Bayesian Sensor Fault Detection in a Markov Jump System
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© 2017 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd.In this paper, the fault detection of a latent fault in a sensor for a Markov jump system is studied. It is equivalent to detecting a change point in a coefficient vector of a measurement equation in the state space representation of a system. Indeed, the fault detection procedure is evaluated as detecting this change point and the time that the change point has occurred. To this end, first, the recursive least square (RLS) filter is proposed and under Yao's Prior setting, the Bayesian fault detection algorithm is proposed. The Smith-Gelfand re-sampling method is applied to approximate the posterior distribution. The performance of the Bayesian method is studied under the null and alternative hypotheses. The delay in diagnosis of the fault is measured. To study the effect of the fault time point in the performance of the Bayesian method, the sensitivity analysis is studied. The probability of the fault is studied and the Martingale approach is used to obtain the lower and upper bounds for this probability. The fault detection in integrated systems is studied and a Kalman filter, as a parallel filter, is considered to estimate the state and the effect of the unknown coefficient jump on state estimation is also studied.
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