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This paper proposes a new passive robust fault detection scheme using non-linear models that include parameter uncertainty. The non-linear model considered here is described by a group method of data handling (GMDH) neural network. The problem of passive robust fault detection using models including parameter uncertainty has been mainly addressed by checking if the measured behaviour is inside the region of possible behaviours based on the so-called forward test since it bounds the direct image of an interval function. The main contribution of this paper is to propose a new backward test, based on the inverse image of an interval function, that allows checking if there exists a parameter in the uncertain parameter set that is consistent with the measured system behaviour. This test is implemented using interval constraint satisfaction algorithms which can perform efficiently in deciding if the measured system state is consistent with the GMDH model and its associated uncertainty. Finally, this approach is tested on the servoactuator being a FDI benchmark in the European Project DAMADICS. [Copyright &y& Elsevier]