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In this paper, the fault isolation (FI) problem is investigated for nonlinear non-Gaussian 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 estimation error is maximized in the presence of 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 probability density functions (PDFs) of the stochastic error in terms of the PDFs of the noises and the 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. Finally, simulations are given to demonstrate the effectiveness of the proposed data-driven FI filtering algorithms.