Development of a Conservative Hamiltonian Dynamic System for the Early Detection of Leaks in Pressurized Pipelines
DOI:
https://doi.org/10.28991/CEJ-2024-010-04-01Keywords:
®Arduino, Conservative Systems, Hamiltonian System, IoT, Leaks, ODE45, Real-Time, Pipelines.Abstract
In this study, we propose an innovative approach for real-time leakage detection in pipelines by integrating conservative Hamiltonian equations and experimental Internet of Things (IoT) technologies. The proposed method combines a hybrid model that utilizes sensors and IoT devices to acquire real-time data and solves the coupled system of Hamiltonian equations using the ODE45 numerical integration method. Spectral frequency analysis is an essential part of this method, as it reveals specific patterns in the pressure and flow signals. The findings highlighted 95% accuracy in leak detection, which was validated through a comparison of the theoretical and experimental data. The novelty of this approach lies in its ability to maintain constant total system energy, thereby enabling continuous monitoring for early leak detection. As an improvement, the proper handling of sensor signals is emphasized, underscoring its contribution to the efficient management of water resources in potable water distribution systems.
Doi: 10.28991/CEJ-2024-010-04-01
Full Text: PDF
References
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[21] Phipps Electronics. (2024). YF-S201 Hall Effect Water Flow Meter / Sensor. Phipps Electronics, North Revesby, Australia. Available online: https://www.phippselectronics.com/product/yf-s201-hall-effect-water-flow-meter-sensor/ (accessed on March 2024).
[22] Urbanowicz, K., Duan, H. F., & Bergant, A. (2020). Transient liquid flow in plastic pipes. Strojniski Vestnik/Journal of Mechanical Engineering, 66(2), 77–90. doi:10.5545/sv-jme.2019.6324.
[23] Kulmány, I. M., Bede-Fazekas, í., Beslin, A., Giczi, Z., Milics, G., Kovács, B., Kovács, M., Ambrus, B., Bede, L., & Vona, V. (2022). Calibration of an Arduino-based low-cost capacitive soil moisture sensor for smart agriculture. Journal of Hydrology and Hydromechanics, 70(3), 330–340. doi:10.2478/johh-2022-0014.
[24] Bedford, A. (2021). Hamilton's Principle in Continuum Mechanics. Springe, Cham. Switzerland. doi:10.1007/978-3-030-90306-0.
[2] Speziali, S., Bianchi, F., Marini, A., Menculini, L., Proietti, M., Termite, L. F., Garinei, A., Marconi, M., & Delogu, A. (2021). Solving Sensor Placement Problems in Real Water Distribution Networks Using Adiabatic Quantum Computation. IEEE International Conference on Quantum Computing and Engineering (QCE), Broomfield, Colorado, United States. doi:10.1109/qce52317.2021.00079.
[3] Verde, C., & Torres, L. (2017). Modeling and monitoring of pipelines and networks. Springer, Cham, Switzerland. doi:10.1007/978-3-319-55944-5.
[4] Rodríguez Calderón, W., & Pallares Muñoz, M. R. (2007). A numerical water-hammer model using Scilab. Ingeniería e Investigación, 27(3), 98–105. doi:10.15446/ing.investig.v27n3.14850. (In Spanish).
[5] Firouzi, A., Yang, W., Shi, W., & Li, C.-Q. (2021). Failure of corrosion affected buried cast iron pipes subject to water hammer. Engineering Failure Analysis, 120, 104993. doi:10.1016/j.engfailanal.2020.104993.
[6] Sánchez-Jiménez, A. D., Torres, L., & López-Estrada, F. R. (2020). Euler-Lagrange approach for modeling water pipelines with leaks. Memorias del Congreso Nacional de Control Automático, 1-7.
[7] Macias, G., & Lee, K. (2022). Optimal Gas Leak Localization and Detection using an Autonomous Mobile Robot. Proceedings of the 9th International Conference of Control, Dynamic Systems, and Robotics (CDSR'22), Niagara Falls, Canada. doi:10.11159/cdsr22.122.
[8] Schneider, J., Tél, T., & Neufeld, Z. (2002). Dynamics of "leaking” Hamiltonian systems. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 66(6), 6. doi:10.1103/PhysRevE.66.066218.
