Sequential Convex Optimization for Detecting and Locating Blockages in Water Distribution Networks
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 8
Abstract
Unreported partially/fully closed valves or other types of pipe blockages in water distribution networks result in unexpected energy losses within the systems, which we also refer to as faults. We investigate the problem of detection and localization of such faults. We propose a novel optimization-based method, which relies on the solution of a nonlinear inverse problem with regularization. We develop a sequential convex optimization algorithm to solve the resulting nonsmooth nonconvex optimization problem. The proposed algorithm enables the use of nonsmooth terms within the problem formulation, and exploits the sparse structure inherent in water network models. The performance of the developed method is numerically evaluated to detect and localize blockages in a large water distribution network using both simulated and experimental data. In all experiments, the sequential convex optimization algorithm converged in less than 3 s, suggesting that the proposed fault detection and localization method is suitable for near real-time implementation. Furthermore, we experimentally validate the developed method for near real-time fault diagnosis in a large operational water network from the United Kingdom. The method is shown to successfully detect and localize blockages, with real system modeling uncertainties.
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Data Availability Statement
The hydraulic data and model of BWFLnet used during the study are available in a repository in accordance with funder data retention policies: https://doi.org/10.17632/srt4vr5k38.2.
Acknowledgments
This research was supported by EPSRC (EP/P004229/1, Dynamically Adaptive and Resilient Water Supply Networks for a Sustainable Future). We thank Cla-Val and Bristol Water for their support in the implementation and operation of BWFLnet.
References
Abraham, E., and I. Stoianov. 2016. “Sparse null space algorithms for hydraulic analysis of large-scale water supply networks.” J. Hydraul. Eng. 142 (3): 04015058. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001089.
Aster, R. C., B. Borchers, and C. H. Thurber. 2012. Parameter estimation and inverse problems. Amsterdam, Netherlands: Elsevier.
Benzi, M., G. H. Golub, and J. Liesen. 2005. “Numerical solution of saddle point problems.” Acta Numer. 14 (May): 1–137. https://doi.org/10.1017/S0962492904000212.
Bertsekas, D. 1999. Nonlinear programming. Belmont: Athena Scientific.
Boyd, S., and L. Vandenberghe. 2004. Convex optimization. Cambridge, UK: Cambridge University Press.
Collins, M., and L. Cooper. 1978. “Solving the pipe network analysis problem using optimization techniques.” Manage. Sci. 24 (7): 747–760. https://doi.org/10.1287/mnsc.24.7.747.
Conn, A. R., N. I. M. Gould, and P. L. Toint. 2000. Trust-region methods. Philadelphia, PA: SIAM.
D’Ambrosio, C., A. Lodi, S. Wiese, and C. Bragalli. 2015. “Mathematical programming techniques in water network optimization.” Eur. J. Oper. Res. 243 (3): 774–788. https://doi.org/10.1016/j.ejor.2014.12.039.
Delgado, D. M., and K. E. Lansey. 2009. “Detection of closed valves in water distribution systems.” In Proc., 10th Annual Water Distribution Systems Analysis Conf. WDSA2008, 932–938. Reston, VA: ASCE.
Diestel, R. 2000. Graph theory (Graduate Texts in Mathematics). Berlin: Springer.
Do, N. C., A. R. Simpson, J. W. Deuerlein, and O. Piller. 2016. “Calibration of water demand multipliers in water distribution systems using genetic algorithms.” J. Water Resour. Plann. Manage. 142 (11): 04016044. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000691.
Do, N. C., A. R. Simpson, J. W. Deuerlein, and O. Piller. 2018. “Locating inadvertently partially closed valves in water distribution systems.” J. Water Resour. Plann. Manage. 144 (8): 04018039. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000958.
Donoho, D. L. 2006. “Compressed sensing.” IEEE Trans. Inf. Theory 52 (4): 1289–1306. https://doi.org/10.1109/TIT.2006.871582.
Elhay, S., A. R. Simpson, J. Deuerlein, B. Alexander, and W. Schilders. 2014. “A Reformulated co-tree flows method competitive with the global gradient algorithm for solving the water distribution system equations.” J. Water Resour. Plann. Manage. 140 (12): 04014040. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000431.
Friedman, J., T. Hastie, and R. Tibshirani. 2010. “Regularization paths for generalized linear models via coordinate descent.” J. Stat. Software 33 (1): 1–22. https://doi.org/10.18637/jss.v033.i01.
Gorinevsky, D., S. Boyd, and S. Poll. 2009. “Estimation of faults in DC electrical power system.” In Proc., American Control Conf., 4334–4339. New York: IEEE.
Gurobi Optimization. 2017. “Gurobi optimizer reference manual.” Accessed April 17, 2020. https://www.gurobi.com/documentation/8.0/refman/index.html.
Kang, D., and K. Lansey. 2011. “Demand and roughness estimation in water distribution systems.” J. Water Resour. Plann. Manage. 137 (1): 20–30. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000086.
