Bayesian estimator of a faulty state: Logarithmic odds approach

Fault detection and isolation is crucial for efficient operation and safety of any industrial process. Methods from all the areas of data analysis are being used for this task including Bayesian reasoning and Kalman filtering. In this paper authors use the discrete Field Kalman Filter for detecting and recognising faulty conditions of the system. Proposed approach, devised for stochastic linear systems allows analysis of faults that can be expressed both as parameter and disturbance variations. It is formulated for the situations when the fault catalogue is known, but because of that very efficient algorithm can be obtained. For implementation logarithmic odds are considered to improve numerical properties. Its operation is illustrated with numerical examples and both its merits and limitations are critically discussed.