Fault detection for NARMAX stochastic systems using entropy optimization principle

In this paper, the fault detection (FD) problem is studied for a class of NARMAX models with non-Gaussian disturbances and faults, as well as a time delay. Since generally (extended) Kalman filtering approaches are insufficient to characterize the non-Gaussian variables, entropy is adopted to describe the uncertainty of the error system. After a filter is constructed to generate the detected error, the FD problem is reduced to an entropy optimization problem. 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 estimation errors resulting from other stochastic noises. To improve the FD performance, a multi-step-ahead predictive nonlinear cumulative cost function is adopted rather than the instantaneous performance index. Following the formulation of the probability density function of the stochastic error in terms of those of both of the disturbances and the faults via a constructed mapping, new recursive approaches are established to calculate the entropies of the detection errors. Renyi's entropy has also been used to simplify the cost function. Finally, simulations are given to demonstrate the effectiveness of the proposed control algorithm.