Evaluation of Fault Diagnosability for Dynamic Systems With Unknown Uncertainties

In this paper, the quantitative fault diagnosability problem for a stochastic dynamic system subjects to unknown uncertainties is proposed. Reliable isolability, reliable detectability, and reliable distinguishability are newly defined for the studied uncertain system. By considering model uncertainties, norm-bounded disturbances, and noises, the quantitative diagnosability problem is originally transferred to an optimization problem. A novel methodology is proposed to quantify the fault diagnosability based on a new sliding window model, which greatly alleviates the computation task. To quantify the disturbance effect on the diagnosability performance, disturbance ratio is defined. Furthermore, the reliable isolability conditions for a fault vector with a specific fault time profile is theoretically analyzed. Effectiveness of the proposed method is verified by a numerical example.