Optimal design of water distribution systems considering uncertainties in demands and roughness coefficients

The optimal design of water distribution system has been usually performed with fixed hydraulic variables and single objective. However, a realistic water distribution system should take inherent uncertainties of data into consideration. This study suggests a method to minimize the system cost and maximize the robustness of network based on uncertainties in nodal demands and pipe roughness coefficients. Multi-Objective Genetic Algorithm (MOGA) implements two separate optimization models for the least cost and the best robustness design as the initial population. The model considers the uncertainties in roughness coefficient and water demand by using Latin Hypercube sampling techniquewith the assumption of beta probability density function. Several beta probability density functions with wide range of data are evaluated in the procedure. The proposed approach is tested in case study of the New York Tunnels. The parameter for the assessment of pressure variability a is introduced and the critical node is defined as the node having the highest pressure difference when random nodal demands are applied. Robustness is estimated by minimizing the pressure variation at the critical node and the sum of those at all nodes in the system and evaluated using the disturbance index (DI). As a result, the robustness of entire system is decreased or not guaranteed when only critical node is considered to estimate the robustness. Therefore, the entire system's nodes are recommended to be considered when robustness of water distribution system is evaluated to design more reliable networks.