13th Computer Control for Water Industry Conference, CCWI 2015 Graph-theoretic surrogate measures for analysing the resilience of water distribution networks

AbstractHydraulic resilience can be formulated as a measure of the ability of a water distribution network to maintain a minimum level ofservice under operational and failure conditions. This paper explores a hybrid approach to bridge the gap between graph-theoreticand hydraulic measures of resilience. We extend the concept of geodesic distance of a pipeline by taking into account energy lossesassociated with flow. New random-walk algorithms evaluate hydraulically feasible routes and identify nodes with different levelsof hydraulic resilience. The nodes with the lowest scores are further analysed by considering the availability and capacity of theirsupply routes.c 2015 The Authors. Published by Elsevier Ltd.Peer-review under responsibility of the Scientific Committee of CCWI 2015. Keywords: Water distribution systems; network resilience; graph theory; complex networks 1. IntroductionResilience can be understood as the capacity of a system to maintain its performance level under alterations to itsnormal status. It measures a system’s ability to deal with adverse scenarios by absorbing their undesirable effectson its operations and adapting itself to the new operational environment [1,2]. The analysis of network resilience isbecoming increasingly important in ma domains. These range from safety-critical control systems for space shuttlesand train networks to ubiquitous computing and communications systems like the Internet [3,4]. For non-engineeredand natural systems, this same concept of resilience is also used to measure the ability of humans [5] and ecologicalsystems [6] to effectively deal with the extremes of trauma, stress and disasters.There are no universally accepted definitions for the concept of water distribution network (WDN) resilience.A common method is based on the work of Todini [7], where hydraulic resilience is formulated as a measure ofthe capability to get over failure conditions in supply. Todini [7] proposed a resilience index based on the steadystate flow analysis of the WDN and the energy dissipated through its pipes. From this perspective, the resilienceof a water network is a measure of the surplus energy available in the supply. More recent work builds upon thisindex, for example: Raad [8] approached surrogate measures of this index focused on network design, di Nardo etal. [9] included the use of this index in their methodology for sectorising a WDN, and Banos˜ et al. [10] proposed an

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