Auxiliary Signal Design for Active Fault Detection Based on Set-membership★

In this paper, a new active fault detection method based on set-membership is proposed. Similar to the existing methods, the normal and faulty modes of the system are assumed to be two linear discrete time-invariant systems with bounded energy uncertainty, which is represented by a bounded ellipsoid under the framework of set-membership. Then the minimal energy auxiliary signal is derived in the case with worst cases of uncertainties by adopting a geometric method, such that desired fault detection performance can be guaranteed. Note that with comparison to the existing methods, the proposed method has a clear physical meaning and the set-membership technique makes it more feasible to calculate the fault detection rates relative to different choices of auxiliary signals with smaller energy. Hence the energy of auxiliary signal can be determined by a trade off between the fault detection rate and the impact on normal operation of the system. Simulation results are provided to show the effectiveness of the proposed method.