A Probabilistic Projection Approach to Data-Driven Dynamic Fault Detection⋆

Abstract

In this work, a probabilistic projection approach is proposed to data-driven fault detection (FD) for stochastic dynamic systems. To this end, a stable kernel representation based residual generator is first constructed with main attention to the design of a projection matrix based on system input and output data in kernel space. Concerning the practically inaccessible probability distribution for stochastic disturbance and limited priori knowledge of fault, a distributionally robust optimal FD problem is formulated in the sense of maximizing the fault detectability for an acceptable upper bound of false alarm rate, wherein the distributional profile of stochastic disturbance is characterized by a mean-covariance based ambiguity set. By means of worst-case conditional value-at-risk and singular value decomposition, an analytical solution to the targeting FD problem is derived in the probabilistic context, that achieves the best fault detectability in worst-case setting. Simultaneously, the robustness of the designed FD system against distributional uncertainties can be guaranteed. A simulation study is finally illustrated to show the applicability of the proposed method.