Reliability-Based Optimal Design of Water Distribution Networks
Publication: Journal of Water Resources Planning and Management
Volume 125, Issue 6
Abstract
A new approach for reliability-based optimization of water distribution networks is presented. The approach is capable of recognizing the uncertainty in nodal demands and pipe capacity as well as the effects of mechanical failure of system components. A probabilistic hydraulic model is used in the model to account for uncertainty in nodal demands and pipe capacity. The primary innovation of the model is the use of a first-order reliability-method-based algorithm to compute approximate values of the capacity reliability of water distribution networks. Capacity reliability is defined as the probability that the nodal demand is met at or over the prescribed minimum pressure for a fixed network configuration under random nodal demands and random pipe roughnesses. The model also incorporates a strategy for identifying the critical nodes on which the reliability constraints are imposed in the cost minimizing step. The computational efficiency of the optimization is shown to be enhanced by deriving the first-order derivatives analytically using a sensitivity-analysis-based technique. The efficiency and capacity of the proposed algorithm are illustrated by application to two sample networks.
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References
1.
Alperovits, E., and Shamir, U. (1977). “Design of optimal water distribution systems.” Water Resour. Res., 13(6), 885–900.
2.
Awumah, K., Goulter, I. C., and Bhatt, S. K. (1990). “Assessment of reliability in water distribution networks using entropy based measures.” Stochastic Hydro. and Hydr., 4, 309–320.
3.
Awumah, K., Goulter, I. C., and Bhatt, S. K. (1991). “Entropy-based redundancy measures in water distribution network design.”J. Hydr. Engrg., ASCE, 117(5), 595–614.
4.
Awumah, K., and Goulter, I. C. (1992). “Maximizing entropy defined reliability of water distribution networks.” Engrg. Optimization, 20(1), 57–80.
5.
Bao, Y., and Mays, L. W. (1990). “Model for water distribution system reliability.”J. Hydr. Engrg., ASCE, 116(9), 1119–1137.
6.
Biem, G., and Hobbs, G. (1988). “Analytical simulation of water system capacity reliability. 2: A Markov-chain approach and verification models.” Water Resour. Res., 24(9), 1445–1458.
7.
Bouchart, F., and Goulter, I. (1991). “Reliability improvements in design of water distribution networks recognizing valve location.” Water Resour. Res., 27(12), 3029–3040.
8.
Cullinane, M. J., Lansey, K. E., and Mays, L. W. (1992). “Optimization-availability-based design of water distribution networks.”J. Hydr. Engrg., ASCE, 118(3), 420–441.
9.
Der Kiureghian, A., Lin, H. Z., and Hwang, S. J. (1987). “Second order reliability approximations.”J. Engrg. Mech., ASCE, 113(8), 1208–1225.
10.
Duan, N., Mays, L. W., and Lansey, K. E. (1990). “Optimal reliability-based design of pumping and distribution systems.”J. Hydr. Engrg., ASCE, 116(2), 249–268.
11.
Eiger, G., Shamir, U., and Be-Tal, A. (1994). “Optimal design of water distribution networks.” Water Resour. Res., 30(9), 2637–2646.
12.
Fujiwara, O., and Tung, H. D. (1991). “Reliability improvement for water distribution networks through increasing pipe size.”Water Resour. Res., 27(7), 1395–1402.
13.
Germanopoulis, G., Jowitt, P. W., and Lumbers, J. (1986). “Assessing the reliability of supply and level of service for water distribution systems.” Proc., Instn. of Civ. Engrs., Part 1, 80, 413–428.
14.
Goulter, I. (1992). “Systems analysis in water distribution network design: From theory to practice.”J. Water Resour. Plng. and Mgmt., ASCE, 118(3), 238–248.
15.
Goulter, I. ( 1995). “Analytical and simulation models for reliability analysis in water distribution systems.” Improving efficiency and reliability in water distribution systems, E.Cabrera and A. F. Vela, eds., Kluwer Academic, London, 235–266.
16.
Goulter, I., and Bouchart, F. (1990). “Reliability-constrained pipe network model.”J. Hydr. Engrg., ASCE, 116(2), 211–229.
17.
Goulter, I., and Coals, A. (1986). “Quantitative approaches to reliability assessment in pipe networks.”J. Transp. Engrg., ASCE, 112(3), 287–301.
18.
