Asymptotic behavior of a fault diagnosis performance measure for linear systems

Abstract

Fault detection and fault isolation performance of a model based diagnosis system mainly depends on the level of model uncertainty and the time allowed for detection. The longer time for detection that can be accepted, the more certain detection can be achieved and the main objective of this paper is to show how the window length relates to a diagnosis performance measure. A key result is an explicit expression for asymptotic performance with respect to window length and it is shown that there exists a linear asymptote as the window length tends to infinity. The gradient of the asymptote is a system property that can be used in the evaluation of diagnosis performance when designing a system. A key property of the approach is that the model of the system is analyzed directly, which makes the approach independent of detection filter design.