Optimal Threshold Functions for Fault Detection and Isolation

Fault diagnosis systems usually comprises two parts: a filtering part and a decision part, the latter typically based on threshold functions. In this paper, systematic ways to choose the threshold values are proposed. Two different test functions for the filtered signals are discussed and a method is described for determining the optimal threshold value for these test functions in order to detect presence or absence of a certain fault in the filtered signal. Optimal is in this context taken to mean minimizing the larger of the probalilities for making a false positive decision and for making a false negative decision, which is equivalent to balancing these two probabilities.