Flow-Uniformity Index for Reliable-Based Optimal Design of Water-Distribution Networks

The reliability of water distribution network (WDN) designs for satisfying water demands under normal and abnormal operating conditions, including during pipe bursts and as systems age, is typically evaluated with surrogate measures of system resistance to potential hydraulic and mechanical stressors. The resilience index and its modifications have been applied to assess the reliability of a WDN in the face of hydraulic variances, including alterations in network friction characteristics, inputs, and demands. A limitation of these indices is that they may only be used as an indirect measure of network reliability in the face of mechanical failures. A uniformity index is proposed to address this limitation. While the definition of the index is simple, the maximization of it is expected to lead to network designs with an increasingly uniform flow, at each node, in which the burden of carrying inflows (or outflows) at each node is shared evenly among all input (or output) pipes. Using a single-loop network example, this paper demonstrates that increasing this index leads to increased mechanical reliability. The incorporation of the uniformity index, along with the goals of maximizing the resilience index and minimizing design costs, in a multiobjective optimization modelling framework, is likely to result in WDN designs with increased mechanical reliability, relative to those based solely on resilience and cost. The efficacy of the multiobjective approach that includes these goals, for improving overall reliability in response to mechanical and hydraulic disturbances, is demonstrated for two WDNs, the two-loop benchmark, and the municipality of Farhadgerd, Iran.