Fuzzy Approach for Analysis of Pipe Networks

An analysis of the hydraulic behavior of pipe networks often involves imprecise or uncertain quantities. Typical examples of these quantities are the roughness coefficient of old pipes, which becomes increasingly difficult to determine as the network ages, and the demands of the network, which can vary significantly according to the number of users connected to the network. These are quantities for which there is often only semiquantitative information which generally implies a degree of subjectiveness and that cannot therefore be expressed either with precise values or through statistical distributions. In this article we show how the fuzzy set theory provides conceptual tools for one to deal with this kind of information and to calculate how the uncertainties of the available information can spread to the unknowns of the problem, that is, to the discharges and piezometric heads. After a brief review of the fuzzy set theory, the way the hydraulic problem can be described within a fuzzy approach framework is given. Following this review, a suitable method, based on interval algebra and optimization theory, is introduced to solve the corresponding fuzzy equations and it is illustrated through examples.