Incorporating uncertainty in the design of water distribution systems

During the design stage of urban water supply and distribution systems several assumptions and projections to future horizons are made. The analysis and design is then based on a deterministic basis in which all the involved parameters have crisp values. In reality however, most of the parameters exhibit significant variability over the life span of the system. The resistance to flow is among the most important parameters exhibiting variability. This is caused by the variability of the friction coefficient of pipes and the variability of internal diameters of the pipes. This study attempts to incorporate these uncertainties in the analysis and design of urban water supply and distribution systems, following a copula approach. Because of the low data availability, fuzzy membership functions are assigned to describe both variability of friction coefficients and variability of internal pipe diameters. Instead of the min intersection, the use of copulas is proposed in order to combine the uncertainties and calculate the fuzziness of the pipe resistance to flow. Thus, the input variables are fuzzy numbers and the problem is to find the output of the system which will consists also of fuzzy quantities. The system itself is described by the set of precise (crisp) nonlinear Q-equations. Finally, the uncertainty analysis concludes to an optimization problem. A numerical example is presented to demonstrate this innovative methodology.