Computation of Minimal Detectable Fault under Hybrid Stochastic and Deterministic Framework

This paper proposes a confidence set-based computational method of minimal detectable fault (MDF) based on the confidence set-separation condition between the healthy and faulty residual sets for discrete linear time-invariant system. The state-estimation-error dynamics for the analysis of MDF under hybrid random and bounded uncertainties is divided into two sub-dynamics. The first sub-dynamics is only affected by the bounded uncertainties. While the second sub-dynamics is only affected by the random uncertainties following the Gaussian distributions. The MDF for actuator and sensor can be obtained by solving a non-convex optimization problem to minimize the magnitude of fault subjected to the separation constraints on the healthy and faulty confidence residual sets, which is shown to be equivalent to compute a distance from the origin to hyperplane along a fixed direction. At the end of this paper, a two-link robotic manipulator model is used to verify the effectiveness of our proposed method.