Abstract
Recently, an approach for the rapid detection of small oscillation faults based on deterministic learning theory was proposed for continuous-time systems. In this paper, a fault detection scheme is proposed for a class of nonlinear discrete-time systems via deterministic learning. By using a discrete-time extension of deterministic learning algorithm, the general fault functions (i.e., the internal dynamics) underlying normal and fault modes of nonlinear discrete-time systems are locally-accurately approximated by discrete-time dynamical radial basis function (RBF) networks. Then, a bank of estimators with the obtained knowledge of system dynamics embedded is constructed, and a set of residuals are obtained and used to measure the differences between the dynamics of the monitored system and the dynamics of the trained systems. A fault detection decision scheme is presented according to the smallest residual principle, i.e., the occurrence of a fault can be detected in a discrete-time setting by comparing the magnitude of residuals. The fault detectability analysis is carried out and the upper bound of detection time is derived. A simulation example is given to illustrate the effectiveness of the proposed scheme.
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This work was supported by the National Science Fund for Distinguished Young Scholars (No. 61225014), the National Major Scientific Instruments Development Project (No. 61527811), the National Natural Science Foundation of China (Nos. 61304084, 61374119), the Guangdong Natural Science Foundation (No. 2014A030312005), and the Space Intelligent Control Key Laboratory of Science and Technology for National Defense.
Junmin HU is a Ph.D. candidate at the Center for Control and Optimization, School of Automation Science and Engineering, South China University of Technology. Her research interest covers adaptive NN control/identification, deterministic learning theory and oscillation fault diagnosis.
Cong WANG received the B.E. and M.E. degrees from Beijing University of Aeronautic & Astronautics in 1989 and 1997, respectively, and the Ph.D. degree from the Department of Electrical&Computer Engineering, The National University of Singapore in 2002. From 2001 to 2004, he did his postdoctoral research at the Department of Electronic Engineering, City University of Hong Kong. He has been with the School of Automation Science and Engineering, South China University of Technology, Guangzhou, China, since 2004, where he is currently a professor. He has authored and co-authored over 60 international journal and conference papers and the book Deterministic Learning Theory for Identification, Recognition and Control. He serves as an Associate Editor of the IEEE Transactions on Neural Networks and Learning Systems since 2012, and as an Associate Editor for Control Theory and Technology, and ACTA AUTOMATICA SINICA (two best journals in systems and control area in China) since 2008 and 2011, respectively. He is a member of the Technical Committee on Intelligent Control of the IEEE CSS. His research interest includes intelligent control, neural networks, nonlinear systems and control, dynamical pattern recognition, pattern-based control, dynamical systems, and oscillation fault diagnosis.
Xunde DONG is a Ph.D. candidate at the Center for Control and Optimization, School of Automation Science and Engineering, South China University of Technology. His research interest covers adaptive NN control/identification, deterministic learning theory and distributed parameter system.
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Hu, J., Wang, C. & Dong, X. Fault detection for nonlinear discrete-time systems via deterministic learning. Control Theory Technol. 14, 159–175 (2016). https://doi.org/10.1007/s11768-016-4140-z
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DOI: https://doi.org/10.1007/s11768-016-4140-z