Two Simultaneous Leak Diagnosis in Pipelines Based on Input–Output Numerical Differentiation

Abstract

This paper addresses the two simultaneous leak diagnosis problem in pipelines based on a state vector reconstruction as a strategy to improve water shortages in large cities by only considering the availability of the flow rate and pressure head measurements at both ends of the pipeline. The proposed algorithm considers the parameters of both leaks as new state variables with constant dynamics, which results in an extended state representation. By applying a suitable persistent input, an invertible mapping in x can be obtained as a function of the input and output, including their time derivatives of the third-order. The state vector can then be reconstructed by means of an algebraic-like observer through the computation of time derivatives using a Numerical Differentiation with Annihilatorsconsidering its inherent noise rejection properties. Experimental results showed that leak parameters were reconstructed with accuracy using a test bed plant built at Cinvestav Guadalajara.