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

• Published in: IEEE transactions on industrial electronics (1982) Vol. 64; no. 5; pp. 3930 - 3939
• Main Authors: Maiying Zhong, Ligang Zhang, Ding, Steven X., Donghua Zhou
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Alarm systems; Design analysis; Estimation; Evaluation function; Extended Kalman filter; Fault detection; fault detection (FD); Hafnium; Kalman filters; Nonlinear control; nonlinear system; Nonlinear systems; Optimization; Probabilistic analysis; Probabilistic logic; probabilistic verification; Robustness; threshold; Unmanned aerial vehicles
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2016.2637308

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 ∞ 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.