Abstract
The replacement of existing pipes is a strategy for the rehabilitation of water distribution networks that is frequently adopted by water companies. Usually, the optimal choice of the pipes diameter is a difficult optimization task, because limited budgets are available. In order to support the selection of a rehabilitation strategy, surrogate reliability measures are often used as an indirect measure of the water distribution system hydraulic performance. Among others, the resilience and entropy indices have attracted considerable interest because they both represent a measure of the network robustness. In the present work, a comparison between these indices is provided in the framework of the optimal rehabilitation of an existing network under limited budget constraint. The resilience and entropy indices are applied to the case of a realistic water distribution network in an extended period simulation framework. Several values of the maximum budget allocable for rehabilitation are considered, and hydraulic calculations are undertaken by means of a pressure driven approach within a modified EPANET 2 environment. The effectiveness of the two surrogate reliability measures is demonstrated by an a-posteriori reliability assessment.
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References
Alvisi S, Franchini M (2006) Near-optimal rehabilitation scheduling of water distribution systems based on a multi-objective genetic algorithm. Civ Eng Environ Syst 23(3):143–160
Ardenti P, Ciaponi C, Franchioli L, Papiri S (2007) Simulazione idraulica delle reti di distribuzione idrica in condizioni di pressione insufficienti in uno o più nodi
Atkinson S, Farmani R, Memon FA, Butler D (2014) Reliability indicators for water distribution system design: comparison. J Water Res Plan Manag 140:160–168
Ciaponi C, Franchioli L, Papiri S (2012) Simplified procedure for water distribution networks reliability assessment. J Water Resour Plann Manag: 368–376. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000184
Cimorelli L, Cozzolino L, Covelli C, Della Morte R, Pianese D (2014) Enhancing the efficiency of the automatic design of rural drainage networks. J Irrig Drain Eng: 04014015. https://doi.org/10.1061/(ASCE)WR.1943-5452.0000184
Cimorelli L, Cozzolino L, Covelli C, Mucherino C, Palumbo A, Pianese D (2013) Optimal design of rural drainage networks. J Irrig Drain Eng. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000526,137-144
Cimorelli L, Morlando F, Cozzolino L, Covelli C, Della Morte R, Pianese D (2016) Optimal positioning and sizing of detention tanks within urban drainage networks. J Irrig Drain Eng 142(1):04015028
Covelli C, Cimorelli L, Cozzolino L, Della Morte R, Pianese D (2016a) Reduction in water losses in water distribution systems using pressure reduction valves. Water Sci Technol Water Supply 16(4):1033–1045
Covelli C, Cozzolino L, Cimorelli L, Della Morte R, Pianese D (2016b) Optimal location and setting of PRVs in WDS for leakage minimization. Water Resour Manag 30(5):1803–1817
Cozzolino L, Cimorelli L, Covelli C, Mucherino C, Pianese D (2015) An innovative approach for drainage network sizing. Water 7(2):546–567
Creaco, E., Fortunato, A., Franchini, M., and Mazzola, M. (2014a), Comparison between entropy and resilience as indirect measures of reliability in the framework of water distribution network design. Proc Eng: 379–388. https://doi.org/10.1016/j.proeng.2014.02.043
Creaco E, Franchini M, Todini E (2014b) The combined use of resilience and loop diameter uniformity as a good indirect measure of network reliability. Urban Water J. https://doi.org/10.1080/1573062X.2014.949799
Creaco E, Franchini M, Todini E (2016) Generalized resilience and failure indices for use with pressure driven modeling and leakage. J Water Resour Plan Manag (ISI) 142(8):04016019 ASCE (ISSN: 0733-9496)
Cullinane MJ, Lansey KE, Mays LW (1992) Optimization availability-based design of water-distribution networks. J Hydr Eng ASCE 118(3):420–441
Dandy GC, Engelhardt MO (2006) Multi-objective trade-offs between cost and reliability in the replacement of water mains. J Water Resour Plan Manag 132(2)
Farmani R, Walters GA, Savic DA (2005) Trade-off between Total cost and reliability for Anytown water distribution network. J Water Resour Plan Manag 131(3)
Gargano R, Pianese D (2000) Reliability as tool for hydraulic network planning. J Hydraul Eng 126(5):354–364
