A projection-based method of fault detection for linear discrete time-varying systems

Abstract

This article is aimed at the development of a residual generator by making use of an arbitrary linear combination of measurement output estimation error sequence. First, Gramian matrix-based criteria are proposed to measure the influences of an unknown input and a fault on the residual. Then, the design of the residual generator is formulated into a sensitivity/robustness ratio maximisation problem. It is shown that the optimal solution is not unique and one of them can be derived by directly applying an orthogonal projection of the measurement output and, with the aid of an innovation analysis, a more generalised residual generator is also obtained. Furthermore, it is demonstrated that the obtained residual generators in state space description also provide optimal observer-based fault detection filters for the linear discrete time-varying systems subject to l ₂-norm bounded unknown inputs or stochastic noise sequences. To show the effectiveness of the proposed method, a numerical example is given.

Keywords:

• fault detection
• residual
• Gramian matrix
• projection
• linear discrete time-varying system

Acknowledgements

This work was supported in part by the NSFC No. 61174121 and No. 61121003, the National 863 Program No. 2008AA121302 and the 973 Program No. 2009CB724000. The authors would like to thank professor John Zarnecki from the Open University, UK, for his help with the Language in this paper.