Uncertainty in the Analysis of Water Conveyance Systems

Conventionally, the design of water conveyance and distribution systems is based on the assumption that all the involved parameters are known a priori and remain unaltered throughout the life cycle of the system. This type of approach offers simplicity in the calculations by neglecting a variety of uncertainties which accompany the parameters and processes involved. However, significant uncertainties do appear during the analysis and design of these systems, such as the equivalent pipe roughness and the actual internal diameters of the pipes. Furthermore, the demands at the nodes of the system are dependent on several ambiguous assumptions which are not always met at the operation stage. To deal with these uncertainties, several mathematical data demanding approaches have been proposed in the past. In this study these uncertainties are incorporated in the analysis of the system, using the extension principle of the fuzzy sets and a new operation of the fuzzy subtraction. Based on the calculation of head losses for each branch of the system, the nodal heads are derived as fuzzy numbers. The proposed methodology, being a low data demand methodology, is illustrated by a numerical example of a water conveyance system.