Uncertainty Analysis toward confidence limits to hydraulic state predictions in Water Distribution Networks

International audienceCalculating the hydraulic state, through and across elements such as pipes, valves and control devices is an important task in managing a water distribution network. Although hydraulic models are widely used by water utilities and engineers, they are governed by a huge number of uncertain parameters like the diameter and roughness of pipes, consumer demands, leakages and internal state of valves inside the distribution network. In the past, extensive work has been done on the calibration of these parameters [1-3] but there is still an uncertainty attached to the result. The objective of the research done as part of the French-German project ResiWater [4] is to analyse the propagation of uncertainties in water distribution networks (WDN). Uncertainty analysis investigates the influence of model errors and parameter uncertainties on the results of numerical simulation models. Numerous methods have been developed to achieve this goal and some of the most influential ones are given by Monte Carlo methods, perturbation methods and adjoint methods. But most of these methods have limitations either in their convergence behaviour or the computational complexity. Here we concentrate on three basic approaches to the propagation of uncertainties. In calculating the moment equations we approximate the moments for uncertainty in the results. This is done by the first order second moment (FOSM) and the second order second moment (SOSM) method [5]. In the calculation of the moment equation the sensitivities play a vital role. The adjoint sensitivity analysis procedure [5] is applied to hydraulic network equations and evaluated as an alternative to the direct calculation of the sensitivities. For comparison with sensitivity methods and moment methods, a spectral approach is evaluated using the generalized polynomial chaos expansion (gPCE) [6]. Sampling based Monte Carlo simulations are used as basic validation method. The performance of the different approaches to the quantification of uncertainty in system parameters will be evaluated and discussed on a small illustrative network