Model-Based Fault Diagnosis System Verification Using Reachability Analysis

In model-based fault detection and isolation (FDI) systems, fault indicating signals (FISs) such as residuals and fault estimates are corrupted by various noises, uncertainties and variations. It becomes challenging to verify whether an FDI system still works or not in real life applications. It is also challenging to select a threshold so that false alarm rate and missed detection rate are kept low depending on real operation conditions. This paper proposes solutions to the aforementioned problems by quantitatively analyzing the effect of uncertainties on FIS. The problems are formulated into reachability analysis problem for uncertain systems. The reachable sets of FIS are calculated under normal and selected faulty cases, respectively. From these reachable sets, the effectiveness of an FDI system can be qualitatively verified under described uncertainties. A dedicated threshold can be further chosen to be robust to all possible described uncertainties. As a by-product, the minimum detectable fault can also be quantitatively determined by checking the intersection of the computed reachable sets. The proposed approach is demonstrated by evaluating an FDI algorithm of a motor in the presence of parameter uncertainties, unknown load, and sensor noises, where a fault estimation-based approach is adopted to diagnose amplifier, velocity, and current sensor faults.