Analysis of Water Distribution System under Uncertainty Based on Genetic Algorithm and Trapezoid Fuzzy Membership

Abstract

In most studies of hydraulic simulation of water distribution systems (WDS), the uncertain input parameters such as nodal demands, pipe roughness coefficients, pipe diameters, water levels in reservoirs, and pump characteristics usually are considered to be fuzzy, with triangular distribution membership functions. In this paper, pipe roughness coefficients were considered to be fuzzy parameters affecting pipe flows and nodal pressures due to their significant effects on hydraulic simulation, and trapezoid distribution membership functions instead of triangular distribution membership functions were considered for pipe roughness coefficients. At each α-cut level of roughness coefficients, a genetic algorithm (GA) was applied to obtain the minimum and maximum pipe flows and nodal pressures. The proposed method was applied to four networks to analyze the fuzziness of pipe flows and nodal pressures based on two parameters, dispersion degree and relative flat line rate. This study will help in the fuzziness analysis of hydraulic simulation results in WDS under uncertain pipe roughness coefficients.