Optimal auxiliary input design for fault detection based on Kullback divergence

Introduction of an auxiliary input may be useful to detect the system fault quickly without affecting the original system behavior in normal mode. Such an auxiliary input is designed to enlarge the distance between the system models corresponding to the normal and fault modes. The distance can be measured by the Kullback divergence. In this paper, the optimal auxiliary input design for fault detection is derived based on ´one-step-at-a-time´ maximization of the time increment of the Kullback divergence under the assumption that the system models corresponding to normal and fault modes are known exactly to the designers. However, the system models are, in some cases, hardly known without uncertainties in practice. Hence, this paper also deals with the optimal auxiliary input design for fault detection in the case of the models with uncertainties. Numerical simulation results indicate that the proposed auxiliary input in fault detection using the CUSUM test reduces the mean detection time without making much effect on original system behavior and false alarm rate.