The Use of Posterior Knowledge in Statistical Pattern Recognition with Particular Application to Fault Diagnosis

This paper considers the problem of posterior knowledge inclusion into fault diagnosis systems. The problem is framed in the context of set theory and elementary probability theory. A methodology of posterior probability updating is proposed for cases where fault conditions are rejected on the basis of external knowledge. Cases of exclusive, conditionally independent and dependent faults classes are considered. A possible fault hierarchy is generated following the estimation of fault class probability functions. It is shown that a simple renormalisation of existing probabilities does not apply in the dependent class case and can lead to erroneous results: the fault hierarchy may change following the exclusion of fault classes known not to have occurred.A radial basis function network with second-order regularisation is proposed as a solution to the underlying probability function estimation problem.