Coping with Uncertainty in the Reliability Evaluation of Water Distribution Systems

The application of the reliability analysis techniques to the water distribution systems aims to properly achieve in probabilistic terms the fulfilment of the nodal demand in a conceptual and physical context subject to different causes of uncertainties. The availability of system components, like pumps or pipes subjected to failure, the uncertainty in the spatial - temporal behaviour of nodal demand, the pipe roughness, the reservoir level as well as the availability of supply resources contribute to the definition of the system reliability. Nevertheless the complexity of a reliability model increases with the number of different uncertainties, and usually, for each specific case, only few parameters are assumed as random while the remaining are fixed as deterministic. This fact always implies more or less limitations in the system description also when deterministic assumptions are based on reasonable hypotheses. To overcome this shortcoming, a mixed analytical - numerical approach, able to take into account both the mechanical failure of system components and the random spatial - temporal distribution of nodal demands, is here developed. The goal is achieved by joining a Monte Carlo numerical approach based on the head-driven simulation with a First Order Second Moment (FOSM) closed form solution (Xu and Goulter, 1998). The Monte Carlo approach lets to analyze the series of partial shutdowns related to the renewal process of pipes and the time evolution of the demand, while the spatial variability of the latter and the uncertainty in the pipe roughness are described by the FOSM approach. An illustrative example developed in the well-known case of the Anytown network, demonstrates that the uncertainty related to the spatial nodal demand and pipe roughness may have a relevant impact on the reliability evaluation of a distribution network whose pipes are subject to the mechanical failure.