Estimating Distribution System Water Demands Using Markov Chain Monte Carlo
Publication: Journal of Water Resources Planning and Management
Volume 145, Issue 7
Abstract
The use of drinking water distribution system models has been around for decades and requires good demand estimates to ensure adequate hydraulic and water quality representation. Traditional demand estimation processes are capable of estimating demands, often for highly skeletonized systems, with approximations to represent uncertainties in demand estimates and hydraulic states. This study implemented a Markov chain Monte Carlo (MCMC) algorithm to estimate hourly demand multipliers and uncertainties for a synthetic network using a previously developed clustering algorithm to reduce the number of unknowns. The MCMC approach also provided the flexibility to accommodate potential spatial correlation in demand multipliers through, for example, the use of a Markov Random Field (MRF) prior. The MCMC algorithm produced adequate representation of demand multipliers, similar to weighted least squares (WLS), and improved representation of the uncertainties relative to the approximations based on WLS results. The incorporation of the MRF prior resulted in more spatially correlated demand multipliers but did not provide any significant benefits for representing the network being studied. Increasing the number of clusters, reducing measurement uncertainty, and including additional flow measurements (rather than pressure) improved the ability to represent system-wide flows. However, increasing the number of clusters also resulted in larger uncertainties in the demand multiplier estimates as the estimation problem became more ill-conditioned. A generalized discussion associated with clustering approaches and measurement locations is included to provide a broader perspective on demand estimation.
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Acknowledgments
The authors would like to gratefully acknowledge the partial funding support provided by the Water Research Foundation through Project No. 04345 and the Chemical, Bioengineering, Environmental and Transport Systems (CBET) Directorate, Environmental Engineering [National Science Foundation (NSF)] through Award No. 1511959.
References
Bascià, A., and T. Tucciarelli. 2003. “Simultaneous zonation and calibration of pipe network parameters.” J. Hydraul. Eng. 129 (5): 394–403. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:5(394).
Bates, B. C., and E. P. Campbell. 2001. “A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling.” Water Resour. Res. 37 (4): 937–947. https://doi.org/10.1029/2000WR900363.
Bhave, P. R. 1988. “Calibrating water distribution network models.” J. Environ. Eng. 114 (1): 120–136. https://doi.org/10.1061/(ASCE)0733-9372(1988)114:1(120).
Boulos, P. F., and D. J. Wood. 1990. “Explicit calculation of pipe-network parameters.” J. Hydraul. Eng. 116 (11): 1329–1344. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:11(1329).
Cheng, W., and Z. He. 2011. “Calibration of nodal demand in water distribution systems.” J. Water Resour. Plann. Manage. 131 (1): 31–40. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000093.
Clark, R. M., G. Smalley, J. A. Goodrich, R. Tull, L. A. Rossman, J. J. Vasconcelos, and P. F. Boulos. 1994. “Managing water quality in distribution systems: Simulating TTHM and chlorine residual propagation.” J. Water SRT Aqua 43 (4): 182–191.
Cutore, P., A. Campisano, Z. Kapelan, C. Modica, and D. Savic. 2008. “Probabilistic prediction of urban water consumption using the SCEM-UA algorithm.” Urban Water J. 5 (2): 125–132. https://doi.org/10.1080/15730620701754434.
Dini, M., and M. Tabesh. 2014. “A new method for simultaneous calibration of demand pattern and Hazen-Williams coefficients in water distribution systems.” Water Resour. Manage. 28 (7): 2021–2034. https://doi.org/10.1007/s11269-014-0592-4.
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.
Du, K., T. Y. Long, J. H. Wang, and J. S. Guo. 2015. “Inversion model of water distribution systems for nodal demand calibration.” J. Water Resour. Plann. Manage. 141 (9): 04015002. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000506.
Huang, J. J., and E. A. McBean. 2007. “Using Bayesian statistics to estimate the coefficients of a two-component second-order chlorine bulk decay model for a water distribution system.” Water Res. 41 (2): 287–294. https://doi.org/10.1016/j.watres.2006.10.027.
Jung, D., Y. H. Choi, and J. H. Kim. 2016. “Optimal node grouping for water distribution system demand estimation.” Water 8 (4): 160. https://doi.org/10.3390/w8040160.
Jung, D. S., and J. H. Kim. 2018. “State estimation network design for water distribution systems.” J. Water Resour. Plann. Manage. 144 (1): 06017006. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000862.
Jung, D. S., and K. Lansey. 2015. “Water distribution system burst detection using a nonlinear Kalman filter.” J. Water Resour. Plann. Manage. 141 (5): 04014070. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000464.
Kang, D. S., and K. Lansey. 2009. “Real-time demand estimation and confidence limit analysis for water distribution systems.” J. Hydraul. Eng. 135 (10): 825–837. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000086.
Kang, D. S., 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.
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. E., and C. Basnet. 1991. “Parameter estimation for water distribution networks.” J. Water Resour. Plann. Manage. 117 (1): 126–144. https://doi.org/10.1061/(ASCE)0733-9496(1991)117:1(126).
Lansey, K. E., W. El-Shorbagy, I. Ahmed, J. Araujo, and C. T. 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).
Lee, H. K. H., D. M. Higdon, Z. Bi, M. A. R. Ferreira, and M. West. 2002. “Markov random field models for high-dimensional parameters in simulations of fluid flow in porous media.” Technometrics 44 (3): 230–241. https://doi.org/10.1198/004017002188618419.
