Leak Localization in Looped Pipe Networks Based on a Factorized Transient Wave Model: Theoretical Framework

Urban water distribution systems are often made of loops to increase redundancy and improve reliability. The inherent feature of multipath wave propagation in looped networks has been the main obstacle to directly derive a factorized wave propagation model with decoupled leak location and size, which is essential for developing a robust and efficient leak localization method. To address this problem, this article proposes an efficient algorithm to estimate the transient hydraulic pressure and discharge at all nodes of a looped network using boundary measurements. Given these hydraulic properties, a factorized wave propagation model is formulated by applying conservation laws to a tree-shaped control volume of the looped network. Based on this factorized model, a fast and efficient one-dimensional search of the leak location along all pipes of a looped network is realized by the matched-field processing technique. Numerical experiments demonstrate that an unknown leak anywhere in a five-loop network with 13 pipes can be accurately and efficiently localized by the proposed method.