Leak detection, size estimation and localization in tree-shaped pipe flow networks

A novel distributed parameter systems approach for detecting and diagnosing leaks in any tree-shaped pipe flow network is provided, requiring only pressure and flow sensors at the network inlet and outlet boundaries. Modelling the pressure and flow transients in the network via linearized transmission line PDEs (partial differential equations), it is shown how the network may be represented by an interconnection (cascade) of systems of linear hyperbolic PDEs, with a depth determined by the network topological radius and width the number of network inlets and outlets. Information about leaks in the network is summarized in a structured way in an unknown additive vector parameter entering the distal boundary of the last PDE system. It is shown how the leak parameter may be used to compute the total amount leaking from the network regardless of how leaks are distributed in the network, and in the event of point leaks entering the network sequentially, pinpoint the location of the leaks in the network. Two methods are provided to estimate the leak parameter: (1) An algebraic calculation for when the system is in steady-state and (2) an adaptive boundary observer for the interconnected system of PDEs with asymptotic convergence guarantees for transient dynamics. A simulation example is provided to demonstrate the leak detection method with transient data.