Mallic, K. N., I. Ahmed, K. S. Tickle, and K. E. Lansey. 2002. “Determining pipe groupings for water distribution networks.” J. Water Resour. Plann. Manage. 182 (2): 130–139. https://doi.org/10.1061/(ASCE)0733-9496(2002)128:2(130).
Malve, O., M. Laine, M. Haario, T. Kirkkala, and J. Sarvala. 2007. “Bayesian modelling of algal mass occurrences—Using adaptive MCMC methods with a lake water quality model.” Environ. Modell. Software 22 (7): 966–977. https://doi.org/10.1016/j.envsoft.2006.06.016.
Marchi, A., G. C. Dandy, and D. L. Boccelli. 2016. “Limitations on real time demand estimation in water distribution systems.” In Proc., 2016 Water Distribution System Analysis Symp. Bogotá, Colombia: Universidad de los Andes.
NRC (National Research Council). 2006. “Drinking water distribution systems: Assessing and reducing risks.” In Integrating approaches to reducing risk from distribution systems, 269–315. Washington, DC: National Academies Press.
Oliveira, P., and D. L. Boccelli. 2018. “Do time series models contribute to water demand clustering?” In Proc., 1st Int. WDSA/CCWI Joint Conf. Kingston, ON, Canada: Queen’s Univ.
Ormsbee, L. E. 1989. “Implicit network calibration.” J. Water Resour. Plann. Manage. 115 (2): 243–257. https://doi.org/10.1061/(ASCE)0733-9496(1989)115:2(243).
Perelman, L., and A. Ostfeld. 2008. “Water distribution system aggregation for water quality analysis.” J. Water Resour. Plann. Manage. 134 (3): 303–309. https://doi.org/10.1061/(ASCE)0733-9496(2008)134:3(303).
Preis, A., A. Whittle, and A. Ostfeld. 2009. “On-line hydraulic state prediction for water distribution systems.” In Proc., 11th Water Distribution Systems Analysis Symp. (WDSA09), World Environmental and Water Resources Congress. Reston, VA: ASCE.
Preis, A., A. 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.
Qin, T., and D. L. Boccelli. 2017. “Grouping water-demand nodes by similarity among flow paths in water-distribution systems.” J. Water Resour. Plann. Manage. 143 (8): 04017033. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000788.
Rana, S. M. M., and D. L. Boccelli. 2016. “Contaminant spread forecasting and confirmatory sampling location identification in a water distribution system network.” J. Water Resour. Plann. Manage. 142 (12): 04016059. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000704.
Rana, S. M. M., D. L. Boccelli, A. Marchi, and G. Dandy. 2017. “Impacts of measurement location and spatial aggregation on demand estimation in water distribution systems.” In Proc., World Environmental and Water Resources Congress, edited by C. N. Dunn and B. V. Weele, 602–610. Reston, VA: ASCE.
Reddy, P. V. N., K. Sridharan, and P. V. Rao. 1996. “WLS method for parameter estimation in water distribution networks.” J. Water Resour. Plann. Manage. 122 (3): 157–164. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:3(157).
Rossman, L. A. 2000. EPANET2 user’s manual. Washington, DC: USEPA and Risk Reduction Engineering Laboratory.
Rossman, L. A., R. M. Clark, and W. M. Grayman. 1994. “Modeling chlorine residuals in drinking water distribution systems.” J. Environ. Eng. 120 (4): 803–820. https://doi.org/10.1061/(ASCE)0733-9372(1994)120:4(803).
Rue, H., and L. Held. 2005. Gaussian Markov random fields: Theory and applications. Boca Raton, FL: CRC Press.
Sanz, G., and R. Pérez. 2015. “Sensitivity analysis for sampling design and demand calibration in water distribution networks using the singular value decomposition.” J. Water Resour. Plann. Manage. 141 (10): 04015020. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000535.
Shang, F., J. Uber, B. van Bloemen Waanders, D. Boccelli, and R. Janke. 2006. “Real time water demand estimation in water distribution systems.” In Proc., 8th Annual Water Distribution Systems Analysis Symp. Reston, VA: ASCE.
Spall, J. C. 2003. “Estimation via Markov chain Monte Carlo.” Control Syst. 23 (2): 34–45. https://doi.org/10.1109/MCS.2003.1188770.
USEPA. 2006. Initial distribution system evaluation guidance manual. Washington, DC: Office of Water.
Vrugt, J. A., H. V. Gupta, W. Bouten, and S. Sorooshian. 2003. “A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters.” Water Resour. Res. 39 (8): 1201–1218. https://doi.org/10.1029/2002WR001642.
Walski, T. M. 1983. “Technique for calibrating network models.” J. Water Resour. Plann. Manage. 109 (4): 360–372. https://doi.org/10.1061/(ASCE)0733-9496(1983)109:4(360).
Yang, X. Y., and D. L. Boccelli. 2016. “Model-based event detection for contaminant warning systems.” J. Water Resour. Plann. Manage. 142 (11): 04016048. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000689.
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Published In
Journal of Water Resources Planning and Management
Volume 145 • Issue 7 • July 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Mar 23, 2018
Accepted: Nov 27, 2018
Published online: Apr 25, 2019
Published in print: Jul 1, 2019
Discussion open until: Sep 25, 2019
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