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.

HSE is known to be a useful monitoring tool for water supply systems. The quality of HSE results is heavily dependent on data and hydraulic model errors, so uncertainty quantification is crucial to assess their reliability. The FOSM method is typically adopted to quantify HSE results’ uncertainty. Even though it is computationally advantageous with respect to Monte Carlo simulations, it still presents poor scalability in large systems due to (1) its high computational expense, and (2) its tendency to numerical ill-conditioning. This work adapts the traditional FOSM formulation so that it can benefit from the available network divisions in large systems. Working in smaller areas (i.e., subnetworks), such as district metered areas, reduces the size of the matrices involved in uncertainty propagation, effectively lowering the execution time and improving numerical conditioning by two orders of magnitude in large systems. Therefore, this new divide and conquer approach improves the applicability of the FOSM philosophy for HSE uncertainty quantification in large networks. Because HSE (and HSE uncertainty quantification) has proved its interest as a decision-making tool, the new method would help water utilities to assess the reliability of their information communication technology (ICT) solutions.