Leak Diagnosis in Branched Pipeline Systems Based on a Robust Differentiation Scheme.

The current study addresses the problem of leak detection and isolation (LDI) in a branched pipeline system. The detection process employs a mass balance approach following mass conservation principles. The leak isolation algorithm is activated upon detecting a leak, comprising a bank of m observers corresponding to the number of pipeline branches in the system. The state-space representation of the branched pipe, derived from a classical dynamic representation of a pipeline system, incorporates two variables defining the leak: its position and magnitude. The observability condition for each observer is fulfilled, ensuring the complete reconstruction of the state. To enhance robustness, a super-twisting algorithm (STA), functioning as an exact differentiator, is introduced to estimate the time derivatives of inputs and outputs. Consequently, the complete state is reconstructed using a set of algebraic equations dependent solely on inputs, outputs, and their time derivatives. The analysis considers only the flow rates and pressure head measurements at the inlets and outlets of the pipeline system. For illustrative purposes, experimental results of five leak scenarios are presented, utilizing databases generated from a test bed plant with two branchings constructed at the Tuxtla Gutiérrez Institute of Technology.