Least-Cost Design of Water Distribution Networks under Demand Uncertainty
Publication: Journal of Water Resources Planning and Management
Volume 131, Issue 5
Abstract
Due to inherent variability in instantaneous water consumption levels, values of demands at nodes in a water distribution system remain one of the major sources of uncertainty in the network design process. Uncertainty in demand leads to uncertainty in head at the nodes, which, in turn, affects the system performance and has to be taken into account when designing new water distribution systems or extending/rehabilitating existing ones. One approach to dealing with this difficulty is to formulate and solve the stochastic optimization problem providing a robust, cost-effective solution. However, stochastic formulation usually requires Monte Carlo simulation, which involves calculation of a large number of state estimates, even for relatively simple networks. This renders the approach intractable when combined with heuristic adaptive search techniques, such as genetic algorithms (GAs) or simulated annealing. These methodologies require the fitness function to be evaluated for thousands of possible network configurations in the course of the search process. In this paper a new approach to quantifying the influence of demand uncertainty on nodal heads is proposed. The original stochastic model is reformulated as a deterministic one, which uses standard deviation as a natural measure of variability. Such an approach allows the use of effective numerical methods to quantify the influence of uncertainty on the robustness of water distribution system solutions. The deterministic equivalent is then coupled with an efficient GA solver to find robust and economic solutions. The proposed methodology was tested on the New York tunnels and Anytown problems. A number of low cost network solutions were found for different levels of reliability and different forms of probability distribution function for demands. The robustness of the solutions found was compared to known solutions for deterministic formulations, whose results were postprocessed using full Monte Carlo simulation.
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Acknowledgments
This work was supported by the United Kingdom Engineering and Physical Sciences Research Council, Grant Nos. EPSRC-GBGR/R14712/01, EPSRC-GBGR/S26446/01, and Advanced Research Fellowship Grant No. UNSPECIFIEDAF/000964.
References
Alperovits, E., and Shamir, U. (1977). “Design of optimal water distribution systems.” Water Resour. Res., 13(6), 885–900.
Babayan, A. V., Savic, D. A., and Walters, G. A. (2003). “Design of water distribution network under uncertain demands.” Pumps, Electromechanical Devices and Systems Applied to Urban Water Management; Proc., International Conf., Valencia, Rotterdam, Balkema, The Netherlands, 137–144.
Bargiela, A., and Hainsworth, G. D. (1989). “Pressure and flow uncertainty in water systems.” J. Water Resour. Plan. Manage., 115(2), 212–229.
Bhave, P. R., (1985). “Optimal expansion of water distribution systems.” J. Environ. Eng., 111(2), 177–197.
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.
Duan, N., Mays, L. W., and Lansey, K. E. (1990). “Optimal reliability-based design of pumping and distribution systems.” J. Hydraul. Eng., 116(2), 249–268.
Gessler, J. (1982). “Optimization of pipe networks.” Proc., Int. Symp. on Urban Hydrology, Hydraulics and Sediment Control, Univ. of Kentucky, 165–171.
Goulter, I. C. (1992). “Systems analysis in water-distribution network design from theory to practice.” J. Water Resour. Plan. Manage., 118(3), 238–248.
Halhal, D., Walters, G. A., Ouazar, D., and Savic, D. A. (1997). “Water network rehabilitation with structured messy genetic algorithm.” J. Water Resour. Plan. Manage., 123(3), 137–146.
Krylov, V. I. (1962). Approximate calculation of integrals, Macmillan, New York.
Lansey, K. E. (2000). “Optimal design of water distribution systems.” L. W. Mays, ed., Water distribution system handbook, McGraw–Hill, New York.
Lansey, K. E., Duan, N., Mays, L. W., and Tung, Y. K. (1989). “Water distribution system design under uncertainties.” J. Water Resour. Plan. Manage., 115(5), 630–645.
Morgan, G. R., and Goulter, I. C. (1985). “Optimal urban water distribution design.” Water Resour. Res., 21(5), 642–652.
Murphy, L. J., Simpson, A. R., and Dandy, G. C. (1993). “Pipe network optimization using an improved genetic algorithm.” Research Rep. No. R109, Dept. of Civil and Environmental Engineering, Univ. of Adelaide, Adelaide, Australia.
Obradovic, D., and Lonsdale, P. (1998). Public water supply, E&FN Spon, London.
Quindry, G. E., Liebman, J. C., and Brill, E. D. (1981). “Optimization of looped water distribution systems.” J. Environ. Eng. Div. (Am. Soc. Civ. Eng.), 107(4), 665–679.
Ross, S. M. (1987). Introduction to probability and statistics for engineers and scientists, Wiley, New York.
Rossman, L. A. (2000). Epanet2 users manual, USEPA, Washington, D.C.
Savic, D. A., and Walters, G. A. (1997). “Genetic algorithms for least-cost design of water distribution networks.” J. Water Resour. Plan. Manage., 123(2), 67–77.
Schaake, J., and Lai, D. (1969). “Linear programming and dynamic programming applications to water distribution network design.” Rep. No. 116, Dept. of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass.
Walski, T. M. (1985). “State of the art: Pipe network optimization.” Proc., Computer Applications in Water Resources, ASCE, New York, 559–568.
Walski, T. M., et al. (1987). “Battle of networks models: Epilogue.” J. Water Resour. Plan. Manage., 113(2), 191–203.
Xu, C., and Goulter, I. C. (1999). “Reliability-based optimal design of water distribution network.” J. Water Resour. Plan. Manage., 125(6), 352–362.
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© 2005 ASCE.
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Received: Jun 20, 2003
Accepted: Mar 31, 2004
Published online: Sep 1, 2005
Published in print: Sep 2005
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