Functional Diagnosability of Possibly Uncertain Systems

Diagnosability is a crucial attribute of systems and their instrumentation, ensuring that specified faults can be uniquely identified using the available sensors. In a model-based context, diagnosability is evaluated through analytical redundancy relations derived from the model by eliminating unknown variables. These relations, evaluated from sensor data, yield residuals, which indicate the system’s normal or faulty state. Ideally, residuals exhibit distinct values for different faults, generating unique fault signatures that facilitate fault discrimination and affirm system diagnosability. This letter presents a sufficient condition for the functional diagnosability of nonlinear dynamical systems, based on the functional linear independence of fault signatures. Unlike conventional diagnosability analysis, which focuses on residuals evaluated in a binary manner, 0 when not sensitive to a fault and 1 otherwise, functional diagnosability emphasizes the system’s behavior by evaluating the functional expressions of residuals defined as functional fault signatures. Evaluated from sensor data, functional signatures allow for an analysis of the whole residual trajectories. This advantageously increases the discriminating power. This approach leverages the symbolic framework of differential algebra, accommodating both deterministic and bounded uncertain systems without the need for a set-membership framework.