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 $l{2}[0,N]$-norm bounded unknown input. The major contribution is to design an evaluation function for robust FD in a unified framework of $l-{2}$-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 $l-{2}[0,N]$-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 $H-{i}/H-{\infty }$ optimization-based FD filter. Based on this, a probabilistic approach to threshold determination and FD performance verification is proposed. In particular, if the $l-{2}[0,N]$-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.