A Spectral Approach to Uncertainty Quantification in Water Distribution Networks
Publication: Journal of Water Resources Planning and Management
Volume 146, Issue 3
Abstract
To date, the hydraulics of water distribution networks are calculated using deterministic models. Because many of the parameters in these models are not known exactly, it is important to evaluate the effects of their uncertainties on the results through uncertainty analysis. For the propagation of uncertain parameters, this article for the first time applies the polynomial chaos expansion to a hydraulic model and compares the results with those from classical approaches like the first-order second-moment method and Monte Carlo simulations. Results presented in this article show that the accuracy of the polynomial chaos expansion is on the same level as the Monte Carlo simulation. Further, it is concluded that due to its computational efficiency, polynomial chaos expansion is superior to the Monte Carlo simulation.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
The code generated the study is available from the corresponding author by request. The propagation code used during the study is available online (https://www.uqlab.com). The data and model used during the study of the branched network are available from the corresponding author by request. The data and model used during the study of the real network are proprietary in nature and may only be provided with restrictions.
Acknowledgments
The work presented in the paper is part of the French-German collaborative research project ResiWater that is funded by the French National Research Agency (ANR) (Project No. ANR-14-PICS-0003) and the German Federal Ministry of Education and Research (BMBF) (Project No. BMBF-13N13690).
References
Adams, B. M., W. Bohnhoff, K. Dalbey, J. Eddy, M. Eldred, D. Gay, K. Haskell, P. D. Hough, and L. P. Swiler. 2009. Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: Version 5.0 user’s manual. Albuquerque, NM: Sandia National Laboratories.
Baudin, M., A. Dutfoy, B. Iooss, and A.-L. Popelin. 2017. “Openturns: An industrial software for uncertainty quantification in simulation.” In Handbook of uncertainty quantification, 2001–2038. Berlin: Springer.
Blatman, G., and B. Sudret. 2011. “Adaptive sparse polynomial chaos expansion based on least angle regression.” J. Comput. Phys. 230 (6): 2345–2367. https://doi.org/10.1016/j.jcp.2010.12.021.
Blokker, E., and W. Van der Schee. 2006. “Simulation of water demands provides insight.” In Proc., Water Supply and Drainage for Buildings Symp. Germany, Frankfurt am Main: Crédit Agricole Corporate and Investment Bank.
Boulos, P. F., K. E. Lansey, and B. W. Karney. 2004. Comprehensive water distribution systems analysis handbook for engineers and planners. Pasadena, CA: MWH Soft.
Braun, M., T. Bernard, O. Piller, and F. Sedehizade. 2014. “24-hours demand forecasting based on SARIMA and support vector machines.” Procedia Eng. 89 (Jan): 926–933. https://doi.org/10.1016/j.proeng.2014.11.526.
Braun, M., O. Piller, J. Deuerlein, and I. Mortazavi. 2017. “Limitations of demand-and pressure-driven modeling for large deficient networks.” Drinking Water Eng. Sci. 10 (2): 93. https://doi.org/10.5194/dwes-10-93-2017.
Buchberger, S. G., and G. J. Wells. 1996. “Intensity, duration, and frequency of residential water demands.” J. Water Resour. Plann. Manage. 122 (1): 11–19. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:1(11).
Bush, C. A., and J. G. Uber. 1998. “Sampling design methods for water distribution model calibration.” J. Water Resour. Plann. Manage. 124 (6): 334–344. https://doi.org/10.1061/(ASCE)0733-9496(1998)124:6(334).
Cacuci, D. G., M. Ionescu-Bujor, and I. M. Navon. 2005. Sensitivity and uncertainty analysis, volume II: Applications to large-scale systems. Boca Raton, FL: CRC Press.
Crous, P., J. Van Zyl, and Y. Roodt. 2012. “The potential of graphical processing units to solve hydraulic network equations.” J. Hydroinf. 14 (3): 603–612. https://doi.org/10.2166/hydro.2011.023.
