Abstract in English:

In this paper, a method of distributionally robust fault detection (FD) is proposed for stochastic linear discrete-time systems by using the kernel density estimation (KDE) technique. For this purpose, an H₂optimization-based fault detection filter is constructed for residual generation. Towards maximizing the fault detection rate (FDR) for a prescribed false alarm rate (FAR), the residual evaluation issue regarding the design of residual evaluation function and threshold is formulated as a distributionally robust optimization problem, wherein the so-called confidence sets are constituted to model the ambiguity of distribution knowledge of residuals in fault-free and faulty cases. A KDE based solution, robust to the estimation errors in probability distribution of residual caused by the finite number of samples, is further developed to address the targeting problem such that the residual evaluation function, threshold as well as the lower bound of FDR can be achieved simultaneously. A case study on a vehicle lateral control system demonstrates the applicability of the proposed FD method.