Graph Neural Networks for State Estimation in Water Distribution Systems: Application of Supervised and Semisupervised Learning
Publication: Journal of Water Resources Planning and Management
Volume 148, Issue 5
Abstract
Emerging trends of resilient and reliable water infrastructure advocate for the development of efficient state estimation (SE) techniques in water distribution systems (WDSs). SE refers to estimating the flows and heads in the WDS at unmonitored locations based on measurements collected from limited monitoring locations. Current physics-based SE methods typically require more exhaustive than readily available information about the WDS and are computationally demanding to attain real-time SE fully. Using neural networks for SE is a promising avenue because neural networks are more adaptable to the availability of sensory data and can shift most of the computation efforts to the offline training phase. Once trained, the inference is more computationally efficient compared to the physics-based SE methods. This work proposes a graph neural network (GNN) model for SE in WDSs. Unlike traditional neural networks, GNNs are more suitable for the SE problem for two main reasons: (1) given a limited number of monitoring locations, the SE problem inherently requires a semisupervised learning method, and (2) GNNs enable learning from the graph structure of a WDS, thus providing a mechanism to incorporate the functional relationships between the monitored and unmonitored locations and incorporate the physical laws during the training process. To evaluate the performance of GNNs for SE, we tested supervised and semisupervised approaches, investigated the impact of GNN architecture choices on its performance, and examined model performance under different levels of noise in the training data. The results demonstrate that GNNs are promising for SE for their ability to learn from graph structure with a limited amount of information while exhibiting robustness to noise. This study contributes toward advancing real-time GNN-based SE in WDSs. Future research is needed to incorporate various hydraulic devices and investigate the scalability of GNNs to large-scale WDSs.
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Data Availability Statement
All the relevant data, code, and training models that support the findings of this study are available from the GitHub repository https://github.com/glorialulu/GNN_StateEstimation_WDS.git.
Acknowledgments
This work was supported by the National Science Foundation under Grant 1943428. The authors would like to acknowledge Balthazar Donon for providing explanations of the GNN implementation for power flows.
References
Alperovits, E., and U. Shamir. 1977. “Design of optimal water distribution systems.” Water Resour. Res. 13 (6): 885–900. https://doi.org/10.1029/WR013i006p00885.
Andersen, J., R. S. Powell, and J. Marsh. 2001. “Constrained state estimation with applications in water distribution network monitoring.” Int. J. Syst. Sci. 32 (6): 807–816. https://doi.org/10.1080/00207720121343.
Andersen, J. H., and R. S. Powell. 2000. “Implicit state-estimation technique for water network monitoring.” Urban Water 2 (2): 123–130. https://doi.org/10.1016/S1462-0758(00)00050-9.
Battaglia, P. W., et al. 2018. “Relational inductive biases, deep learning, and graph networks.” Preprint, submitted October 17, 2018. https://arxiv.org/abs/1806.01261.
Belghaddar, Y., N. Chahinian, A. Seriai, A. Begdouri, R. Abdou, and C. Delenne. 2021. “Graph convolutional networks: Application to database completion of wastewater networks.” Water 13 (12): 1681. https://doi.org/10.3390/w13121681.
Bohorquez, J., A. R. Simpson, M. F. Lambert, and B. Alexander. 2021. “Merging fluid transient waves and artificial neural networks for burst detection and identification in pipelines.” J. Water Resour. Plann. Manage. 147 (1): 04020097. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001296.
Bolz, V., J. Rueß, and A. Zell. 2019. “Power flow approximation based on graph convolutional networks.” In Proc., 18th IEEE In. Conf. on Machine Learning and Applications (ICMLA), 1679–1686. New York: IEEE.
Boulos, P. F., K. E. Lansey, and B. W. Karney. 2006. Comprehensive water distribution systems analysis handbook for engineers and planners. Denver: American Water Works Association.
Díaz, S., J. González, and R. Mínguez. 2016. “Uncertainty evaluation for constrained state estimation in water distribution systems.” J. Water Resour. Plann. Manage. 142 (12): 06016004. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000718.