Kapelan, Z. 2002. “Calibration of water distribution networks.” Ph.D. thesis, School of Engineering and Computer Science, Exeter Univ.
Larock, B. E., R. W. Jeppson, and G. Z. Watters. 1999. Hydraulics of pipeline systems. Boca Raton, FL: CRC Press.
Neumaier, A. 1998. “Solving ill-conditioned and singular linear systems: A tutorial on regularization.” SIAM Rev. 40 (3): 636–666. https://doi.org/10.1137/S0036144597321909.
Nielsen, B. 1989. “Methods for analyzing pipe networks.” J. Hydraul. Eng. 115 (2): 139–157. https://doi.org/10.1061/(ASCE)0733-9429(1989)115:2(139).
Pecci, F., E. Abraham, and I. Stoianov. 2019. “Global optimality bounds for the placement of control valves in water supply networks.” Optim. Eng. 20 (2): 457–495. https://doi.org/10.1007/s11081-018-9412-7.
Pecci, F., E. Abraham, and I. Stoianov. 2019. “Model reduction and outer approximation for optimising the placement of control valves in complex water networks.” J. Water Resour. Plann. Manage. 145 (5): 04019014. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001055.
Piller, O., D. Gilbert, and J. E. Van Zyl. 2012. “Dual calibration for coupled flow and transport models of water distribution systems.” In Proc., Water Distribution System Analysis 2010–WDSA 2010, 722–731. Reston, VA: ASCE.
Piller, O., I. Moltalvo, J. W. Deuerlein, G. Denis, and M. Braun. 2014. “A gradient-type method for real-time state estimation of water distribution networks.” In Proc., HIC 2014–11th Int. Conf. on Hydroinformatics. New York: CUNY Academic Works.
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.
Pudar, R. S., and A. Ligett James. 1992. “Leaks in pipe networks.” J. Hydraul. Eng. 118 (7): 1031–1046. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:7(1031).
Puig, V. 2010. “Fault diagnosis and fault tolerant control using set-membership approaches: Application to real case studies.” Int. J. Appl. Math. Comput. Sci. 20 (4): 619–635. https://doi.org/10.2478/v10006-010-0046-y.
Rossman, L. A. 2000. Epanet 2 users manual. Cincinnati, OH: U.S. Environmental Protection Agency.
Simpson, A., and S. Elhay. 2010. “Jacobian matrix for solving water distribution system equations with the Darcy-Weisbach head-loss model.” J. Hydraul. Eng. 137 (6): 696–700. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000341.
Sophocleous, S., D. Savić, and Z. Kapelan. 2019. “Leak localization in a real water distribution network based on search-space reduction.” J. Water Resour. Plann. Manage. 145 (7): 04019024. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001079.
Tawarmalani, M., and N. V. Sahinidis. 2002. Convexification and global optimization in continuous and mixed-integer nonlinear programming. 1 ed. Berlin: Springer.
Tibshirani, R. 1996. “Regression selection and shrinkage via the Lasso.” J. R. Stat. Soc. 58 (1): 267–288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x.
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, edited by B. Coulbeck and C.-H. Orr, 1–20. London: Research Studies Press Ltd.
Vrachimis, S. G., D. G. Eliades, and M. M. Polycarpou. 2018. “Leak detection in water distribution systems using hydraulic interval state estimation.” In Proc., 2018 IEEE Conf. on Control Technology and Applications, CCTA 2018, 565–570. New York: IEEE.
Waldron, A., F. Pecci, and I. Stoianov. Forthcoming. “The regularisation of an inverse problem for parameter estimation in water distribution networks.” Water Resour. Plann. Manage. https://doi.org/10.1061/(ASCE)WR.1943-5452.0001273.
Water Research Centre. 1989. Network analysis–A code of practice. Swindon, UK: Water Research Centre.
Wright, R., E. Abraham, P. Parpas, and I. Stoianov. 2015. “Control of water distribution networks with dynamic DMA topology using strictly feasible sequential convex programming.” Water Resour. Res. 51 (12): 9925–9941. https://doi.org/10.1002/2015WR017466.
Wright, R., I. Stoianov, P. Parpas, K. Henderson, and J. King. 2014. “Adaptive water distribution networks with dynamically reconfigurable topology.” J. Hydroinf. 16 (6): 1280–1301. https://doi.org/10.2166/hydro.2014.086.
Wu, Z. Y., Y. Song, and J. L. Syed. 2012. “Optimization model for identifying unknown valve statuses and settings.” In Proc., WDSA 2012: 14th Water Distribution Systems Analysis Conf., 975–983. Barton, ACT: Engineers Australia.
Zheng, Y., G. Fantuzzi, A. Papachristodoulou, P. Goulart, and A. Wynn. 2017. “Fast ADMM for semidefinite programs with chordal sparsity.” In Proc., American Control Conf. 2017, 3335–3340. New York: IEEE.
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Received: Jun 25, 2019
Accepted: Jan 15, 2020
Published online: May 23, 2020
Published in print: Aug 1, 2020
Discussion open until: Oct 23, 2020
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