Robust application of Beard-Jones detection filter

Abstract

The problem of BJDF is in fact equivalent to finding a post compensator that diagonalizes the transfer function matrix between the failure events and the corresponding flag coefficient set. Consequently, the FDI task via BJDF becomes a sensitive process to the parameter variations in the dynamic systems. This fact is well recognized in the control problem of output decoupling, which is the dual problem to BJDF.

In the past, the lack of robustness has been the principal cause that prevented the widespread applications of BJDF. Hence in this paper, a strong emphasis was placed on developing design procedures for the cases of uncertain systems. As a result, solutions for the optimal reference model, the optimal detection operator, and the optimal basis set for the hypothesis isolation were derived in section 3, where each of the solution was presented in a closed form.