Fault detection using marginalized likelihood ratio and uniform priors: Justifications and challenges

The marginalized likelihood ratio (MLR) approach to fault detection as proposed by Gustafsson [2] is based on the assumption of improper flat priors with infinite support for fault magnitude. This assumption leads to the problem that the likelihood function cannot be uniquely defined after the occurrence of the fault. In another approach by Dos Santos and Yoneyama [9] the prior is assumed to follow a Gamma distribution which is hard to justify as this selection of prior penalizes low and high magnitude faults. However, with presence of safety shutdown systems as well as range constraints on sensors and actuators, all process variables are generally bounded and this motivates one to investigate the possibility of using uniform priors for fault magnitudes. This study aims to undertake this task and attempts to discuss the justification and the challenges associated with selection of such priors. The outcome of this analysis is a new fault detection and isolation (FDI) scheme that takes advantage of the modified MLR (MMLR) test to accurately estimate the time of the occurrence of the fault. The proposed FDI uses the MMLR as the detector of time of occurrence of the fault and the generalized likelihood ratio (GLR) test for the purpose of isolation of the fault and estimation of its magnitude.