Real-time fault diagnosis using observer and physical parameter estimation

A state of the art for Fault Detection and Isolation (FDI) scheme which combines both the non-parametric and parametric approaches is evaluated on simulated as well as physical system. This scheme retains the advantages of the non-parametric and the parametric approaches in the sense that it is fast and can detect as well as isolate faults. The fault is considered to be multiplicative. The system is assumed linear and is modeled as a series, parallel and feedback combination of functional units whose faults have to be detected and isolated. The feature vector which is a vector whose elements are the coefficients of the system transfer function, is multilinear in the physical parameters which are the coefficients of the transfer function of the functional units. The feature vector and its partials with respect to each of the physical parameter, termed influence vector, are estimated off-line by perturbing each physical parameter one at a time. In real time the residual is generated using an observer. Using a whitening filter the effect of the disturbance and the measurement noise are attenuated at the residual output. A set of equations termed parity equation is derived by relating the feature vector and a matrix derived from the filtered residual output of the observer and the filtered system reference input. Exploiting the multilinear relationship governing the feature vector and the physical parameters, the FDI scheme is obtained. Using the statistical multiple hypothesis testing technique, the FDI scheme is reduced to the problem of geometric alignment. The angle between the transformed feature vector and each of the transformed influence vectors is computed, and the influence vector which is maximally aligned points to the faulty functional unit.