Decomposed Uncertainty Evaluation for Hydraulic State Estimation in Water Supply Systems

Hydraulic state estimation (HSE) can be used to infer the flow and pressure regime in water supply systems based on the available measurements in the network and the associated hydraulic model. Because the inputs involved in the process are noisy, uncertainty quantification is paramount to assess the reliability of HSE results. Numerical and analytical methods have been adopted to quantify HSE uncertainty in the past, but they are associated with poor scalability for large networks. The aim of this paper is to adapt the analytical first-order second-moment (FOSM) formulation for HSE uncertainty assessment, which is the most widely adopted method in the literature, by using decomposition techniques to improve its scalability. The decomposed methodology is equivalent to the original formulation and is here applied to several case studies. Computational times were two orders of magnitude lower in large networks thanks to the decomposed formulation, which loses its computational advantage in small/medium-sized systems. Moreover, the numerical conditioning improves when dividing the network. Therefore, the proposed methodology constitutes a better alternative for HSE uncertainty quantification in large networks and could be key to boost HSE implementation in operational systems.