A Distributionally Robust Data-Driven Approach to Active Fault Detection for Stochastic Dynamic Systems

Practically inaccessible precise probability distribution for disturbance poses significant challenges to stochastic active fault detection (AFD) in achieving satisfactory detection accuracy. In this paper, without making specific distribution assumption on disturbance, a distributionally robust data-driven approach is proposed to AFD for stochastic linear dynamic systems. On the basis of constructing a data-driven stable kernel representation-based residual generator, the distributional uncertainty of disturbance is characterized by the mean-covariance-based ambiguity set of residual both for the fault-free and faulty cases. To minimize the energy of input while guarantee tolerable false alarm rate (FAR) and missed detection rate (MDR), the design of AFD system is formulated as an optimization problem subject to distributionally robust chance constraints (DRCCs). By bridging the DRCCs with deterministic constraints in the probabilistic context, the targeting optimization problem is then converted into a generalized eigenvalue-eigenvector problem, by solving which analytical solutions of the input and separating hyperplane for online detection are derived. Hence, the developed AFD system can not only ensure the FAR and MDR criteria not exceeding predefined levels, but also improve the robustness of the system against distributional uncertainties of disturbance. Besides, a batch-wise realization algorithm is developed for continuous online fault detection. A simulation study based on a four-tank system is demonstrated to validate the effectiveness of the proposed approach.