SpringerLink
Log in

Multivariate multiscale increment entropy: a complexity measure for detecting flow pattern transition in multiphase flows

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Multivariate time series are routinely measured in real complex systems, and effective multivariate multiscale methods for uncovering the complexity of multivariate complex systems are certainly needed. In this paper, a new complexity measure for multiscale analysis of multivariate time series, namely multivariate multiscale increment entropy (MMIE), is proposed and applied to detect the nonlinear dynamic complexity of flow pattern transition in oil–gas–water three-phase flow. The MMIE can map each increment into a word of two letters, which contains sign information and magnitude information, and make coupling analysis of multivariate time series. These endow the MMIE an ability to detect the complexity of multivariate time series. The simulation analysis of typical time series shows the importance of multiscale coupling analysis of multivariate time series and the effectiveness of MMIE in mining the complexity of different multivariate time series. Finally, the MMIE is employed to analyze the multichannel sensor signals of oil–gas–water three-phase flow system, which are of multivariate and correlated. The results indicate that MMIE can effectively reveal the dynamic complexity of different flow patterns and their evolution behavior with the change of flow condition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Cooper, K.D., Hewitt, G.F., Pinchin, B.: Photography of two-phase gas/liquid flow. J. Photo. Sci. 12, 269–278 (1964)

    Google Scholar 

  2. Fordham, E.J., Ramos, R.T., Holmes, A., Simonian, S., Huang, S.M., Lenn, C.: Multi-phase-fluid discrimination with local fiber-optical probes: III. Three-phase flows. Meas. Sci. Technol. 10, 1347–1352 (1999)

    Article  Google Scholar 

  3. Parsi, M., Vieira, R.E., Torres, C.F., Kesana, N.R., Mclaury, B.S., Shirazi, S.A., Schleicher, E., Hampel, U.: Experimental investigation of interfacial structures within churn flow using a dual wire-mesh sensor. Int. J. Multiphas. Flow 73, 155–170 (2015)

    Article  Google Scholar 

  4. Liu, L., Matar, O.K., Lawrence, C.J., Hewitt, G.F.: Laser-induced fluorescence (LIF) studies of liquid–liquid flows, Part I: flow structures and phase inversion. Chem. Eng. Sci. 61, 4007–4021 (2006)

    Article  Google Scholar 

  5. Hu, B., Stewart, C., Hale, C.P., Lawrence, C.J., Hall, A.R.W., Zwiens, H., Hewitt, G.F.: Development of an X-ray computed tomography (CT) system with sparse sources: application to three-phase pipe flow visualization. Exp. Fluids 39, 667–678 (2005)

    Article  Google Scholar 

  6. Roshani, G.H., Nazemi, E., Roshani, M.M.: Intelligent recognition of gas-oil-water three-phase flow regime and determination of volume fraction using radial basis function. Flow Meas. Instrum. 54, 39–45 (2017)

    Article  Google Scholar 

  7. Fan, L.T., Neogi, D., Yashima, M., Nassar, R.: Stochastic analysis of a three-phase fluidized bed: fractal approach. AIChE J. 36, 1529–1535 (1990)

    Article  Google Scholar 

  8. Niu, M.R., Liang, Q.F., Yu, G.S., Wang, F.C., Yu, Z.H.: Multifractal analysis of pressure fluctuation signals in an im**ing entrained-flow gasifier. Chem. Eng. Process. 47, 642–648 (2007)

    Article  Google Scholar 

  9. Wu, B., Briens, L., Zhu, J.X.: Multi-scale flow behavior in gas–solids two-phase flow systems. Chem. Eng. J. 117, 187–195 (2006)

    Article  Google Scholar 

  10. Zbilut, J.P., Webber Jr., C.L.: Embeddings and delays as derived from quantification of recurrence plots. Phys. Lett. A 171, 199–203 (1992)

    Article  Google Scholar 

  11. Schinkel, S., Marwan, N., Dimigen, O., Kurths, J.: Confidence bounds of recurrence-based complexity measures. Phys. Lett. A 373, 2245–2250 (2009)

    Article  Google Scholar 

  12. Vlahogianni, E.I., Karlaftis, M.G.: Comparing traffic flow time-series under fine and adverse weather conditions using recurrence-based complexity measures. Nonlinear Dyn. 69, 1949–1963 (2012)

    Article  Google Scholar 

  13. Rosso, O.A., Larrondo, H.A., Martin, M.T., Plastino, A., Fuentes, M.A.: Distinguishing noise from chaos. Phys. Rev. Lett. 99, 154102 (2007)

    Article  Google Scholar 

  14. Wang, Y.Y., Shang, P.J., Liu, Z.L.: Analysis of time series through complexity–entropy curves based on generalized fractional entropy. Nonlinear Dyn. 96, 585–599 (2019)

    Article  Google Scholar 

  15. Peng, C.K., Havlin, S., Stanley, H.E., Goldberger, A.L.: Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos 5, 82–87 (1995)

    Article  Google Scholar 

  16. Kantelhardt, J.W., Zschiegner, S.A., Koscielny-Bunde, E., Havlin, S., Bunde, A., Stanley, H.E.: Multifractal detrended fluctuation analysis of nonstationary time series. Phys. A 316, 87–114 (2002)

    Article  Google Scholar 

  17. Tiwari, A.K., Albulescu, C.T., Yoon, S.M.: A multifractal detrended fluctuation analysis of financial market efficiency: comparison using Dow Jones sector ETF indices. Physica A 483, 182–192 (2017)

    Article  Google Scholar 

  18. Podobnik, B., Stanley, H.E.: Detrended cross-correlation analysis: a new method for analyzing two non-stationary time series. Phys. Rev. Lett. 100, 084102 (2007)