[9] Torres, L., & Besancon, G. (2019). Port-Hamiltonian Models for Flow of Incompressible Fluids in Rigid Pipelines with Faults. 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France. doi:10.1109/cdc40024.2019.9029170.
[10] Perryman, R., Taylor, J. A., & Karney, B. (2022). Port-Hamiltonian based control of water distribution networks. Systems & Control Letters, 170. doi:10.1016/j.sysconle.2022.105402.
[11] Lopezlena, R. (2014). Computer implementation of a boundary feedback leak detector and estimator for pipelines II: Leak estimation. Memorias del XVI Congreso Latinoamericano, 14-17 October, 2014, Cancún, Mexico.
[12] Rashad, R., Califano, F., Schuller, F. P., & Stramigioli, S. (2021). Port-Hamiltonian modeling of ideal fluid flow: Part II. Compressible and incompressible flow. Journal of Geometry and Physics, 164. doi:10.1016/j.geomphys.2021.104199.
[13] Beattie, C., Mehrmann, V., Xu, H., & Zwart, H. (2018). Linear port-Hamiltonian descriptor systems. Mathematics of Control, Signals, and Systems, 30(4). doi:10.1007/s00498-018-0223-3.
[14] Zi Li, L., Rosli, M. I., & Panuh, D. (2019). Velocity Modelling for Pipeline Inspection Gauge. Jurnal Kejuruteraan, 31(2), 275–280. doi:10.17576/jkukm-2019-31(2)-11.
[15] Bendimerad-Hohl, A., Matignon, D., Haine, G., & Lefèvre, L. (2024). On implicit and explicit representations for 1D distributed port-Hamiltonian systems. arXiv Preprint, arXiv:2402.07628. doi:10.48550/arXiv.2402.07628.
[16] Zhang, J., Zhu, Q., & Lin, W. (2024). Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation laws. Physical Review Research, 6(1), 12031. doi:10.1103/PhysRevResearch.6.L012031.
[17] Eidnes, S., Stasik, A. J., Sterud, C., Bí¸hn, E., & Riemer-Sí¸rensen, S. (2023). Pseudo-Hamiltonian neural networks with state-dependent external forces. Physica D: Nonlinear Phenomena, 446, 446. doi:10.1016/j.physd.2023.133673.
[18] Sultana, S., & Rahman, Z. (2013). Hamiltonian Formulation for Water Wave Equation. Open Journal of Fluid Dynamics, 3(2), 75–81. doi:10.4236/ojfd.2013.32010.
[19] Przystupa, K., AmbroŠ¼kiewicz, B., & Litak, G. (2020). Diagnostics of Transient States in Hydraulic Pump System with Short Time Fourier Transform. Advances in Science and Technology Research Journal, 14(1), 178–183. doi:10.12913/22998624/116971.
[20] Ji'e, M., Yan, D., Sun, S., Zhang, F., Duan, S., & Wang, L. (2022). A Simple Method for Constructing a Family of Hamiltonian Conservative Chaotic Systems. IEEE Transactions on Circuits and Systems I: Regular Papers, 69(8), 3328–3338. doi:10.1109/TCSI.2022.3172313.
[21] Phipps Electronics. (2024). YF-S201 Hall Effect Water Flow Meter / Sensor. Phipps Electronics, North Revesby, Australia. Available online: https://www.phippselectronics.com/product/yf-s201-hall-effect-water-flow-meter-sensor/ (accessed on March 2024).
[22] Urbanowicz, K., Duan, H. F., & Bergant, A. (2020). Transient liquid flow in plastic pipes. Strojniski Vestnik/Journal of Mechanical Engineering, 66(2), 77–90. doi:10.5545/sv-jme.2019.6324.
[23] Kulmány, I. M., Bede-Fazekas, í., Beslin, A., Giczi, Z., Milics, G., Kovács, B., Kovács, M., Ambrus, B., Bede, L., & Vona, V. (2022). Calibration of an Arduino-based low-cost capacitive soil moisture sensor for smart agriculture. Journal of Hydrology and Hydromechanics, 70(3), 330–340. doi:10.2478/johh-2022-0014.
[24] Bedford, A. (2021). Hamilton's Principle in Continuum Mechanics. Springe, Cham. Switzerland. doi:10.1007/978-3-030-90306-0.
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