This paper presents a methodology to find the optimal design or rehabilitation of water distribution system (WDS) under both steady-state and transient conditions. Then, assessing the obtained optimal solution and studying its stability, reliability, due to uncertainty in pipe roughness coefficients (C_HW). The WDS optimization objective is to minimize the rehabilitation cost by installing new pipes parallel to the existing ones achieving all hydraulic constraints. For this purpose, particle swarm optimization (PSO) is used as an optimization tool and Monte Carlo simulation (MCS) is applied to generate multiple realizations of C_HW for different coefficient of variation (COV_CHW). A comparison between crisp shape and continuous shape (S-shape) fuzzy membership functions is carried out to study the hydraulic availability indices to nodal pressure head values resulted from pipe roughness uncertainty. Both steady-state nodal and system reliabilities are estimated while, only the transient system reliability is calculated for the obtained optimal solution. The proposed methodology is applied on the New York City tunnel network (NYCTN) and the corresponding reliability is analyzed. Results show that as pipe roughness uncertainty increases, WDS reliability decreases.

本文提出了一种在稳态和瞬态条件下都能找到最优设计或供水系统（WDS）修复的方法。然后，评估由于管道粗糙度系数（C _HW）的不确定性而获得的最佳解决方案，并研究其稳定性，可靠性。WDS的优化目标是通过与现有管道平行安装新管道，以最大程度地降低修复成本，从而实现所有液压约束。为了这个目的，粒子群优化（PSO）被用作优化工具和蒙特卡罗模拟（MCS）被施加到产生的多个实现Ç _HW为变异系数不同（COV _CHW）。进行了脆形和连续形（S形）模糊隶属函数的比较，以研究由于管道粗糙度不确定性而导致的节点压头值的水力可用性指数。估计稳态节点和系统可靠性，而对于获得的最优解，仅计算瞬态系统可靠性。所提出的方法应用于纽约市隧道网络（NYCTN），并分析了相应的可靠性。结果表明，随着管道粗糙度不确定性增加，WDS可靠性降低。