Towards observer-based fault detection and isolation for branched water distribution networks without cycles

This paper addresses the observer-based, diagonal, fault detection and isolation (FDI) problem for branched water distribution networks without cycles. Specifically, it provides a linear, time-invariant, state-space model for water contamination in such networks based on one-dimensional mass balance and a necessary and sufficient solvability condition for the aforementioned FDI problem. The latter is based on a graph-theoretic characterization of the rank of the model's transfer matrix, which allows one to check for solvability just by analyzing the fault-output paths in the directed graph associated to the model.