Water Distribution Systems Connectivity Analysis
Publication: Journal of Water Resources Planning and Management
Volume 131, Issue 1
Abstract
A water distribution system is a collection of hydraulic control elements jointly connected to convey quantities of water from sources to consumers. Such a system can be described as a graph with the nodes representing the sources and consumers, and the arcs—the connecting elements (e.g., pipes, pumps, and valves). Theoretically, the flow in each arc can reach either direction, resulting in possible digraphs, where equals the number of arcs. However, this number is substantially reduced as Kirchoff’s Laws 1 and 2 (continuity of mass and energy, respectively) hold, and as in certain arcs the flow is constrained to only one direction (e.g., the pipe leading out of a well). This study describes a methodology for establishing the most flexible pair: Operational and backup digraphs of a water distribution system that maintains Kirchoff’s Laws 1 and 2, and yields (if possible) a one-level system redundancy (i.e., if one arc fails, at least one path from at least one source to all consumers is retained by the operational or backup digraphs). The proposed methodology is cast in a genetic algorithm framework and demonstrated through two example applications.
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Acknowledgments
This research was supported by the Japan Technion Society Research Fund, and by the Technion Grand Water Research Institute (GWRI). The writer would also like to acknowledge the assistance of Ziv Amir and Uri Kushnir, undergraduate Technion Civil and Environmental Engineering students, for their valuable assistance and coding work.
References
Dandy, G. C., Simpson, A. R., and Murphy, L. J. (1996). “An improved genetic algorithm for pipe network optimization.” Water Resour. Res., 32(2), 449–458.
Dandy, G. C., and Engelhardt, M. (2001). “The optimal scheduling of water main replacement using genetic algorithms.” J. Water Resour. Plan. Manage., 127(4), 214—223.
Davidson, J. W. (1999). “Evolution program for layout geometry of rectilinear looped networks.” J. Comput. Civ. Eng., 13(4), 246–253.
Goldberg, D. E. (1989). “Genetic algorithms in search, optimization, and machine learning.” Addison–Wesley, New York.
Goulter, I. (1987). “Current and future use of systems analysis in water distribution network design.” Civ. Eng. Sys., 4(4), 175–184.
Halhal, D., Walters, G. A., Savic, D. A., and Ouazar, D. (1999). “Scheduling of water distribution system rehabilitation using structured messy genetic algorithms.” Evol. Comput., 7(3), 311–329.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, Mich.
Jacobs, P., and Goulter, I. (1988). “Evaluation of methods for decomposition of water distribution networks for reliability analysis.” Civ. Eng. Sys., 5(2), 58–64.
Jacobs, P., and Goulter, I. (1989). “Optimization of redundancy in water distribution networks using graph theoretic principles.” Eng. Optimiz., 15(1), 71–82.
Kapelan, Z. S. (2002). “Calibration of WDS hydraulic models.” PhD thesis, Dept. of Engineering, Univ. of Exeter, U.K., 334.
Meier, R. W., and Barkdoll, B. D. (2000). “Sampling design for network model calibration using genetic algorithms.” J. Water Resour. Plan. Manage., 126(4), 245–250.
Morley, M. S., Atkinson, R. M., Savic, D. A., and Walters, G. A. (2001). “GAnet: Genetic algorithm platform for pipe network optimization.” Adv. Eng. Software, 32(6), 467–475.
Ostfeld, A., and Shamir, U. (1996). “Design of optimal reliable multiquality water-supply systems.” J. Water Resour. Plan. Manage., 122(5), 322–333.
Rosenthal, A. (1977). “Computing the reliability of complex networks.” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 32(2), 384–393.
Salomons, E. (2001). “Optimal design of water distribution systems facilities and operation.” MS thesis, Technion, Haifa, Israel, (In Hebrew).
Satyanarayana, A., and Wood, R. K. (1982). “Polygon-to-chain reductions and network reliability.” ORC 82-4, Operations Research Center, Univ. of California, Berkeley, Calif.
Savic, D. A., Walters, G. A., Atkinson, R. M., and Randall, S. M. (1999). “Genetic algorithm optimization of large water distribution system expansion.” J. Meas. Control, 32(4), 104–109.
Savic, D. A., and Walters, G. A. (1997). “Genetic algorithms for the least-cost design of water distribution networks.” J. Water Resour. Plan. Manage., 123(2), 67–77.
Simpson, A. R., Dandy, G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.” J. Water Resour. Plan. Manage., 120(4), 423–443.
Wagner, J. M., Shamir, U., and Marks, D. H. (1988). “Water distribution reliability: analytical methods.” J. Water Resour. Plan. Manage., 114(3), 253–275.
Walski, T. M. (1993). “Water distribution valve topology for reliability analysis.” Reliability Eng. Sys. Safety, 42(1), 21–27.
Weinblatt, H. (1972). “A new search algorithm for finding the simple cycles of a finite directed graph.” J. Assoc. Comput. Mach., 19(1), 43–56.
Wu, Z. Y., and Simpson, A. R. (2001). “Competent genetic-evolutionary optimization of water distribution systems.” J. Comput. Civ. Eng., 15(2), 89–101.
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Information
Published In
Journal of Water Resources Planning and Management
Volume 131 • Issue 1 • January 2005
Pages: 58 - 66
Copyright
© 2005 ASCE.
History
Received: Nov 6, 2002
Accepted: May 15, 2004
Published online: Jan 1, 2005
Published in print: Jan 2005
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