Temporal Logic Inference for Fault Detection of Switched Systems With Gaussian Process Dynamics

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.

Automated summary

This article presents a method for constructing a fault detector using signal temporal logic (STL) formulas for a class of switched nonlinear systems with partially unknown dynamics. The method utilizes a Gaussian process for approximating unknown internal dynamics, and a temporal logic inference algorithm for finding the fault detector with stability guarantees. Simulation results demonstrate that the proposed method can detect faulty trajectories with a probability guarantee.