Using the Kalman Filtering for the Fault Detection and Isolation (FDI) in the Nonlinear Dynamic Processes

This paper presents a Fault Detection and Isolation (FDI) method for stochastic nonlinear dynamic systems. First, the developed fault detection method is based on statistical information generated by the extended Kalman filter (EKF) and is intended to reveal any drift from the normal behaviour of the process. A fault of a chemical origin in a perfectly stirred batch chemical reactor, occurring at an unknown instant, is simulated. The purpose is to detect the presence of this abrupt change, and pinpoint the moment it occurred. It is also shown that the convergence of the EKF is accomplished more or less rapidly according to the nature of the noise generated by the measurement sensors. The state estimate is observed and discussed, as well as the time delay in detection according to the decision threshold. Then, this study shows another method of tackling the problem of the physical origin diagnosis of faults by combining the technique based on the standardized innovations and the technique using the multiple extended Kalman filters for a strongly non-stationary nonlinear dynamic system. The usefulness of this combination is the implementation of all the fault dynamics models if the decision threshold on the standardized innovation exceeds a determined threshold. In the other case, one EKF is enough to estimate all the process state. An algorithm is described and applied to a perfectly stirred chemical reactor operating in a semi-batch mode. The chemical reaction used is an exothermic second order one.