Prior Assumptions for Leak Localisation in Water Distribution Networks with Uncertainties

Hydraulic model-based leak (burst) localisation in water distribution networks is a challenging problem due to a limited number of hydraulic measurements, a wide range of leak properties, and model and data uncertainties. In this study, prior assumptions are investigated to improve the leak localisation in the presence of uncertainties. For example, $$\ell _2$$ -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. The results show that while the sensitivity matrix method often yields a better leak location estimate in single leak scenarios, the $$\ell _2$$ -regularisation successfully identifies a search area for pinpointing the accurate leak location. Furthermore, it is shown 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.