Content-Based Active-Set Method for the Pressure-Dependent Model of Water Distribution Systems
Publication: Journal of Water Resources Planning and Management
Volume 145, Issue 1
Abstract
A new content-based, box-constrained, active-set projected Newton method is presented that solves for the heads, the pipe flows, and the nodal outflows of a water distribution system in which nodal outflows are pressure dependent. The new method is attractive because, by comparison with the previously published weighted least-squares energy and mass residuals (EMR) damped Newton method, (1) it typically takes fewer iterations, (2) it does not require damping, (3) it takes less wall-clock time, (4) it does not require the addition of any virtual elements, and (5) it is algorithmically easier to deal with. Various pressure-outflow relationships (PORs), which model nodal outflows, were considered and two new PORs are presented. The new method is shown, by application to eight previously published case study networks with up to about 20,000 pipes and 18,000 nodes, to be up to five times faster than the EMR method and to take between 34% and 70% fewer iterations than the EMR method.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work presented in this paper is part of the French–German collaborative research project ResiWater that is funded by the French National Research Agency (ANR) (Project: ANR-14-PICS-0003) and the German Federal Ministry of Education and Research (BMBF) (Project: BMBF-13N13690). The authors gratefully acknowledge the anonymous reviewers whose comments led to an improved paper.
References
Bhave, P. R. 1981. “Node flow analysis distribution systems.” Transp. Eng. J. 107 (4): 457–467.
Ciaponi, C., L. Franchioli, E. Murari, and S. Papiri. 2015. “Procedure for defining a pressure-outflow relationship regarding indoor demands in pressure-driven analysis of water distribution networks.” Water Resour. Manage. 29 (3): 817–832. https://doi.org/10.1007/s11269-014-0845-2.
Cramer, J. 2003. Logit models from economics and other fields. Cambridge, UK: Cambridge University Press.
Deuerlein, J. W. 2002. “On the hydraulic system analysis of water supply networks.” [In German.] Ph.D. thesis, Dept. of Civil Engineering and Surveying, Mitteilungen des Instituts für Wasserwirtschaft und Kulturtechnik der Universität Karlsruhe.
Elhay, S., O. Piller, J. W. Deuerlein, and A. R. Simpson. 2016. “A robust, rapidly convergent method that solves the water distribution equations for pressure-dependent models.” J. Water Resour. Plann. Manage. 142 (2): 04015047. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000578.
Fujiwara, O., and T. Ganesharajah. 1993. “Reliability assessment of water supply systems with storage and distribution networks.” Water Resour. Res. 29 (8): 2917–2924. https://doi.org/10.1029/93WR00857.
Germanopoulos, G. 1985. “A technical note on the inclusion of pressure dependent demand and leakage terms in water supply network models.” Civ. Eng. Syst. 2 (3): 171–179. https://doi.org/10.1080/02630258508970401.
Gilchrist, W. 2000. Statistical modelling with quantile functions. London: Chapman & Hall/CRC Press.
Giustolisi, O., D. Savic, and Z. Kapelan. 2008. “Pressure-driven demand and leakage simulation for water distribution networks.” J. Hydraul. Eng. 134 (5): 626–635. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:5(626).
Goldstein, A. 1967. Constructive real analysis. Mineola, NY: Dover.
Gupta, R., and P. Bhave. 1996. “Comparison of methods for predicting deficient network performance.” J. Water Resour. Plann. Manage. 122 (3): 214–217. https://doi.org/10.1061/(ASCE)0733-9496(1996)122:3(214).
Hager, W., and H. Zhang. 2006. “A new active set method for box constrained optimization.” SIAM J. Optim. 17 (2): 526–557. https://doi.org/10.1137/050635225.
IEEE. 2008. Standard for floating-point arithmetic. IEEE 754-2008. New York: IEEE.
Isaacson, E., and H. Keller. 1966. Analysis of numerical methods. New York: Wiley.
Jun, L., and Y. Guoping. 2013. “Iterative methodology of pressure-dependent demand based on EPANET for pressure-deficient water distribution analysis.” J. Water Resour. Plann. Manage. 139 (1): 34–44. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000227.
Lippai, I., and Wright, L. 2014. “Demand constructs for risk analysis.” Procedia Eng. 89: 640–647. https://doi.org/10.1016/j.proeng.2014.11.489.
Mahmoud, H., D. Savic, and Z. Kapelan. 2017. “New pressure-driven approach for modeling water distribution networks.” J. Water Resour. Plann. Manage. 143 (8): 4017031. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000781.
Piller, O., B. Bremond, and M. Poulton. 2003. “Least action principles appropriate to pressure driven models of pipe networks.” In Proc., World Water and Environmental Resources Congress 2003, 1–15. Reston, VA: ASCE.
Piller, O., S. Elhay, J. W. Deuerlein, and A. R. Simpson. 2017. “Why are line search methods needed for hydraulic DDM and PDM solvers.” In Proc., CCWI 2017: Computing and Control for the Water Industry, edited by R. Collins. Sheffield, UK: Univ. of Sheffield.
Piller, O., and J. Van Zyl. 2007. “A unified framework for pressure driven network analysis.” In Proc., Computing and Control for the Water Industry, 25–30. London: Taylor & Francis.
ResiWater. 2018. “Resiwater: Innovative secure sensor networks and model-based assessment tools for increased resilience of water infrastructures.” Accessed September 3, 2018. http://www.resiwater.eu/objectives/.
Shirzad, A., M. Tabesh, R. Farmani, and M. Mohammadi. 2013. “Pressure-discharge relations with application in head-driven simulation of water distribution networks.” J. Water Resour. Plann. Manage. 139 (6): 660–670. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000305.
Siew, C., and T. Tanyimboh. 2012. “Pressure-dependent EPANET extension.” Water Resour. Manage. 26 (6): 1477–1498. https://doi.org/10.1007/s11269-011-9968-x.
Tanyimboh, T., and A. Templeman. 2004. “A new nodal outflow function for water distribution networks.” In Proc., 4th Int. Conf. on Engineering Computational Technology, edited by B. H. V. Topping and C. A. Mota Soares. Stirlingshire, UK: Civil-Comp Press.
Todini, E., and L. Rossman. 2013. “Unified framework for deriving simultaneous equation algorithms for water distribution networks.” J. Hydraul. Eng. 139 (5): 511–526. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000703.
Wagner, J., U. Shamir, and D. Marks. 1988. “Water distribution reliability: Simulation methods.” J. Water Resour. Plann. Manage. 114 (3): 276–294. https://doi.org/10.1061/(ASCE)0733-9496(1988)114:3(276).
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Dec 18, 2017
Accepted: May 30, 2018
Published online: Oct 16, 2018
Published in print: Jan 1, 2019
Discussion open until: Mar 16, 2019
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.