LAUSR

In this article, we present a method for constructing the fault detector in the form of signal temporal logic (STL) formulas, which can be understood by human users and formally proven to detect faults with probabilistic satisfaction guarantees, for a class of switched nonlinear systems with partially unknown dynamics. First, the partially unknown internal dynamics are approximated by the Gaussian process with stability guarantees. Second, a novel temporal logic inference algorithm is proposed to find the fault detector, which takes advantage of the internal properties of temporal logic and searches for the optimal formula along a partially ordered direction. Moreover, the algorithm is not allowed for missing faults but allowed for false alarms during the temporal logic inference process. In addition, we simulate finitely many trajectories with Chua’s circuit and infer the temporal logic formulas with the Gaussian optimization. The results show that the proposed method can find a temporal logic formula to detect the faulty trajectory with a probability guarantee. Note to Practitioners—The method proposed in this article can be used to detect faults for switched systems with partially unknown dynamics. STL is used to describe the behaviors of the system, which acts as a classifier and detector, such that all normal behaviors of the system will satisfy the description, while the faulty behaviors will violate the description. Moreover, STL formulas can be understood by human operators, which is important for the timely response to faulty events. For example, the normal behavior of a smart grid can be described as follows: “if the smart grid is safe, it should reach 9 kV within 15 min when the voltage to region A is above 12 kV,” which can be expressed with STL. Due to the unknown dynamics, the Gaussian process regression is applied to estimate the model and the region that is robust to noises.