The Role of Prior Assumptions for Leak Localisation in Water Networks with Uncertainties

Abstract

Hydraulic model-based leak (burst) localisation in water networks is a challenging problem due to uncertainties, the limited number of hydraulic measurements, and the wide range of leak properties. In this study, we investigate the use of prior assumptions to improve the leak localisation in the presence of model uncertainties. For example, 𝓁2-regularisation relies on the assumption that the Euclidean norm of the leak coefficient vector should be minimised. This approach is compared with a method based on the sensitivity matrix, which assumes the existence of only a single leak. We show that while applying the sensitivity matrix often yields a better estimate of the leak location in single leak scenarios, the 𝓁2-regularisation successfully identifies a leak search area for pinpointing the accurate leak location. Furthermore, we demonstrate that the additional error introduced by a quadratic approximation of the Hazen-Williams formula for the solution of the localisation problem is negligible given the uncertainties in Hazen-Williams resistance coefficients in operational water network models.