The ill-posed inverse problem for detecting and localizing leakage hotspots is solved using a novel optimization-based method which aims to minimize the difference between hydraulic measurement data and simulated steady states of a water distribution network. Regularization constrains the set of leak candidate nodes obtained from a solution to the optimization problem. Hydraulic conservation laws are enforced as nonlinear constraints. The resulting nonconvex optimization problem is solved using smooth mathematical optimization techniques. The solution identifies leakage hotspot areas, which can then be further investigated with alternative methods for precise leak localization. A metric is proposed to quantitatively assess the performance of the developed leak localization approach in comparison with a method that uses the sensitivity matrix. In addition, we propose a strategy to select the regularization parameter when large-scale operational networks are considered. Using two numerical case studies, we demonstrate that the proposed approach outperforms the sensitivity matrix method, with regards to leak isolation, in most single leak scenarios. Moreover, the developed method enables the localization of multiple simultaneous leaks.
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, $$\ell _2$$
ℓ
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 $$\ell _2$$
ℓ
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.
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.
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