Generalization and analysis of sufficient conditions for PCA-based fault detectability and isolability

Fault detectability and fault isolability concepts are necessary to be developed in order to determine whether the process faults are detectable and isolable. In PCA framework, the development of these concepts has been limited to the use of some particular detection indices. This paper provides an extension and a generalization of the fault detectability and the reconstruction-based fault isolabilty concepts in order to be valid for the use of any detection index having a quadratic-form. Fundamental fault detectability as well as fault isolability analyses based on the combined index compared to those using both SPE and Hotelling’s T2 indices are investigated. In addition, we have illustrated the proposed analyses from a simulation example. This one highlights the advantage of the combined index into the isolation of some process faults that have not large enough magnitudes to be isolable neither by SPE index nor by Hotelling’s T2 statistic.