A　modelling　method　is　proposed　and　applied　in　fault　detection　for　non-linear　dynamic　systems　with　bounded　noises.　Since　the　radial　basis　function　(RBF)　neural　network　is　a　universal　approximator,　it　is　used　to　model　the　non-linear　system　when　the　system　runs　without　a　fault.　After　some　input　and　output　data　of　the　system　are　obtained,　the　centres　of　the　hidden　nodes　are　chosen　using　clustering　technology.　Assuming　that　the　system　noise　and　approximation　error　are　unknown　but　bounded,　the　output　weights　of　RBF　neural　network　model　of　the　system　are　determined　by　a　linear-in-parameter　set　membership　estimation　algorithm.　An　interval　containing　the　actual　output　of　the　system　running　without　a　fault　can　be　easily　predicted　based　on　the　result　of　the　estimation.　If　the　measured　output　is　out　of　the　predicted　interval,　it　can　be　determined　that　a　fault　has　occurred.　Simulation　results　show　the　effectiveness　of　the　proposed　method.　Copyright　©　2013　Inderscience　Enterprises　Ltd.