Gupta, R., and Bhave, R. (1994). “Reliability analysis of water distribution systems.”J. Envir. Engrg., ASCE, 120(2), 447–460.
19.
Hasover, A. M., and Lind, N. C. (1974). “Exact and invariant second-moment code format.”J. Engrg. Mech. Div., ASCE, 100(1), 111–121.
20.
Hobbs, B., and Biem, G. (1988). “Analytical simulation of water system capacity reliability. 1: Modified frequency-duration analysis.” Water Resour. Res., 24(9), 1431–1444.
21.
Jacobs, P., and Goultier, I. (1991). “Estimation of maximum cut-set size for water network failure.”J. Water Resour. Plng. and Mgmt., ASCE, 117(5), 588–605.
22.
Jowitt, P., and Xu, C. (1993). “Predicting pipe failure effects in water distribution networks.”J. Water Resour. Plng. and Mgmt., ASCE, 119(1), 18–31.
23.
Kettler, A., and Goulter, I. (1983). “Reliability consideration in the least cost design of looped water distribution networks.” Proc., 10th Int. Symp. on Urban Hydro., Hydr. and Sediment Control, University of Kentucky, Lexington, Ky., 305–312.
24.
Khomsi, D., Walters, G. A., Thorley, A. R. D., and Ouazar, D. (1996). “Reliability tester for water-distribution networks.”J. Comp. in Civ. Engrg., ASCE, 10(1), 10(1), 10–19.
25.
Lansey, K., Duan, N., Mays, L. W., and Tung, Y.-K. (1989). “Water distribution system design under uncertainty.”J. Water Resour. Plng. and Mgmt., ASCE, 115(5), 630–645.
26.
Lansey, K. E., and Mays, L. W. (1989). “Optimization model for water distribution system design.”J. Hydr. Engrg., ASCE, 115(10), 1401–1418.
27.
Lasdon, L. S., and Waren, A. D. (1986). GRG2 user's guide. Dept. of General Business and Admin., University of Texas, Austin, Tex.
28.
Li, D., Dolezal, T., and Haimes, Y. (1993). “Capacity reliability of water distribution networks.” Reliability Engrg. and Sys. Safety, 42, 29–38.
29.
Liu, P. L., and Der Kiureghian, A. (1991). “Optimization algorithms for structural reliability.” Struct. Safety, Amsterdam, 9(3), 161–177.
30.
Madsen, H. O., Krenk, S., and Lind, N. C. (1986). Methods of structural safety. Prentice-Hall, Englewood Cliffs, N.J.
31.
Mays, L. W. (1989). “Methodologies for assessment of aging water distribution systems.” Rep. No. CRWR 227, Ctr. for Res. in Water Resour., The University of Texas, Austin, Tex.
32.
Mays, L. W. ( 1996). “Review of reliability analysis of water distribution systems.” Stochastic hydraulics '96, K. K. Tickle et al., eds., Balkema, Rotterdam, The Netherlands, 53–62.
33.
Melching, C. S., Yen, B. C., and Wenzel, H. G. (1990). “A reliability estimation in modeling watershed runoff with uncertainties.” Water Resour. Res., 26(10), 2275–2286.
34.
Morgan, D. R., and Goulter, I. C. (1985). “Optimal urban water distribution design.” Water Resour. Res., 21(5), 642–652.
35.
Ormsbee, L., and Kessler, A. (1990). “Optimal upgrading of hydraulic network reliability.”J. Water Resour. Plng. and Mgmt., ASCE, 116(6), 784–802.
36.
Ostfeld, A., and Shamir, U. (1996). “Design of optimal reliable multiquality water-supply systems.”J. Water Resour. Plng. and Mgmt., ASCE, 122(5), 322–333.
37.
Park, H., and Leibman, J. (1993). “Redundancy-constrained minimum-cost design of water distribution networks.”J. Water Resour. Plng. and Mgmt., ASCE, 119(1), 83–98.
38.
Quimpo, R., and Shamsi, U. (1991). “Reliability-based distribution system maintenance.”J. Water Resour. Plng. and Mgmt., ASCE, 117(3), 321–339.
39.
Quindry, G., Brill, E. D., and Liebman, J. C. (1981). “Optimization of looped distribution systems.”J. Envir. Engrg. Div., ASCE, 107(4), 665–679.
40.
