Fault Detectability and Isolability Conditions in the Frequency Domain

In this paper, a fault is defined to be a change in the plant parameter vector which subsequently alters the frequency response of the plant. In this context, fault detection refers to the ability to identify when a change in the frequency response has occurred while fault isolation refers to the identification of the plant parameter which has changed. Both these are achieved without the specific identification of the parameter vector. Instead, fault detection and isolation (FDI) are achieved by the construction of a residual vector based on the estimated frequency response. Since this approach is closely related to frequency response identifiability, the relationship between identifiability, detectability and isolability are derived in this paper. The conditions of detectability and isolability are proposed in terms of the residual vector. Some simulations studies are presented to illustrate the results