Gheisi A, Naser G (2015) Multistate reliability of water-distribution systems: comparison of surrogate measures. J Water Resour Plan Manag 141(10):04015018
Giustolisi O, Berardi L (2009) Prioritizing pipe replacement: from multiobjective genetic algorithms to operational decision support. J Water Resour Plan Manag 135(6)
Greco R, Di Nardo A, Santonastaso G (2012) Resilience and entropy as indices of robustness of water distribution networks. J Hydroinf 14(3):761–771
Halhal D, Walters GA, Ouazar D, Savic DA (1997) Water network rehabilitation with structured messy genetic algorithm. J Water Resour Plan Manag, 123(3)
Hashimoto T, Loucks DP, Stedinger J (1982) Reliability, resiliency, and vulnerability criteria for water resource system performance evaluation. Water Resour Res 18(1):14–20
Jayaram N, Srinivasan K (2008) Performance based optimal design and rehabilitation of water distribution networks using life cycle costing. Water Resour Res, 44(1)
Martínez-Rodríguez JB (2010) Cost and reliability comparison between branched and looped water supply networks. J Hydroinf 12:150–160
Martínez-Rodríguez JB, Montalvo I, Izquierdo J, Pérez-García R (2011) Reliability and tolerance comparison in water supply networks. Water Resour Manag 25(5):1437–1448
Nafi A, Kleiner Y (2010) Scheduling renewal of water pipes while considering adjacency of infrastructure works and economies of scale. J Water Resour Plan Manag 136(5)
Palumbo A, Cimorelli L, Covelli C, Cozzolino L, Mucherino C, Pianese D (2014) Optimal design of urban drainage networks. Civ Eng Environ Syst 31(1):79–96
Quimpo RG, Shamsi UM (1991) Reliability-based distribution system maintenance. J Water Resour Plan Manag 117(3):321–339
Raad DN, Sinske AN, Van Vuuren JH (2010) Comparison of four reliability surrogate measures for water distribution systems design. Water Resour Res 46(5):W05524
Rossman LA (2000) Epanet 2 users manual. U.S. Environmental Protection Agency, Cincinnati, USA
Santonastaso, G.F.; Di Nardo, A.; Di Natale, M.; Giudicianni, C.; Greco, R. Scaling-laws of flow entropy with topological metrics of water distribution networks. Entropy 2018, 20, 95
Setiadi Y, Tanyimboh TT, Templeman AB (2005) Modelling errors, entropy and the hydraulic reliability of water distribution systems. Adv Eng Softw 36(11):780–788
Siew C, Tanyimboh TT, Seyoum AG (2014) Assessment of penalty-free multi-objective evolutionary optimization approach for the design and rehabilitation of water distribution systems. Water Resour Manag 28(2):373–389
Tanyimboh TT, Templeman AB (2000) A quantified assessment of the relationship between the reliability and entropy of water distribution systems. Eng Optim 33(2):179–199
Tanyimboh TT, Tietavainen MT, Saleh S (2011) Reliability assessment of water distribution systems with statistical entropy and other surrogate measures. Water Sci Technol Water Supply 11(4):437–443
Tanyimboh TT, Siew C, Saleh S et al (2016) Comparison of surrogate measures for the reliability and redundancy of water distribution systems. Water Resour Manag 30:3535. https://doi.org/10.1007/s11269-016-1369-8
Tanyimboh TT (2017) Informational entropy: a failure tolerance and reliability surrogate for water distribution networks. Water Resour Manag 31(10):3189–3204
Todini E (2000) Looped water distribution networks design using a resilience index based heuristic approach. Urban Water J 2(3):115–122
Tolson B, Maier H, Simpson A, Lence B (2004) Genetic algorithms for reliability-based optimization of water distribution systems. J Water Resour Plan Manag. https://doi.org/10.1061/(ASCE)0733-9496(2004)130:1(63),63-72
Wagner J, Shamir U, Marks D (1988) Water distribution reliability: simulation methods. J Water Resour Plan Manag 114(3):276–294
Walski TM (1985) Cleaning and lining versus parallel mains. J Water Resour Plan Manag 1111:43–53
Xu Q, Chen Q, Ma J, Blanckaert K (2013) Optimal pipe replacement strategy based on break rate prediction through genetic programming for water distribution network. J Hydro-Environ Res 7(2):134–140
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Cimorelli, L., Morlando, F., Cozzolino, L. et al. Comparison Among Resilience and Entropy Index in the Optimal Rehabilitation of Water Distribution Networks Under Limited-Budgets. Water Resour Manage 32, 3997–4011 (2018). https://doi.org/10.1007/s11269-018-2032-3
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DOI: https://doi.org/10.1007/s11269-018-2032-3