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Vector visibility graph from multivariate time series: a new method for characterizing nonlinear dynamic behavior in two-phase flow

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Abstract

Visibility graph provides a well-tried and tested framework for graph-theoretical time series analysis. However, further research still needs to be conducted to extend visibility graph from univariate time series to multivariate time series. In this paper, we propose an algorithm to convert multivariate time series into a directed complex network termed vector visibility graph (VVG). The algorithm maps the multivariate time series to vector space and defines the visibility criteria between vectors. The constructed graphs inherit major property of the series in their topology demonstrated by the fact that random graphs are derived from multivariate random series, and scale-free networks are derived from multivariate fractal series. Finally, the VVG is employed to analyze the conductance sensor signals of typical flow patterns (bubble flow, slug flow, and churn flow) of gas–liquid two-phase flow. The average degree of vector visibility graphs can be utilized for flow pattern recognition. Moreover, the migration of the peak position of the degree distribution can effectively characterize the changes in fluid structure. The result indicates that VVG can effectively characterize nonlinear dynamic behavior in gas–liquid flow patterns.

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Acknowledgements

This study was supported by National Natural Science Foundation of China (Grant Nos. 51527805, 11572220).

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  1. School of Electrical and Information Engineering, Tianjin University, Tianjin, 300072, People’s Republic of China

    Weikai Ren & Ningde Jin

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  1. Weikai Ren
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  2. Ningde Jin
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Correspondence to Ningde Jin.

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Ren, W., Jin, N. Vector visibility graph from multivariate time series: a new method for characterizing nonlinear dynamic behavior in two-phase flow. Nonlinear Dyn 97, 2547–2556 (2019). https://doi.org/10.1007/s11071-019-05147-7

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