Complete Diagnosability of Abrupt Faults Using Set-Based Sensitivities

To ensure the safe operation of technical processes, the occurrence of a fault has to be reliably detected for a supervisory component to react in time. We investigate the sensitivity of the measured outputs with respect to abrupt or parametric faults for polynomial hybrid systems. For this we define a sensitivity measure based on the reachable sets of the outputs. The approach allows for the consideration of discrete changes in variables as well as unknown-but-bounded parameters or output measurements. Guaranteed outer bounds of the reachable sets are derived by employing mixed-integer relaxations. Furthermore, we present an algorithm to derive an upper bound on the allowed measurement error such that the faults can be detected and isolated within a specified amount of time. The upper bounds can be used to select or optimize sensors to guarantee complete fault diagnosibility. We illustrate the proposed algorithm considering fault detection and isolation for a three tank system.