Robustness of model-based fault diagnosis: Decisions with information-gap models of uncertainty

Abstract

Fault diagnosis is analysed here as a decision between alternative hypotheses, based on uncertain evidence. W e consider severe lack of information, and perceive the uncertainty as an information gap between what is known, and what needs to be known for a perfect decision. This uncertainty is quantified with info-gap models of uncertainty, which require less information than probabilistic models. Previous work with convex set-models is extended to linear info-gap models which are not necessarily convex, as well as to more general info-gap models with arbitrary expansion properties. We define a decision algorithm based on info-gap models and prove three theorems, one establishing the connection with the earlier work on convex models, the other two showing that the algorithm is maximally robust for linear info-gap models as well as for general infogap models of uncertainty. An illustrative example is presented which shows how these results can be used for optimizing the design of a model-based fault diagnosis algorithm.