Sensor fault detection and isolation: a game theoretic approach

ABSTRACT

This paper studies sensor fault detection using a game theoretic approach. Sensor fault detection is considered as change point analysis in the coefficients of a regression model. A new method for detecting faults, referred to as two-way fault detection, is introduced which defines a game between two players, i.e. the fault detectors. In this new strategic environment, assuming that the independent states of the regression model are known, the test statistics are derived and their finite sample distributions under the null hypothesis of no change are derived. These test statistics are useful for testing the fault existence, as well as, the pure and mixed Nash equilibriums are derived for at-most-one-change and epidemic change models. A differential game is also proposed and solved using the Pontryagin maximum principle. This solution is useful for studying the fault detection problem in unknown state cases. Kalman filter and linear matrix inequality methods are used in finding the Nash equilibrium for the case of unknown states. Illustrative examples are presented to show the existence of the Nash equilibriums. Also, the proposed fault detection scheme is numerically evaluated via its application on a practical system and its performance is compared with the cumulative sum method.

Keywords:

• AMOC
• differential game
• epidemic model
• Kalman filtering
• LMI
• Nash equilibrium
• Pontryagin maximum principle
• two-way fault detection

Acknowledgements

The authors would like to thank the editors and the reviewers for their helpful comments and constructive suggestions, which helped to improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hamed Habibi http://orcid.org/0000-0002-7393-6235

Additional information

Notes on contributors

Hamed Habibi

Hamed Habibi received the B.Sc. degree from Khaje Nasir University, Tehran, Iran, in 2010, and the M.Sc. degree from the University of Tehran, Tehran, in 2013, all in mechanical engineering. He is currently pursuing the Ph.D. degree with Curtin University, Perth, Australia. His current research interests include control systems, fault detection, isolation, identification, accommodation, and fault tolerant control with applications on wind turbines.

Ian Howard

Ian Howard received the bachelor’s and Ph.D. degrees in mechanical engineering from The University of Western Australia in 1984 and 1988, respectively. He was with the Defense Science and Technology Organization for five years. In 1994, he joined Curtin University as a Lecturer in applied mechanics and dynamic systems, where he was promoted to Full Professor in 2016 and continues to supervise research in the dynamic behavior of rotating machinery for fault detection and classification for industry applications.

Reza Habibi

Reza Habibi has a PhD in Statistics from the Department of Statistics at Shiraz University, Shiraz, Iran. In 2005 he was a visiting researcher in the Department of Mathematics at the University of Ottawa. He has worked on change point analysis in infinite variance observations, Computational Statistics, Stochastic Differential Equations, Game Theory, Data Mining, Financial Mathematics. He has published 67 papers and has written five English books. He was a free researcher in the Department of Statistics at the Central Bank of Iran (CBI). He is currently a lecturer at the Iran Banking Institute of the CBI. He recently graduated in Financial Engineering from Amirkabir University, Tehran, Iran. His research interests include arbitrage pricing, algorithmic trading, applications of heuristic and computational methods in finance, and portfolio management.