Spectral Propagation of Parameter Uncertainties in Water Distribution Networks

The hydraulic state of a water distribution network is governed by a large number of uncertain parameters. These parameters may be given by uncertain consumer demand, valves states, the value of pipe diameters or the roughness of the pipes. In practice, the influence of parameter variations is important in the decision-making process of water utilities, which emphasizes the need for proper quantification of the resulting uncertainties in head and flow. The central step in uncertainty quantification is the propagation of uncertainties through the system. In the past, the influence of parameter uncertainties on the system state has been studied using perturbation methods, stochastic collocation and interval state estimation. This paper presents the results of an alternative spectral approach that has been examined as part of the French-German research project ResiWater. The generalized Polynomial Chaos Expansion is applied to a small looped water distribution network with multiple uncertain input parameters using a non-intrusive projection method. These results are compared to the Monte Carlo simulation as representative of stochastic collocation methods. It is demonstrated that the Polynomial Chaos Expansion is capable to capture a high order of non-linear effects like the Monte Carlo simulation for a considerably lower computational effort.