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The problem of residual evaluation for fault detection in nonlinear systems is addressed in this article. Using the factorisation approach, a post-filter is designed and a threshold is computed to achieve an optimal trade-off between fault detectability and the number of false alarms. Furthermore, it is shown that the proposed post-filter also guarantees ℋ₋/ℋ_∞ multi-objective optimisation of the residual signal. The effectiveness of the proposed method is demonstrated by fault detection of the three-tank benchmark system.