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Fault detection for non-linear non-Gaussian stochastic systems using entropy optimization principle

In this paper, a fault detection (FD) problem is studied for non-linear dynamic stochastic systems with non-Gaussian disturbances and faults (or abrupt changes of system parameters). After a filter is constructed to generate the detected error, the FD problem is reduced to an optimization problem for the error system, which is represented by a non-linear non-Gaussian stochastic system. Since generally (extended) Kalmen filtering approaches are insufficient to characterize the non-Gaussian variables, we propose the entropy optimization principle for the stochastic error system. The design objective is to maximize the entropies of the stochastic detection errors when the faults occur, and to minimize the entropies of the stochastic estimator errors resulting from the other stochastic noises. Following the formulation of the probability density functions of the stochastic error in terms of those of both the disturbances and the faults, new recursive approaches are established to calculate the entropies of the detection errors. By using the novel performance index and the formulations for the entropies, the real-time optimal FD filter design method is provided. Finally, simulations are given to demonstrate the effectiveness of the proposed FD filtering algorithms.