In this paper, the robust fault detection problem for non-linear systems considering both bounded parametric modelling errors and measurement noises is addressed. The non-linear system is monitored by using a state estimator with bounded modelling uncertainty and bounded process and measurement noises. Additionally, time-variant and time-invariant system models are taken into account. Fault detection is formulated as a set-membership state estimation problem, which is implemented by means of constraint satisfaction techniques. Two solutions are presented: the first one solves the general case while the second solves the time-variant case, being this latter a relaxed solution of the first one. The performance of the time-variant approach is tested in two applications: the well-known quadruple-tank benchmark and the dynamic model of a representative portion of the Barcelona's sewer network. In both applications, different scenarios are presented: a faultless situation and some faulty situations. All considered scenarios are intended to show the effectiveness of the presented approach.

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