Abstract
Generalized-likelihood-ratio (GLR) method is well-known for its most rapid failure detection speed. But, in its use, it has a drawback such that we must assume a priori several hypotheses which are likely to happen. Step one has been often used for its convenience for the case where an anomalous function adds to the dynamics or sensor equation when anomaly occurs.
In this paper, we first discuss the detectability of such a failure in linear discrete dynamical systems by the step-hypothesized GLR method by introducing the discriminating measure “divergence” and show that if the system is observable and the anomalous function has a bias in some sense, the anomaly or failure is in principle detectable.
It is also shown that if the bias is included in a weakly-diagnosable-space (WDS), the probability of missed alarm cannot be made smaller than a certain value, even if many observation data are used. In order to overcome the problem, we next develop a weighted step-hypothesized GLR method which gives a large weight on the GLR for the bias component in the direction of WDS, and enables the detection rate to raise totally.