Fishman, G. 2013. Monte Carlo: Concepts, algorithms, and applications. Berlin: Springer.
Hagos, M., D. Jung, and K. E. Lansey. 2016. “Optimal meter placement for pipe burst detection in water distribution systems.” J. Hydroinf. 18 (4): 741–756. https://doi.org/10.2166/hydro.2016.170.
Hart, W. E., and R. Murray. 2010. “Review of sensor placement strategies for contamination warning systems in drinking water distribution systems.” J. Water Resour. Plann. Manage. 136 (6): 611–619. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000081.
Herrera, M., L. Torgo, J. Izquierdo, and R. Pérez-García. 2010. “Predictive models for forecasting hourly urban water demand.” J. Hydrol. 387 (1): 141–150. https://doi.org/10.1016/j.jhydrol.2010.04.005.
Hwang, H., K. Lansey, and D. Jung. 2017. “Accuracy of first-order second-moment approximation for uncertainty analysis of water distribution systems.” J. Water Resour. Plann. Manage. 144 (2): 04017087. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000864.
Kapelan, Z. S., D. A. Savic, and G. A. Walters. 2007. “Calibration of water distribution hydraulic models using a Bayesian-type procedure.” J. Hydraul. Eng. 133 (8): 927–936. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:8(927).
Lansey, K. 1996. “Uncertainty in water distribution network modeling.” J. Contemp. Water Res. Educ. 103 (1): 5.
Lansey, K., W. El-Shorbagy, I. Ahmed, J. Araujo, and C. Haan. 2001. “Calibration assessment and data collection for water distribution networks.” J. Hydraul. Eng. 127 (4): 270–279. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:4(270).
Le Maître, O., and O. M. Knio. 2010. Spectral methods for uncertainty quantification: With applications to computational fluid dynamics. Berlin: Springer.
Lu, Z., and V. V. Vesselinov. 2015. “Analytical sensitivity analysis of transient groundwater flow in a bounded model domain using the adjoint method.” Water Resour. Res. 51 (7): 5060–5080. https://doi.org/10.1002/2014WR016819.
Marelli, S., and B. Sudret. 2014. “UQLab: A framework for uncertainty quantification in matlab.” In Proc., 2nd Int. Conf. on Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management, 2554–2563. Reston, VA: ASCE.
Ostfeld, A., and E. Salomons. 2004. “Optimal layout of early warning detection stations for water distribution systems security.” J. Water Resour. Plann. Manage. 130 (5): 377–385. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:5(377).
Ostfeld, A., and U. Shamir. 1996. “Design of optimal reliable multiquality water-supply systems.” J. Water Resour. Plann. Manage. 122 (5): 322–333. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:5(322).
Pasha, M., and K. Lansey. 2010. “Effect of parameter uncertainty on water quality predictions in distribution systems-case study.” J. Hydroinf. 12 (1): 1–21. https://doi.org/10.2166/hydro.2010.053.
Pecci, F., E. Abraham, and I. Stoianov. 2017. “Quadratic head loss approximations for optimisation problems in water supply networks.” J. Hydroinf. 19 (4): 493–506. https://doi.org/10.2166/hydro.2017.080.
Perelman, L., M. Housh, and A. Ostfeld. 2013. “Robust optimization for water distribution systems least cost design.” Water Resour. Res. 49 (10): 6795–6809. https://doi.org/10.1002/wrcr.20539.
Perelman, L., M. L. Maslia, A. Ostfeld, and J. B. Sautner. 2008. “Using aggregation/skeletonization network models for water quality simulations in epidemiologic studies.” J. Am. Water Works Assn. 100 (6): 122–133. https://doi.org/10.1002/j.1551-8833.2008.tb09659.x.
Piller, O., and B. Brémond. 2002. “Stochastic model for peak period analysis of pipe networks.” In Proc., ASCE Environmental and Water Resources Systems Analysis. Reston, VA: ASCE.
