Probabilistic Model for Water Distribution Reliability
Publication: Journal of Water Resources Planning and Management
Volume 124, Issue 4
Abstract
A two-stage methodology for assessment of reliability of water distribution networks recognizing uncertainties in nodal demands, pipe capacity, reservoir/tank levels, and availability of system components is proposed. In the first stage, the probability distribution functions for nodal heads are derived from a linearized hydraulic model on the basis of known probability distribution functions of the nodal demands, pipe roughnesses, and reservoir/tank levels. The effects of nonlinearity in the network hydraulic model are accounted for in this step by partitioning the nodal demands into a number of categories or intervals. The probability of supply failure calculated in this first stage assumes that the system state or configuration is fixed, e.g., certain pipes and pumps are specified as being out of operation; that the pipe capacity varies randomly; and that demands vary around a specified level. The second step involves combining this probability with the probabilities of different system configurations and demand levels to generate the overall reliability measured for the whole system or a particular area of the system.
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References
1.
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.
2.
Bao, Y., and Mays, L. W.(1990). “Model for water distribution system reliability.”J. Hydr. Engrg., ASCE, 116(9), 1119–1137.
3.
Bargiela, A., and Hainsworth, G.(1989). “Pressure and flow uncertainty in water system.”J. Water Resour. Plng. and Mgmt., ASCE, 115(2), 212–229.
4.
Beim, 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.
5.
Bouchart, F., and Goulter, I.(1991). “Reliability improvements in design of water distribution networks recognizing valve location.”Water Resour. Res., 27(12), 3029–3040.
6.
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.
7.
Duan, N., and Mays, L. W.(1990). “Reliability analysis of pumping systems.”J. Hydr. Engrg., ASCE, 116(2), 230–248.
8.
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.
9.
Fujiwara, O., and Tung, H. D.(1991). “Reliability improvement for water distribution networks through increasing pipe size.”Water Resour. Res., 27(7), 1395–1402.
10.
Germanopoulos, G., Jowitt, P., and Lumbers, J. (1986). “Assessing the reliability of supply and level of service for water distribution system.”Proc., Instn. Civ. Engrs., Part 1, 80(Apr.), 413–428.
11.
Goulter, I.(1987). “Current and future use of system analysis in water distribution network design.”Civ. Engrg. Sys., 4(4), 175–184.
12.
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.
13.
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 Publishers, London, U.K., 235–266.
14.
Goulter, I., and Bouchart, F.(1990). “Reliability-constrained pipe network model.”J. Hydr. Engrg., ASCE, 116(2), 211–229.
15.
Goulter, I., and Coals, A.(1986). “Quantitative approaches to reliability assessment in pipe networks.”J. Transp. Engrg., ASCE, 112(3), 287–301.
16.
Gupta, R., and Bhave, R.(1994). “Reliability analysis of water distribution systems.”J. Envir. Engrg., ASCE, 120(2), 447–460.
17.
Hobbs, B., and Beim, G.(1988). “Analytical simulation of water system capacity reliability. 1: Modified frequency-duration analysis.”Water Resour. Res., 24(9), 1431–1444.
18.
Jacobs, P., and Goulter, I.(1991). “Estimation of maximum cut-set size for water network failure.”J. Water Resour. Plng. and Mgmt., ASCE, 117(5), 588–605.
19.
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.
20.
Khomsi, D., Walters, G. A., Thorley, A. R. D., and Ouazar, D.(1996). “Reliability tester for water-distribution networks.”J. Computing in Civ. Engrg., ASCE, 10(1), 10–19.
21.
Lansey, K., and Basnet, C.(1991). “Parameter estimation for water distribution network.”J. Water Resour. Plng. and Mgmt., ASCE, 117(1), 126–144.
22.
Lansey, K., Duan, N., Mays, L. W., and Tung, Y.-K.(1989). “Water distribution design under uncertainty.”J. Water Resour. Plng. and Mgmt., ASCE, 115(5), 630–645.
23.
Li, D., Dolezal, T., and Haimes, Y.(1993). “Capacity reliability of water distribution networks.”Reliability Engrg. and Sys. Safety, 42, 29–38.
24.
Mays, L. W. (1996). “Review of reliability analysis of water distribution systems.”Stochastic Hydr. '96, K. S. Tickle et al., eds., A. A. Balkema, Rotterdam, The Netherlands, 53–62.
25.
Ormsbee, L., and Kessler, A.(1990). “Optimal upgrading of hydraulic network reliability.”J. Water Resour. Plng. and Mgmt., ASCE, 116(6), 784–802.
26.
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.
27.
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.
28.
Quimpo, R., and Shamsi, U.(1991). “Reliability-based distribution system maintenance.”J. Water Resour. Plng. and Mgmt., ASCE, 117(3), 321–339.
29.
Shamir, U., and Howard, C. D. D.(1968). “Water distribution systems analysis.”J. Hydr. Div., ASCE, 94(1), 219–234.
30.
Su, Y., Mays, L. W., Duan, N., and Lansey, K.(1987). “Reliability based optimization for water distribution system.”J. Hydr. Engrg., ASCE, 113(12), 589–596.
31.
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.
32.
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.
33.
Walters, G. (1988). “Optimal design of pipe networks: a review.”Proc., 1st Int. Conf. on Comp. and Water Resour., Vol. 2, Computational Mechanics Publications, Southampton, U.K., 21–31.
34.
Wu, S. J., Yoon, Y. H., and Quimpo, R.(1993). “Capacity-weighted water distribution system reliability.”Reliability Engrg. and Sys. Safety, 42, 39–46.
35.
Xu, C., and Goulter, I. C. (1996). “Uncertainty analysis of water distribution networks.”Stochastic Hydr. '96, K. S. Tickle et al., eds., A. A. Balkema, Rotterdam, The Netherlands, 609–616.
36.
Xu, C., and Goulter, I. C. (1997). “Reliability assessment of water distribution networks using the first order reliability method.”Managing Water: Coping with Scarcity and Abundance, Proc. 27th IAHR Congr., M. English and A. Szollosi-Nagy, eds., ASCE, 429–434.
37.
Yen, B. C., Cheng, S. T., and Melching, C. S. (1986). “First-order reliability analysis.”Stochastic and risk anal. in hydr. engrg., B. C. Yen, ed., Water Resources Publications, Littleton, Colo., 1–36.
38.
Zollenkopf, K. (1971). “Bi-factorization: basic computational algorithm and programming techniques.”Large sparse sets of linear equations, J. K. Reid, ed., Academic Press, London, U.K.
Information & Authors
Information
Published In
Journal of Water Resources Planning and Management
Volume 124 • Issue 4 • July 1998
Pages: 218 - 228
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Jul 1, 1998
Published in print: Jul 1998
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