Hydraulic Analysis of Water Distribution System Under Interval-Valued Fuzzy Set

Hydraulic analysis of Water Distribution System (WDS) is usually performed with single uncertainty of pipe roughness coefficient. However, in real world multiple uncertainties exist. In this paper, dual uncertainties of pipe roughness coefficient were considered, which is represented by Interval-Values Fuzzy Set (IVFS). In addition, the fuzziness was assumed to follow trapezoidal fuzzy distribution. The measure of fuzziness and interval of variables based on IVFS were defined. By applying Interval-Values Fuzzy Set-Genetic Algorithm (IVFS-GA) algorithm, pipe flow and nodal pressure under uncertain effects of pipe roughness coefficients were analyzed. The method proposed was applied to three cases to analyze the fuzziness and interval of pipe flow and nodal pressure, which were defined with trapezoidal membership distributions. The fuzziness and interval of pipe flow have no direct relationship, while the fuzziness and interval of nodal pressure have the same trend. In the three WDSs, the intervals of nodal pressures are more significant than pipe flows. The results obtained can help the manager analyze the hydraulic performance of WDS under uncertainty of pipe roughness coefficients.