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Water Distribution System Reliability Based on Minimum Cut – Set Approach and the Hydraulic Availability

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Reliability analysis of water distribution systems is a complex task, as it requires both definition and calculation of several reliability measures. In this paper, a methodology for evaluating water distribution system reliability is developed and demonstrated on a simple water distribution network based on the minimum cut-set approach. In general, the definition of the minimum cut-set can arise either from the mechanical reliability or from the concept of hydraulic reliability. In the case of mechanical reliability, a new method based on graph theory is developed, in order to determine the minimum cut-set. This method is based on the counting of paths between nodes. Furthermore, the general concept of reliability is proposed, to include apart from the mechanical reliability, more generally, the pressure availability at nodes as a main hydraulic property. Based on the pressure availability, the sense of hydraulic availability can be expressed as a fuzzy set, while the combination of the water unavailability of the nodes can be achieved by using fuzzy averaging aggregator. Finally, an overall reliability index is proposed based on both the hydraulic and the mechanical reliability. An illustrative example is developed to indicate the methodology.

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  1. Al-Zahrani MA, Syed JL (2005) Evaluation of municipal water distribution system reliability using minimum cut-set method. J King Saud Univ Eng Sci 18(1):67–82

  2. Awumah K, Goulter IC (1992) Maximizing entropy defined reliability of water distribution networks. Eng Optim 20:57–80

  3. Baños R, Reca J, Martínez J, Gil C, Márquez A (2011) Resilience indexes for water distribution network design: a performance analysis under demand uncertainty. Water Resour Manag 25:2351–2366

  4. Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: A guide for practitioners. Studies in fuzziness and soft computing, Volume 221. Springer.

  5. Branisavljevic N, Ivetic M (2006) Fuzzy approach in the uncertainty analysis of the water distribution network of Becej. Civ Eng Environ Syst 23(2):221–236

  6. Cancelliere A, Ancarini A, Rossi G (2002) A neural networks approach for deriving irrigation reservoir operating rules. Water Resour Manag 16:71–88

  7. Cavallo A, Di Nardo A (2008) Optimal Fuzzy Management of Reservoir based on Genetic Algorithm. In: Lowen, R, Verschoren, A (eds) Foundations of Generic Optimization Vol II: Applications of Fuzzy Control, Genetic Algorithms and Neural Networks. Series: Mathematical Modelling: Theory and Applications. Springer Verlag, London, pp 139–159

  8. Chen HW, Chang NB (2010) Using fuzzy operators to address the complexity in decision making of water resources redistribution in two neighboring river basins. Adv Water Resour 33:652–666

  9. Cullinane MJ, Lansey KE, Mays LW (1992) Optimization availability-based design of water distribution networks. J Hydraul Eng ASCE 118(3):420–441

  10. Di Nardo A, Di Natale M (2011) A heuristic design support methodology based on graph theory for district metering of water supply networks. Eng Optim 43(2):193–211

  11. Firat M, Gungor G (2008) Hydrological time-series modelling using an adaptive neuro-fuzzy inference system. Hydrol Process 2:2122–2132

  12. Giustolisi O, Kapelan Z, Savic DA (2008) Algorithm for automatic detection of topological changes in water distribution networks. J Hydraul Eng ASCE 134(4):435–446

  13. Giustolisi O, Laucelli D, Colombo AF (2009) Deterministic versus stochastic design of water distribution networks. J Water Resour Plan Manag ASCE 135(2):117–127

  14. Goulter IC (1995) Analytical and simulation models for reliability analysis in water distribution systems. In: Cabrera E, Vela A (eds) Improving efficiency and reliability in water distribution systems. Kluwer Academic Publishers

  15. Goulter IC, Coals AV (1986) Quantitative approaches to reliability assessment in pipe networks. J Transp Eng ASCE 112(3):278–301

  16. Kaufmann AD, Grouchko D, Croun R (1977) Mathematical models for the study of the reliability of systems. Academic, New York

  17. Li L, Lai KK (2000) A fuzzy approach to the multiobjective transportation problem. Comput Oper Res 27:43–57

  18. Ostfeld A (2004) Reliability analysis of water distribution systems. J Hydroinf 6(4):281–294

  19. Ostfeld A, Kogan D, Shamir U (2002) Reliability simulation of water distribution systems — single and multiquality. Urban Water 4:53–61

