Modified Factorized Transient Wave Model in Tree Pipe Networks for Leak Localization With Less Boundary Measurements

Pressure measurement within each boundary pipe of a tree network has been the prerequisite to the formulation of its factorized transient wave propagation model, which is essential for developing a robust and efficient leak localization algorithm. However, the accessibility of all boundary pipes cannot be always guaranteed in underground pipe networks. The inaccessibility of any one boundary pipe for pressure sensor placement would result in the complete invalidity of this elegant algorithm. To address this problem, this paper reformulates and modifies the factorized wave propagation model, which allows the leak localization algorithm to be implemented without the strict accessibility requirement of all boundary pipes. This is realized by linearizing and factorizing the point transfer matrices of boundary pipes based on the small leak approximation. Numerical experiments demonstrate that the modified algorithm can accurately localize a single leak and give a good estimation of multiple co-existing leaks in a tree network. Moreover, the modified algorithm is verified by recent laboratory experiments conducted in a tree network of viscoelastic pipes, where a leak is successfully localized.