Factorized wave propagation model in tree-type pipe networks and its application to leak localization

In a leaky tree-structured pipe network, transient head and discharge at a measurement location arise from a superposition of the waves along the set of pipes linking the measurement location to each boundary node. Moreover, the solution can be split into a leak-free part and a term that accounts for the scattering from the leak, the latter varies linearly with leak size and nonlinearly with leak location. It is then shown that if the head adjacent to each boundary node is measured, any reasonably-sized leak can be uniquely and efficiently identified by the matched-field processing approach. The efficiency of the leak identification scheme stems from the linear dependence of wave scattering on leak size. The proposed method is successfully applied both numerically and to pilot data from a tree-structured system of viscoelastic pipes.