Uncertainty Analysis of Optimal Instruction for WDN Pipes Repair and Replacement Using Fuzzy α-cut - hydraulic Simulation Approach

The optimization of the initial design or the development of repair and replacement strategies for pipes within the water distribution network (WDN) during its operational phase relies on the utilization of crisp values. Some input variables such as nodes demand, pipe’s roughness coefficient and reservoir water level have the uncertain nature. Alterations in input parameter values during the operational period, attributed to uncertainty, induce shifts in the behavior and performance of the WDN compared to scenarios with crisp input parameters. Recognizing and analyzing these variations are imperative for making informed decisions to address their ramifications and mitigate problems within the water distribution network. This research analyzes the uncertainty surrounding WDN node pressures, post-implementation of optimal instructions for pipe repair and replacement. The input parameters considered for this analysis include the uncertainty associated with the pipe’s roughness coefficient and the nodes demand within the network. To achieve this objective, a combined approach utilizing both a simulation model (EPANET) and the fuzzy α-cut methodology is employed. Triangular fuzzy membership functions (MF) are chosen for both the input and output variables in the analysis. The extreme value combinations of the two uncertain input variables, at each level of uncertainty, are formulated into four distinct scenarios, serving as the input fuzzy set for the simulation model. Among the research scenarios, the second scenario, characterized by the combination of the minimum pipe’s roughness coefficient and the maximum demand, is designated as the critical scenario. The findings indicate that in the critical scenario, under the highest level of uncertainty, the WDN reliability index diminishes significantly, ranging from approximately 30–40%. This decrease is primarily attributed to the inadequate supply of required pressure to most nodes within the network. At lower levels of uncertainty, the reliability index of the network surpasses 75%, indicating a relatively acceptable performance. Specifically, in the first and fourth scenarios, the network reliability index consistently exceeds 72%. Notably, in the third scenario, the network reliability index remains consistently above 90% across all uncertainty levels.