A Probabilistic Approach to Robust Fault Detection for a Class of Nonlinear Systems

This paper presents a probabilistic approach to fault detection (FD) for nonlinear systems subject to l2[0, N]-norm bounded unknown input. The major contribution is to design an evaluation function for robust FD in a unified framework of l2-norm estimation of unknown input and determine a threshold based on probabilistic analysis of FD performance. The problem of robust FD is first formulated as to find a minimal estimation of the l2[0, N]-norm of unknown input including unknown initial state. It is shown that such an estimation leads to a unified design of evaluation function for FD using extended Kalman filter or Hi/H∞optimization-based FD filter. Based on this, a probabilistic approach to threshold determination and FD performance verification is proposed. In particular, if the l2[0, N]-norm boundedness of unknown input is not available, a choice of threshold can be made in the framework of probabilistic analysis for achieving a tradeoff between false alarm rate and FD rate. Finally, a nonlinear UAV control system model is given to demonstrate the effectiveness of the proposed method and show the feasibility of practical application.