Localization estimation of two leaks in pipelines through Monte Carlo simulations and hydraulic-spatial constraints

Abstract

The problem of localizing two leaks using only flow rate and pressure measurements at the boundaries of a pipeline, and under steady-state flow conditions, is ill-posed due to the undetermined nature of the inverse problem, which involves two coupled equations with four unknowns associated with the presence of the leaks: two emitter coefficients and two locations. Therefore, attempting to solve this problem using any method without imposing additional constraints leads to an unbounded solution space, which contains solutions that may be physically meaningless. In this article, we propose a four-algorithm method that incorporates both spatial and hydraulic constraints to filter out physically infeasible solutions. The proposed method is based on Monte Carlo simulations, which use input data from hydraulic instruments installed at the boundaries of the pipeline, as well as random values with predefined probabilities that are bounded by the hydraulic-spatial constraints. The outputs of the method are probability distributions for the four unknowns. To demonstrate the feasibility of the method, results obtained through simulations and experimental testing on a test bed are presented.