    Article  Google Scholar 

  19. Jiang, Z.Q., Zhou, W.X.: Multifractal detrending moving-average crosscorrelation analysis. Phys. Rev. E 84, 016106 (2011)

    Article  Google Scholar 

  20. Yuan, N.M., Fu, Z., Zhang, H., Lin, P., Elena, X., Juerg, L.: Detrended partial-crosscorrelation analysis: a new method for analyzing correlations in complex system. Sci. Rep. 5, 08143 (2015)

    Article  Google Scholar 

  21. Yan, C., Zhai, L.S., Zhang, H.X., Wang, H.M., **, N.D.: Cross-correlation analysis of interfacial wave and droplet entrainment in horizontal liquid-liquid two-phase flows. Chem. Eng. J. 320, 416–426 (2017)

    Article  Google Scholar 

  22. Pincus, S.M.: Approximate entropy as a measure of system complexity. Proc. Natl. Acad. Sci. USA 88, 2297–2301 (1991)

    Article  MathSciNet  Google Scholar 

  23. Richman, J.S., Moorman, J.R.: Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol Heart C. 278, 2039–2049 (2000)

    Article  Google Scholar 

  24. Costa, M., Goldberger, A.L., Peng, C.K.: Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 89, 068102 (2002)

    Article  Google Scholar 

  25. Thuraisingham, R.A., Gottwald, G.A.: On multiscale entropy analysis for physiological data. Phys. A 366, 323–332 (2006)

    Article  Google Scholar 

  26. Yan, R., Yang, Z., Zhang, T.: Multiscale cross entropy: a novel algorithm for analyzing two time series, In: Proceedings of the 5th International Conference on Natural Computation, pp. 411–413 (2009)

  27. Wang, D.Y., **, N.D., Han, Y.F., Wang, F.: Measurement of gas phase characteristics in vertical oil-gas-water slug and churn flows. Chem. Eng. Sci. 177, 53–73 (2018)

    Article  Google Scholar 

  28. Bandt, C., Pompe, B.: Permutation entropy: a natural complexity measure for time series. Phys. Rev. Lett. 88, 174102 (2002)

    Article  Google Scholar 

  29. Liu, X.F., Wang, Y.: Fine-grained permutation entropy as a measure of natural complexity for time series. Chin. Phys. B 18, 2690–2695 (2009)

    Article  Google Scholar 

  30. Fadlalah, B., Chen, B.D., Keil, A., Príncipe, J.: Weighted-permutation entropy: a complexity measure for time series incorporating amplitude information. Phys. Rev. E 87, 022911 (2013)

    Article  Google Scholar 

  31. Liu, X.F., Jiang, A.M., Xu, N., Xue, J.R.: Increment entropy as a measure of complexity for time series. Entropy 18, 22–35 (2016)

    Article  Google Scholar 

  32. Liu, X.F., Wang, X., Zhou, X., Jiang, A.M.: Appropriate use of the increment entropy for electrophysiological time series. Comput. Biol. Med. 95, 13–23 (2018)

    Article  Google Scholar 

  33. Ahmed, M.U., Mandic, D.P.: Multivariate multiscale entropy: a tool for complexity analysis of multichannel data. Phys. Rev. E 84, 061918 (2011)

    Article  Google Scholar 

  34. Yin, Y., Shang, P.J.: Multivariate multiscale sample entropy of traffic time series. Nonlinear Dyn. 86, 479–488 (2016)

    Article  MathSciNet  Google Scholar 

  35. Gao, Z.K., Yang, Y.X., Zhai, L.S., Ding, M.S., **, N.D.: Characterizing slug to churn flow transition by using multivariate pseudo Wigner distribution and multivariate multiscale entropy. Chem. Eng. J. 291, 74–81 (2016)

    Article  Google Scholar 

  36. Morabito, F.C., Labate, D., Foresta, F.L., Bramanti, A., Morabito, G., Palamara, I.: Multivariate multi-scale permutation entropy for complexity analysis of Alzheimer’s disease EEG. Entropy 14, 1186–1202 (2012)

    Article  Google Scholar 

  37. Yin, Y., Shang, P.J.: Multivariate weighted multiscale permutation entropy for complex time series. Nonlinear Dyn. 88, 1707–1722 (2017)

    Article  MathSciNet  Google Scholar 

  38. Han, Y.F., **, N.D., Zhai, L.S., Ren, Y.Y., He, Y.S.: An investigation of oil–water two-phase flow instability using multivariate multi-scale weighted permutation entropy. Phys. A 518, 131–144 (2019)

    Article  MathSciNet  Google Scholar 

  39. Wang, D.Y., **, N.D., Zhai, L.S., Ren, Y.Y.: Characterizing flow instability in oil-gas-water three-phase flow using multi-channel conductance sensor signals. Chem. Eng. J. (2019). https://doi.org/10.1016/j.cej.2019.03.113

    Article  Google Scholar 

  40. Wang, D.Y., **, N.D., Zhuang, L.X., Zhai, L.S., Ren, Y.Y.: Development of a rotating electric field conductance sensor for measurement of water holdup in vertical oil-gas-water flows. Meas. Sci. Technol. 29, 075301 (2018)

    Article  Google Scholar 

Download references

Acknowledgements

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

Author information

Authors and Affiliations

  1. School of Electrical and Information Engineering, Tian** University, Tian**, 300072, China

    Dayang Wang & Ningde **

Authors
  1. Dayang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ningde **
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ningde **.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest concerning the publication of this manuscript.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, D., **, N. Multivariate multiscale increment entropy: a complexity measure for detecting flow pattern transition in multiphase flows. Nonlinear Dyn 100, 3853–3865 (2020). https://doi.org/10.1007/s11071-020-05733-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05733-0

Keywords

Search

Navigation