Identification of multiple leaks in pipeline II: Iterative beamforming and leak number estimation

Abstract

Abstract This paper considers the problem of detecting multiple leaks in a water-filled pipe using transient waves. A previous paper by the authors proposes a maximum likelihood (ML) method for leak detection based on an approximate linear model of wave propagation in pipe and shows that it is efficient, robust with noise, and super-resolved. However, that ML method needs to solve an N-parameter optimization problem (N is the leak number) which is high dimensional, non-convex and has many local maxima when N is large. The present paper deals with the multiple-leak detection problem where the leak number is high. A ML based iterative procedure, known as the iterative beamforming (IB) method, is proposed. Given an initial value of model parameter (locations and sizes of leaks) in each iteration, the complex inverse problem with 2 N unknown parameters is decomposed into N one-dimensional optimization problems, which largely decreases the computational complexity. More specifically, IB iteratively estimates the contributions from various leaks to the pressure head measurement and then performs a 1-D ML method on these estimates. In order to estimate the unknown number of leaks, model selection methods, known as Akaike information criterion (AIC) and Bayesian information criterion (BIC), are used and they are proven to be efficient to estimate the actual leak number. Numerical simulations show that five leaks can be accurately identified with super-resolution and the leak number can be correctly estimated using the methods proposed in this paper.