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. 2024 Feb 23:12:102620.
doi: 10.1016/j.mex.2024.102620. eCollection 2024 Jun.

Method for phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines

Edgar Orlando Ladino-Moreno  1 , César Augusto García-Ubaque  1 , Eduardo Zamudio-Huertas  1
Affiliations

Method for phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines

Edgar Orlando Ladino-Moreno et al. MethodsX. .

Abstract

In this study, we propose a method based on phase space reconstruction to estimate the short-term future behavior of pressure signals in pipelines. The pressure time series data were obtained from an IoT experimental model conducted in the laboratory. The proposed hydraulic system demonstrated the presence of traces of weak chaos in the time series of the pressure signal. Fractal dimension analysis revealed a complex fractal structure in the data, indicating the existence of nonlinear dynamics. Similarly, Lyapunov coefficients, divergent trajectories, and autocorrelation analysis confirmed the presence of weak chaos in the time series. The results demonstrated the existence of apparently chaotic patterns that follow the theory proposed by Kolmogorov for deterministic dynamic systems that exhibit apparently random behaviors. Phase space reconstruction allowed us to show the dynamic characteristics of the signal so that short-term predictions were stable. Finally, the study of strange attractors in pipeline pressure time series can have significant contributions to anomaly detection.•A methodology is proposed for the reconstruction of the phase space to estimate the short-term future behavior of pressure signals in pipelines in real time.•The analysis of the proposed hydraulic system revealed some indications of weak chaos in the time series of the pressure signal obtained experimentally.•The methodology implemented and the results of this study showed that the short-term predictions were very accurate and consistent; Chaotic patterns were also identified that support the theory proposed by Kolmogorov.

Keywords: Arduino; Chaos; IoT; Method phase space reconstruction; Phase space reconstruction; Signals; Transients in pipelines.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Image, graphical abstract
Graphical abstract
Fig 1
Fig. 1
Hydraulic design.
Fig 2
Fig. 2
Electronic system.
Fig 3
Fig. 3
Experimental design (Hydraulics Laboratory, Universidad Distrital Francisco José de Caldas).
Fig 4
Fig. 4
Original signal - filtered signal (Pressure).
Fig 5
Fig. 5
Signal analysis methodology.
Fig 6
Fig. 6
Spectrogram.
Fig 7
Fig. 7
Filters pressure signal filters.
Fig 8
Fig. 8
Detection of chaotic behavior.
Fig 9
Fig. 9
Autocorrelation and spectral density.
Fig 10
Fig. 10
Indications of the existence of chaotic behavior.
Fig 11
Fig. 11
Phase space reconstruction methodology.
Fig 12
Fig. 12
Phase space and short-term prediction.
See this image and copyright information in PMC

References

    1. Mukhopadhyay y S. Banerjee S. Learning dynamical systems in noise using convolutional neural networks. Chaos. 2020;30:103125–103131. doi: 10.1063/5.0009326. - DOI - PubMed
    1. F.J. Vázquez Hernández, «Caos y complejiddad en la economía,» De Las Teorías del Caos y Los Sistemas complejos: Proyecciones físicas, biológicas, Sociales y Económicas, Madrid, 2001.
    1. Draho J., Puncochar y V. Tramutoli M. «Evidence of weak chaos within plug-slug transition in horizontal two-phase flow,». Europhys. Lett. 1995;32(2):75–80.
    1. Wang y Z. e. Li L.Y. «Pressure signal prediction of aviation hydraulic pumps based on phase space reconstruction and support vector machine,». IEEE. 2021;9:2966–2974. doi: 10.1109/ACCESS.2020.3047988. - DOI
    1. Shi W., Cai R., et al. «Chaotic analysis of pressure fluctuation in bulb tubular pump under different flow conditions». J. Drain. Irrig. Mach. Eng. 2022;40:345–352. doi: 10.3969/j.issn.1674-8530.21.0346. - DOI

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