Minimum entropy fault detection for dynamic multivariate nonlinear non-Gaussian stochastic systems

In this paper, fault detection is further investigated for uncertain multivariate nonlinear non-Gaussian stochastic systems. Entropy is introduced to characterize the stochastic behavior of the detection errors, and entropy optimization principle is established for the fault detection problem. The principle is to maximize the entropies of the stochastic detection errors in the presence of the faults, and to minimize the entropies of the detection errors in the presence of the disturbances. In order to calculate the entropies, the formulations of the joint probability density functions (JPDFs) of the stochastic errors are presented in terms of the known JPDFs of both the disturbances and the faults. By using the performance indexes and the formulations for the entropies of the detection errors, new fault detection design methods are provided for the considered multivariate nonlinear non-Gaussian plants.