Generalized least-squares fault detection filter

Abstract

A fault detection and identification algorithm is determined from a generalization of the least-squares derivation of the Kalman filter. The objective of the filter is to monitor a single fault called the target fault and block other faults which are called nuisance faults. The filter is derived from solving a min-max problem with a generalized least-squares cost criterion which explicitly makes the residual sensitive to the target fault, but insensitive to the nuisance faults. It is shown that this filter approximates the properties of the classical fault detection filter such that in the limit where the weighting on the nuisance faults is zero, the generalized least-squares fault detection filter becomes equivalent to the unknown input observer where there exists a reduced-order filter. Filter designs can be obtained for both linear time-invariant and time-varying systems.