Isolability of faults in sensor fault diagnosis

A major concern with fault detection and isolation (FDI) methods is their robustness with respect to noise and modeling uncertainties. With this in mind, several approaches have been proposed to minimize the vulnerability of FDI methods to these uncertainties. But, apart from the algorithm used, there is a theoretical limit on the minimum effect of noise on detectability and isolability. This limit has been quantified in this paper for the problem of sensor fault diagnosis based on direct redundancies. In this study, first a geometric approach to sensor fault detection is proposed. The sensor fault is isolated based on the direction of residuals found from a residual generator. This residual generator can be constructed from an input-output or a Principal Component Analysis (PCA) based model. The simplicity of this technique, compared to the existing methods of sensor fault diagnosis, allows for more rational formulation of the isolability concepts in linear systems. Using this residual generator and the assumption of Gaussian noise, the effect of noise on isolability is studied, and the minimum magnitude of isolable fault in each sensor is found based on the distribution of noise in the measurement system. Finally, some numerical examples are presented to clarify this approach.