Sensor fault detection and isolation: a game theoretic approach

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.