Prior Assumptions for Leak Localisation in Water Distribution Networks with Uncertainties
Caroline Blocher, Filippo Pecci, Ivan Stoianov
Abstract
Abstract 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, $$\ell _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -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 $$\ell _2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> -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.