Fault detection in linear systems via interval parity relations

The problem of fault detection via interval parity relations designed for systems described by linear models under the external disturbances and measurement noise is considered. To solve the problem, the reduced-order model of minimal dimension insensitive or having minimal sensitivity to the external disturbances is used. Based on this model, the interval parity relations are designed. The relations that allow to construct two residuals are obtained and theorem showing that zero is between these residuals for healthy system is proved. Theoretical results are illustrated by example.