Rackwitz, R., and Fiessler, B. (1978). “Structural reliability under combined random load sequences.” Comp. and Struct., 9, 489–494.
41.
Rowell, W. F., and Barnes, J. W. (1982). “Obtaining the layout of water distribution systems.”J. Hydr. Div., ASCE, 108(1), 137–148.
42.
Savic, D., and Walters, G. (1997). “Genetic algorithms for least-cost design of water distribution networks.”J. Water Resour. Plng. and Mgmt., ASCE, 123(2), 67–77.
43.
Simpson, A. R., Dandy, G. C., and Murphy, L. J. (1994). “Genetic algorithms compared to other techniques for pipe optimization.”J. Water Resour. Plng. and Mgmt., ASCE, 120(4), 423–443.
44.
Sitar, N., Cawlfield, J. D., and Der Kiureghian, A. (1987). “First-order reliability approach to stochastic analysis of subsurface flow and contaminant transport.” Water Resour. Res., 23(5), 794–804.
45.
Skaggs, T. H., and Barry, D. A. (1997). “The first order reliability method of predicting cumulative mass flux in heterogeneous porous formations.” Water Resour. Res., 33(6), 1485–1494.
46.
Su, Y., Mays, L. W., Duan, N., and Lansey, K. (1987). “Reliability based optimization model for water distribution systems.”J. Hydr. Engrg., ASCE, 113(12), 1539–1556.
47.
Tanyimboh, T. T., and Templeman, A. B. (1993). “Optimum design of flexible water distribution networks.” Civ. Engrg. Sys., 10(3), 243–258.
48.
Tung, Y. K. ( 1996). “Uncertainty analysis in water resources engineering.” Stochastic hydraulics '96, K. S. Tickle et al., eds., Balkema, Rotterdam, The Netherlands, 29–46.
49.
Wagner, J. M., Shamir, U., and Marks, D. H. (1988a). “Water distribution reliability: Analytical methods.”J. Water Resour. Plng. and Mgmt., ASCE, 114(3), 253–275.
50.
Wagner, J. M., Shamir, U., and Marks, D. H. (1988b). “Water distribution reliability: Simulation methods.”J. Water Resour. Plng. and Mgmt., ASCE, 114(3), 276–292.
51.
Wu, S. J., Yoon, Y. H., and Quimpo, R. (1993). “Capacity-weighted water distribution system reliability.” Reliability Engrg. and Sys. Safety, 42, 39–46.
52.
Xu, C., and Goulter, I. C. ( 1996). “Uncertainty analysis of water distribution networks.” Stochastic hydraulics '96, K. S. Tickle et al., eds., Balkema, Rotterdam, The Netherlands, 609–616.
53.
Xu, C., and Goulter, I. C. ( 1997a). “Reliability assessment of water distribution networks using the first order reliability method.”Managing water: Coping with scarcity and abundance, M. English and A. Szollosi-Nagy, eds., ASCE, Reston, Va., 429–434.
54.
Xu, C., and Goulter, I. (1997b). “Simulation-based optimal design of reliable water distribution networks.” Proc., 3rd Int. Conf. on Modeling and Simulation, A. Zayegh, ed., Victoria University of Technology, Melbourne, 107–112.
55.
Xu, C., and Goulter, I. (1998). “Probabilistic model for water distribution reliability.”J. Water Resour. Plng. and Mgmt., ASCE, 124(4), 218–228.
56.
Xu, C., Goulter, I., and Tickle, K. S. (1998). “Probabilistic hydraulic models for assessing capacity reliability of aging water distribution infrastructure.” Proc., HydraStorm '98, D. J. Walker and T. M. Daniell, eds., Institution of Engineers, Australia, 165–170.
57.
Yen, B. C., Cheng, S. T., and Melching, C. S. ( 1986). “First-order reliability analysis.” Stochastic and risk analysis in hydraulic engineering, B. C. Yen, ed., Water Resources Publications, Littleton, Col., 1–36.
58.
Zollenkopf, K. ( 1971). “Bi-factorization: Basic computational algorithm and programming techniques.” Large sparse sets of linear equations, J. K. Reid, ed., Academic, London.
Information & Authors
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Published In
Journal of Water Resources Planning and Management
Volume 125 • Issue 6 • November 1999
Pages: 352 - 362
History
Received: Dec 2, 1998
Published online: Nov 1, 1999
Published in print: Nov 1999
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