Fuzzy parameters in pipe network analysis

Lengths, diameters, and friction coefficients of pipes, nodal demands, and reservoir water levels are normally used as independent parameters in the analysis of pipe networks. Some of these parameters such as pipe lengths are precisely known and remain so over time, whereas some others such as friction coefficients of pipes and nodal demands are not precisely known and are fuzzy. For such fuzzy parameters a range giving minimum, most-likely and maximum values is fixed depending on manuals and experience. The usual network analysis uses the most-likely values as normal values, i.e., unique values for the fuzzy independent parameters; therefore, it also provides unique values of the dependent parameters such as pipe discharges and nodal hydraulic gradient levels. However, the fuzzy parameters give a wide range of extreme-minimum and maximum-values of dependent parameters. Revelli and Ridolfi [Fuzzy approach for analysis of pipe networks. J. Hydraul. Eng., ASCE, 2002, 128(1), 93-101] suggested an optimization-based methodology to obtain membership functions, and thereby obtain extreme values of the dependent parameters. An approach based on the usual network analysis using unique values from the range of values of fuzzy independent parameters is provided to determine the extreme values, and also to obtain the membership functions of the dependent parameters. The proposed methodology requires less computational effort and time and is illustrated through examples. Application to field network is also described.