simulation and applied to actual recorded data to confirm the advantages. The synthetic data study shows that the proposed method’s significant advantage is its reduced noise sensitivity. The methods can sense the topological structure change of the noise reconstruction network caused by weak acoustic signals. To further show the utility of these two methods, we provide new evidence of their application in actual recorded data collected in the south China sea. We can easily distinguish ship signals from the marine ambient noise by comparing the spectral entropy value. Meanwhile, compared with the existing network construction and characterization methods, both show that weighted dynamic transfer network and spectral entropy methods can distinguish nonlinear time series from noise more effectively.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This study was supported by the National Natural Science Foundation of China (Key projects) (Grant No. 62031021), National Natural Science Foundation of China (Grant No.61671386, 61901385, 62271404 ), and Northwestern Polytechnical University - Xunsheng Joint Laboratory Innovation Fund Project (LFXS-JLESS-KT20220701).

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Authors and Affiliations

  1. School of Marine Science and Technology, Northwestern Polytechnical University, 127 Youyi West Road, Beilin District, Xi’an, 710072, Shaanxi, China

    Hongwei Zhang, Yongsheng Yan, Xiaohong Shen & Chao Wang

  2. Key Laboratory of Ocean Acoustics and Sensing (Northwestern Polytechnical University), Ministry of Industry and Information Technology, 127 Youyi West Road, Beilin District, Xi’an, 710072, Shaanxi, China

    Hongwei Zhang, Haiyan Wang, Yongsheng Yan, Xiaohong Shen & Chao Wang

  3. School of Electronic Information and Artificial Intelligence Shaanxi University of Science and Technology, Weiyang University Park,Northern Suburb, Xi’an, 710021, Shaanxi, China

    Haiyan Wang

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  1. Hongwei Zhang
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Correspondence to Haiyan Wang.

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No conflict of interest exists in the submission of this manuscript, and all authors approved the manuscript publication. I want to declare on behalf of my co-authors that the work described was original research that has not been published previously and is not under consideration for publication elsewhere, in whole or in part. All the authors listed have approved the manuscript that is enclosed.

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Zhang, H., Wang, H., Yan, Y. et al. Weighted dynamic transfer network and spectral entropy for weak nonlinear time series detection. Nonlinear Dyn 111, 9345–9359 (2023). https://doi.org/10.1007/s11071-023-08310-3

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