Donon, B., R. Clément, B. Donnot, A. Marot, I. Guyon, and M. Schoenauer. 2020a. “Neural networks for power flow: Graph neural solver.” Electr. Power Syst. Res. 189 (Dec): 106547. https://doi.org/10.1016/j.epsr.2020.106547.
Donon, B., Z. Liu, W. Liu, I. Guyon, A. Marot, and M. Schoenauer. 2020b. “Deep statistical solvers.” Adv. Neural Inf. Process. Syst. 33: 7910–7921.
Fan, W., Y. Ma, Q. Li, Y. He, E. Zhao, J. Tang, and D. Yin. 2019. “Graph neural networks for social recommendation.” In Proc., World Wide Web Conf., 417–426. New York: Association for Computing Machinery. https://doi.org/10.1145/3308558.3313488.
Friedman, J., T. Hastie, and R. Tibshirani. 2001. The elements of statistical learning, Vol. 1. Springer series in statistics. New York: Springer.
Gilmer, J., S. S. Schoenholz, P. F. Riley, O. Vinyals, and G. E. Dahl. 2017. “Neural message passing for quantum chemistry.” In Proc., Int. Conf. on Machine Learning, PMLR, 1263–1272. London: Proceedings of Machine Learning Research.
Goswami, S., C. Anitescu, S. Chakraborty, and T. Rabczuk. 2020. “Transfer learning enhanced physics informed neural network for phase-field modeling of fracture.” Theor. Appl. Fract. Mech. 106 (Apr): 102447. https://doi.org/10.1016/j.tafmec.2019.102447.
Guo, G., X. Yu, S. Liu, Z. Ma, Y. Wu, X. Xu, X. Wang, K. Smith, and X. Wu. 2021. “Leakage detection in water distribution systems based on time–frequency convolutional neural network.” J. Water Resour. Plann. Manage. 147 (2): 04020101. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001317.
Hajiramezanali, E., A. Hasanzadeh, N. Duffield, K. R. Narayanan, M. Zhou, and X. Qian. 2019. “Variational graph recurrent neural networks.” Preprint, submitted April 23, 2020. https://arxiv.org/abs/1908.09710.
He, K., X. Zhang, S. Ren, and J. Sun. 2016. “Deep residual learning for image recognition.” In Proc., IEEE Conf. on Computer Vision and Pattern Recognition, 770–778. New York: IEEE.
Isufi, E., F. Gama, and A. Ribeiro. 2020. “Edgenets: Edge varying graph neural networks.” Preprint, submitted July 27, 2021. https://arxiv.org/abs/2001.07620.
Johnson, D. B. 1973. “A note on Dijkstra’s shortest path algorithm.” J. ACM (JACM) 20 (3): 385–388. https://doi.org/10.1145/321765.321768.
Kang, D., and K. Lansey. 2010. “Optimal meter placement for water distribution system state estimation.” J. Water Resour. Plann. Manage. 136 (3): 337–347. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000037.
Kang, J., Y.-J. Park, J. Lee, S.-H. Wang, and D.-S. Eom. 2018. “Novel leakage detection by ensemble CNN-SVM and graph-based localization in water distribution systems.” IEEE Trans. Ind. Electron. 65 (5): 4279–4289. https://doi.org/10.1109/TIE.2017.2764861.
Karniadakis, G. E., I. G. Kevrekidis, L. Lu, P. Perdikaris, S. Wang, and L. Yang. 2021. “Physics-informed machine learning.” Nat. Rev. Phys. 3 (6): 422–440. https://doi.org/10.1038/s42254-021-00314-5.
Kashinath, K., et al. 2021. “Physics-informed machine learning: Case studies for weather and climate modelling.” Philos. Trans. R. Soc. A 379 (2194): 20200093. https://doi.org/10.1098/rsta.2020.0093.
Kingma, D. P., and J. Ba. 2014. “Adam: A method for stochastic optimization.” Preprint, submitted January 30, 2017. https://arxiv.org/abs/1412.6980.