  20. Papadopoulos B, Sirpi M (1999) Similarities in fuzzy regression models. J Optim Theory Appl 102(2):373–383

  21. Perny P (1998) Multicriteria filtering methods based on concordance and non-discordance principle. Ann Oper Res 80:137–165

  22. Revelli R, Ridolfi L (2002) Fuzzy approach for analysis of pipe networks. J Hydraul Eng ASCE 128(1):93–101

  23. Rosen K (2003) Discrete mathematics and applications (5th edition). McGraw Hill

  24. Ross SM (1985) Introduction to probability models. Academic, New York

  25. Savic DA, Walters GA (1995) An evolution program for optimal pressure regulation in water distribution networks. Eng Optim 24(3):197–219

  26. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–428

  27. Shinstine D, Ahmed I, Lansey K (2002) Reliability/availability analysis of municipal water distribution networks: case studies. J Water Resour Plan Manag 128(2):140–151

  28. Spiliotis K, Siettos C (2011) A timestepper-based approach for the coarse-grained analysis of microscopic neuronal simulators on networks: bifurcation and rare-events micro-to macro-computations. Neurocomputing 74:3576–3589

  29. Spiliotis M, Tsakiris G (2007) Minimum cost irrigation network design using interactive fuzzy integer programming. J Irrig Drain Eng (ASCE) 133:242–248

  30. Spiliotis M, Tsakiris G (2011) Water distribution system analysis: the Newton - Raphson method revisited. J Hydraul Eng 137:852–856

  31. Spiliotis M, Tsakiris G (2012a) Water distribution network design under variable water demand. J Civ Eng Environ Syst 29(2):107–122

  32. Spiliotis M, Tsakiris G (2012b) Closure to “Water distribution system analysis: Newton-Raphson method revisited” by M. Spiliotis and G. Tsakiris. J Hydraul Eng ASCE 138(9):824–826

  33. Spyrou P (1997) Graph theory. University of Athens, Mathematical Department, Athens (in Greek)

  34. Su Y, Mays L, Duan N, Lansey K (1987) Reliability based optimization for water distribution systems. J Hydraul Eng ASCE 113:589–596

  35. Tanyimboh TT, Templeman AB (2000) A quantified assessment of the relationship between the reliability and entropy of water distribution systems. Eng Optim 33:179–199

  36. Todini E (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water 2(3):15–122

  37. Tsakiris G, Spiliotis M (2011) Planning against long term water scarcity: a fuzzy multicriteria approach. Water Resour Manag 25(4):1103–1129

  38. Tsakiris G, Spiliotis M, Paritsis S, Alexakis D (2009) Assessing the water potential of karstic saline springs by applying a fuzzy approach: the case of Almyros (Heraklion - Crete). Desalination 237:54–64

  39. Tung YK (1985) Evaluation of water distribution network reliability. Proc Int Conf Hydraul Hydrol Small Comput Age NY ASCE 1:359–364

  40. Vasan A, Simonovic S (2010) Optimization of water distribution network design using differential evolution. J Water Resour Plan Manag 136(2):279–287

  41. Wagner JM, Shamir U, Marks DH (1988) Water distribution reliability: analytical methods. J Water Resour Plan Manag Div ASCE 114(3):253–275

  42. Yannopoulos St, Vohaitis D (2003) Estimation of water distribution networks reliability with the minum cut — set method. Proc. of 9th Symposium of Hellenic Hydrotechnical Association, Thessaloniki 2–5, April: 293–300 (in Greek)

  43. Yannopoulos St, Dermissis V, Dermissi N (1997) Availability and reliability in supply systems. Proc. of 7th Symposium of Hellenic Hydrotechnical Association, Patra 14–18, October: 148–155 (in Greek)

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Correspondence to Mike Spiliotis.

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Yannopoulos, S., Spiliotis, M. Water Distribution System Reliability Based on Minimum Cut – Set Approach and the Hydraulic Availability. Water Resour Manage 27, 1821–1836 (2013). https://doi.org/10.1007/s11269-012-0163-5

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  • Water distribution networks
  • Reliability
  • Minimum cut-set
  • Hydraulic availability
  • Graph theory
  • Fuzzy sets