Entropy optimization filtering for fault isolation of non-gaussian systems

In this paper, the fault isolation (FI) problem is investigated for nonlinear non-Gaussian dynamic systems with multiple faults (or abrupt changes of system parameters) in the presence of noises. By constructing a filter to estimate the states, the FI problem can be reduced to an entropy optimization problem subjected to the non-Gaussian estimation error systems. The design objective for the FI purpose is that the entropy of the estimator error is maximized in the presence of the diagnosed fault and is minimized in the presence of the nuisance faults or noises. It is shown that the error dynamics is represented by a nonlinear non-Gaussian stochastic system, for which new relationships are applied to formulate the PDFs of the stochastic error in terms of PDFs of the noises and faults. The Renyi's entropy has been used to simplify the computations in the filtering for the recursive design algorithms. It is noted that the output can be supposed to be immeasurable (but with known stochastic distributions), which is different from the existing results where the output is always measurable for feedback.