Piller, O., S. Elhay, J. Deuerlein, and A. R. Simpson. 2016. “Local sensitivity of pressure-driven modeling and demand-driven modeling steady-state solutions to variations in parameters.” J. Water Resour. Plann. Manage. 143 (2): 04016074. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000729.
Piller, O., D. Gilbert, and J. E. Van Zyl. 2010. “Dual calibration for coupled flow and transport models of water distribution systems.” In Proc., 12th Annual Conf. on Water Distribution Systems Analysis. 722–731. Reston, VA: ASCE.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. 1988. Vol. 1 of Numerical recipes in C. Cambridge, UK: Cambridge University Press.
Razavi, S., and H. V. Gupta. 2015. “What do we mean by sensitivity analysis? The need for comprehensive characterization of ‘global’ sensitivity in earth and environmental systems models.” Water Resour. Res. 51 (5): 3070–3092. https://doi.org/10.1002/2014WR016527.
ResiWater. 2019. “Resiwater: Innovative secure sensor networks and model-based assessment tools for increased resilience of water infrastructures.” Accessed October 6, 2019. https://www.resiwater.eu.
Rossman, L. A., P. F. Boulos, and T. Altman. 1993. “Discrete volume-element method for network water-quality models.” J. Water Resour. Plann. Manage. 119 (5): 505–517. https://doi.org/10.1061/(ASCE)0733-9496(1993)119:5(505).
Savic, D. A., Z. S. Kapelan, and P. M. Jonkergouw. 2009. “Quo vadis water distribution model calibration?” Urban Water J. 6 (1): 3–22. https://doi.org/10.1080/15730620802613380.
Savic, D. A., and G. A. Walters. 1997. “Genetic algorithms for least-cost design of water distribution networks.” J. Water Resour. Plann. Manage. 123 (2): 67–77. https://doi.org/10.1061/(ASCE)0733-9496(1997)123:2(67).
Smith, R. C. 2013. Vol. 12 of Uncertainty quantification: Theory, implementation, and applications. Philadelphia: Society for Industrial and Applied Mathematics.
Todini, E. 2011. “Extending the global gradient algorithm to unsteady flow extended period simulations of water distribution systems.” J. Hydroinf. 13 (2): 167–180. https://doi.org/10.2166/hydro.2010.164.
Van Zyl, J., and A. Cassa. 2013. “Modeling elastically deforming leaks in water distribution pipes.” J. Hydraul. Eng. 140 (2): 182–189. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000813.
Walski, T. M., D. V. Chase, D. A. Savic, W. Grayman, S. Beckwith, and E. Koelle. 2003. Advanced water distribution modeling and management. Waterbury, CT: Haestad.
Wiener, N. 1938. “The homogeneous chaos.” Am. J. Math. 60 (4): 897–936. https://doi.org/10.2307/2371268.
Xiu, D. 2010. Numerical methods for stochastic computations: A spectral method approach. Princeton, NJ: Princeton University Press.
Xiu, D., and G. E. Karniadakis. 2002. “Wiener–Askey polynomial chaos for stochastic differential equations.” SIAM J. Sci. Comput. 24 (2): 619–644. https://doi.org/10.1137/S1064827501387826.
Zheng, F., A. R. Simpson, A. C. Zecchin, and J. W. Deuerlein. 2013. “A graph decomposition-based approach for water distribution network optimization.” Water Resour. Res. 49 (4): 2093–2109. https://doi.org/10.1002/wrcr.20175.
Zwillinger, D. 2002. CRC standard mathematical tables and formulae. Boca Raton, FL: CRC Press.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 146 • Issue 3 • March 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 1, 2018
Accepted: Apr 26, 2019
Published online: Dec 23, 2019
Published in print: Mar 1, 2020
Discussion open until: May 23, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.