Kumar, S. M., S. Narasimhan, and S. M. Bhallamudi. 2008. “State estimation in water distribution networks using graph-theoretic reduction strategy.” J. Water Resour. Plann. Manage. 134 (5): 395–403. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:5(395).
Larock, B. E., R. W. Jeppson, and G. Z. Watters. 1999. Hydraulics of pipeline systems. Boca Raton, FL: CRC Press.
Li, Y., D. Tarlow, M. Brockschmidt, and R. Zemel. 2015. “Gated graph sequence neural networks.” Preprint, submitted September 22, 2017. https://arxiv.org/abs/1511.05493.
Liao, W., B. Bak-Jensen, J. R. Pillai, Y. Wang, and Y. Wang. 2021. “A review of graph neural networks and their applications in power systems.” Preprint, submitted June 12, 2021. https://arxiv.org/abs/2101.10025.
Mai, V. V., and M. Johansson. 2021. “Stability and convergence of stochastic gradient clipping: Beyond Lipschitz continuity and smoothness.” Preprint, submitted June 10, 2021. https://arxiv.org/abs/2102.06489.
Mounce, S. R., and J. Machell. 2006. “Burst detection using hydraulic data from water distribution systems with artificial neural networks.” Urban Water J. 3 (1): 21–31. https://doi.org/10.1080/15730620600578538.
Nagar, A. K., and R. S. Powell. 2002. “LFT/SDP approach to the uncertainty analysis for state estimation of water distribution systems.” IEEE Proc. Control Theory Appl. 149 (2): 137–142. https://doi.org/10.1049/ip-cta:20020096.
Ortega, A., P. Frossard, J. Kovačević, J. M. Moura, and P. Vandergheynst. 2018. “Graph signal processing: Overview, challenges, and applications.” Proc. IEEE 106 (5): 808–828. https://doi.org/10.1109/JPROC.2018.2820126.
Preis, A., A. J. Whittle, A. Ostfeld, and L. Perelman. 2011. “Efficient hydraulic state estimation technique using reduced models of urban water networks.” J. Water Resour. Plann. Manage. 137 (4): 343–351. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000113.
Raissi, M., P. Perdikaris, and G. E. Karniadakis. 2019. “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.” J. Comput. Phys. 378 (Feb): 686–707. https://doi.org/10.1016/j.jcp.2018.10.045.
Rossman, L., H. Woo, M. Tryby, F. Shang, R. Janke, and T. Haxton. 2020. EPANET 2.2 user’s manual. Washington, DC: USEPA.
Sanchez-Gonzalez, A., J. Godwin, T. Pfaff, R. Ying, J. Leskovec, and P. Battaglia. 2020. “Learning to simulate complex physics with graph networks.” In Proc., Int. Conf. on Machine Learning, PMLR, 8459–8468. London: Proceedings of Machine Learning Research.
Scarselli, F., M. Gori, A. C. Tsoi, M. Hagenbuchner, and G. Monfardini. 2009. “The graph neural network model.” IEEE Trans. Neural Networks 20 (1): 61–80. https://doi.org/10.1109/TNN.2008.2005605.
Sela, L., and W. Abbas. 2020. Distributed sensing for monitoring water distribution systems, 1–9. London: Springer.
Shafiee, M. E., Z. Barker, and A. Rasekh. 2018. “Enhancing water system models by integrating big data.” Sustainable Cities Soc. 37 (Feb): 485–491. https://doi.org/10.1016/j.scs.2017.11.042.
Shafiee, M. E., A. Rasekh, L. Sela, and A. Preis. 2020. “Streaming smart meter data integration to enable dynamic demand assignment for real-time hydraulic simulation.” J. Water Resour. Plann. Manage. 146 (6): 06020008. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001221.
Shukla, K., P. C. Di Leoni, J. Blackshire, D. Sparkman, and G. E. Karniadakis. 2020. “Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks.” J. Nondestr. Eval. 39 (3): 1–20. https://doi.org/10.1007/s10921-020-00705-1.
Smart Energy International. 2018. “Global smart water meters market trends.” Accessed December 18, 2021. https://www.smart-energy.com/magazine-article/global-smart-water-meters-market-trends/.
