Fault Detection in Linear Dynamic Systems by a Functional Vector Space Method

Abstract

The author previously proposed a functional subspace method in the framework of the generalized-likelihood-ratio (GLR) technique for fault detection in linear discrete dynamic systems. This method detects the fault by estimating the unknown anomaly function in the system as a linear combination of adequate basis functions. Since it is important to decrease the number of the basis functions to raise the detectability, system informations (signals), such as the state and the input of the system, are utilized to construct the basis functions.
To construct specifically effective basis functions, a unified approach based on a sensitivity analysis is taken ; that is, based on a sensitivity analysis in innovation sequence, optimal time-variant aggregation vectors are first sought for each system information, and then the linearly-independence and the magnitudes of the resultant basis functions are taken into account.
Finally, the robustness of the proposed method to some system uncertainties is mentioned.