Unified Sufficient Conditions for PCA-based Fault Detectability and Isolability*

Fault detectability and isolability concepts are necessaries to be developed in order to determine if faults are detectable and isolable. In PCA framework, the development of these issues has been limited to some detection indices. In this paper, we have extended and unified the fault detectability and isolabilty concepts in order to be valid for any quadratic detection index. In particular, an isolability analysis based on the combined index against those of SPE and T2 statistics is investigated. From a simulation example, we have confirmed the theoretical analysis that shows the feature of the combined index in the isolation of some faults that have not enough magnitudes to be isolable neither by SPE nor by T2 indices.