Todini, E., and S. Pilati. 1988. “A gradient algorithm for the analysis of pipe networks.” In Computer applications in water supply: Vol. 1—Systems analysis and simulation, 1–20. Baldock, UK: Research Studies Press.
Tshehla, K. S., Y. Hamam, and A. M. Abu-Mahfouz. 2017. “State estimation in water distribution network: A review.” In Proc., IEEE 15th Int. Conf. on Industrial Informatics (INDIN), 1247–1252. New York: IEEE.
Tsiami, L., and C. Makropoulos. 2021. “Cyber—Physical attack detection in water distribution systems with temporal graph convolutional neural networks.” Water 13 (9): 1247. https://doi.org/10.3390/w13091247.
Veličković, P., G. Cucurull, A. Casanova, A. Romero, P. Lio, and Y. Bengio. 2017. “Graph attention networks.” Preprint, submitted February 4, 2018. https://arxiv.org/abs/1710.10903.
Wang, J.-X., J.-L. Wu, and H. Xiao. 2017. “Physics-informed machine learning approach for reconstructing Reynolds stress modeling discrepancies based on DNS data.” Phys. Rev. Fluids 2 (3): 034603. https://doi.org/10.1103/PhysRevFluids.2.034603.
Wang, S., A. F. Taha, N. Gatsis, L. Sela, and M. H. Giacomoni. 2022. “Probabilistic state estimation in water networks.” IEEE Trans. Control Syst. Technol. 30 (2): 507–519. https://doi.org/10.1109/TCST.2021.3066102.
Wang, X., Y. Ma, Y. Wang, W. Jin, X. Wang, J. Tang, C. Jia, and J. Yu. 2020. “Traffic flow prediction via spatial temporal graph neural network.” In Proc., Web Conf. 2020, 1082–1092. New York: Association for Computing Machinery. https://doi.org/10.1145/3366423.3380186.
Wu, J.-L., H. Xiao, and E. Paterson. 2018. “Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework.” Phys. Rev. Fluids 3 (7): 074602. https://doi.org/10.1103/PhysRevFluids.3.074602.
Xing, L., and L. Sela. 2021. “Graph neural networks for state estimation in water distribution systems.” Accessed September 5, 2021. https://github.com/glorialulu/GNN_StateEstimation_WDS.git.
Yin, R., K. Li, G. Zhang, and J. Lu. 2019. “A deeper graph neural network for recommender systems.” Knowl.-Based Syst. 185 (Dec): 105020. https://doi.org/10.1016/j.knosys.2019.105020.
Ying, R., R. He, K. Chen, P. Eksombatchai, W. L. Hamilton, and J. Leskovec. 2018. “Graph convolutional neural networks for web-scale recommender systems.” In Proc., 24th ACM SIGKDD Int. Conf. on Knowledge Discovery & Data Mining, 974–983. New York: Association for Computing Machinery. https://doi.org/10.1145/3219819.3219890.
Zhang, J., T. He, S. Sra, and A. Jadbabaie. 2019a. “Why gradient clipping accelerates training: A theoretical justification for adaptivity.” Preprint, submitted February 10, 2020. https://arxiv.org/abs/1905.11881.arXiv preprint arXiv:1905.11881.
Zhang, S., H. Tong, J. Xu, and R. Maciejewski. 2019b. “Graph convolutional networks: A comprehensive review.” Comput. Soc. Networks 6 (1): 1–23. https://doi.org/10.1186/s40649-019-0069-y.
Zhou, J., G. Cui, S. Hu, Z. Zhang, C. Yang, Z. Liu, L. Wang, C. Li, and M. Sun. 2020. “Graph neural networks: A review of methods and applications.” AI Open 1 (Jan): 57–81. https://doi.org/10.1016/j.aiopen.2021.01.001.
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Journal of Water Resources Planning and Management
Volume 148 • Issue 5 • May 2022
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© 2022 American Society of Civil Engineers.
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Received: Apr 23, 2021
Accepted: Jan 10, 2022
Published online: Mar 14, 2022
Published in print: May 1, 2022
Discussion open until: Aug 14, 2022
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