Active fault diagnosis under hybrid bounded and Gaussian uncertainties

Abstract

In this paper, an active fault diagnosis method is proposed to diagnose faults of linear time-invariant systems under the effect of hybrid bounded and Gaussian uncertainties, which can guarantee an arbitrary confidence level of fault diagnosis. Zonotopes are used to characterize bounded uncertainties. Gaussian uncertainties are handled as ellipsoids by the given confidence coefficient. The confidence domains of output are formulated as the Minkowski sum of a zonotope and an ellipsoid. The fault diagnosis task is done based on the separation of all the confidence domains of different fault situations, which leads to a Mathematical Program with Complementarity Constraints (MPCC). A branch-and-bound method and a smoothing method are provided to solve the program. The effectiveness of the proposed active fault diagnosis method is illustrated by two examples at the end of the paper.