Improved Loop-Flow Method for Hydraulic Analysis of Water Distribution Systems
Publication: Journal of Water Resources Planning and Management
Volume 144, Issue 4
Abstract
Different methods have been developed in the past to formulate and solve steady-state hydraulics of a water distribution system (WDS). The most widely used method nowadays is probably the global gradient algorithm (GGA). The loop-flow method (also known as the method) represents a viable alternative to GGA, especially when combined with suitably preprocessed network data. The main advantage of the method over the GGA is in the smaller number of unknowns to solve for, which is coming from the fact that real WDSs typically have far less loops than nodes. A new loop-flow-type method, relying on the novel triangulation based loops identification algorithm (TRIBAL) that was implemented in the corresponding new hydraulic solver (), is presented in this paper (TRIBAL-). The new method aims to exploit this advantage, while overcoming key drawbacks of existing methods. The performance of the TRIBAL--based solver is compared with the GGA-based solver on four large real networks of different complexity and topology. The results obtained demonstrate that, despite requiring an increased number of iterations to converge, the TRIBAL- method–based solver is substantially computationally faster, has slightly better numerical stability, and is equally accurate in making predictions when compared with the GGA-based hydraulic solver.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alvarruiz, F., Martinez-Alzamora, F., and Vidal, M. (2015). “Improving the efficiency of the loop method for the simulation of water distribution systems.” J. Water Resour. Plann. Manage., 04015019.
Arsene, C. T. C., Bargiela, A., and Al-Dabass, D. (2004). “Modelling and simulation of the water systems based on loop equations.” Int. J. Simul. Sci. Technol., 5(1–2), 61–72.
Cheng, S. W., Dey, T. K., and Shewchuk, J. R. (2013). Delaunay mesh generation, CRC Press, Boca Raton, FL.
Creaco, E., and Franchini, M. (2014). “Comparison of Newton-Raphson global and loop algorithms for water distribution network resolution.” J. Hydraul. Eng., 313–321.
Creaco, E., and Franchini, M. (2015). “The identification of loops in water distribution networks.” Procedia Eng., 119, 506–515.
Cross, H. (1936). “Analysis of flow in networks of conduits or conductors.”, Univ. of Illinois at Urbana Champaign, Champaign, IL.
De Pina, J. (1995). “Applications of shortest path methods.” Ph.D. thesis, Univ. of Amsterdam, Amsterdam, Netherlands.
Deuerlein, J. W. (2008). “Decomposition model of a general water supply network graph.” J. Hydraul. Eng., 822–832.
Deuerlein, J. W., Elhay, S., and Simpson, A. R. (2016). “Fast graph matrix partitioning algorithm for solving the water distribution system equations.” J. Water Resour. Plann. Manage., 04015037.
Dijkstra, E. W. (1959). “A note on two problems in connexion with graphs.” Numerische Mathematik, 1(1), 269–271.
Elhay, S., Simpson, A. R., Deuerlein, J., Alexander, B., and Schilders, W. H. A. (2014). “Reformulated co-tree flows method competitive with the global gradient algorithm for solving water distribution system equations.” J. Water Resour. Plann. Manage., 04014040.
Epp, R., and Fowler, A. G. (1970). “Efficient code for steady-state flows in networks.” J. Hydraul. Div., 96(1), 43–56.
George, A., and Liu, J. W.-H. (1981). Computer solution of large sparse positive definite systems, Prentice-Hall, Englewood Cliffs, NJ.
Ivetić, D., Vasilić, Ž., Stanić, M., and Prodanović, D. (2016). “Speeding up the water distribution network design optimization using the ΔQ method.” J. Hydroinf., 18(1), 33–48.
Jha, K. (2007). “Automatic minimal loop extraction and initialisation for water pipe network analysis.” Int. J. Simul. Syst. Sci. Technol., 8(2), 8–19.
Kavitha, T., Mehlhorn, K., Michail, D., and Paluch, K. (2004). “A faster algorithm for minimum cycle basis of graphs.” Proc., 31st Int. Colloquium on Automata, Languages and Programming, ICALP, Springer, Berlin, 846–857.
Larock, B. E., Jeppson, R. W., and Watters, G. Z. (2000). Hydraulics of pipeline systems, CRC Press, Boca Raton, FL.
MATLAB [Computer software]. MathWorks, Natick, MA.
Ostfeld, A., et al. (2008). “The battle of the water sensor networks (BWSN): A design challenge for engineers and algorithms.” J. Water Resour. Plann. Manage., 556–568.
Perelman, L., and Ostfeld, A. (2012). “Water distribution systems simplifications through clustering.” J. Water Resour. Plann. Manage., 218–229.
Piller, O. (1995). “Modelling the behavior of a network: Hydraulic analysis and sampling procedures for parameter estimation.” Ph.D. thesis, Univ. of Bordeaux I, Bordeaux, France.
Rossman, L. A. (2000). “EPANET 2 user’s manual.”, National Risk Management Research Laboratory, Cincinnati.
Simpson, A., and Elhay, S. (2011). “The Jacobian for solving water distribution system equations with the Darcy-Weisbach head loss model.” J. Hydraul. Eng., 696–700.
Simpson, A., Elhay, S., and Alexander, B. (2014). “Forest-core partitioning algorithm for speeding up analysis of water distribution systems.” J. Water Resour. Plann. Manage., 435–443.
Stanić, M., Kapelan, Z., and Avakumović, D. (1998). “Evolutionary algorithm for determining optimal tree layout of water distribution networks.” Proc., Hydroinformatics ‘98: The 3rd Int. Conf. on Hydroinformatics, V. Babovic and L. C. Larsen, eds., A.A. Balkema, Rotterdam, Netherlands, 901–910.
Todini, E. (2008). “On the convergence properties of the different pipe network algorithms.” Proc., Water Distribution Systems Analysis Symp., ASCE, Reston, VA, 1–16.
Todini, E., and Pilati, S. (1988). A gradient algorithm for the analysis of pipe networks, B. Coulbeck and O. Chun-Hou, eds., Wiley, London, 1–20.
Todini, E., and Rossman, L. A. (2013). “Unified framework for deriving simultaneous equation algorithms for water distribution networks.” J. Hydraul. Eng., 511–526.
University of Exeter. (2018). “Benchmarks.” ⟨http://emps.exeter.ac.uk/engineering/research/cws/resources/benchmarks/⟩ (Jan. 25, 2018).
Water Simulation. (2018). “BWCN—Battle of the water calibration networks.” ⟨http://www.water-simulation.com/wsp/about/bwcn/⟩ (Jan. 25, 2018).
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Feb 14, 2017
Accepted: Oct 10, 2017
Published online: Feb 14, 2018
Published in print: Apr 1, 2018
Discussion open until: Jul 14, 2018
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.