This paper proposes a methodology for incipient fault diagnosis and the corresponding trend prediction in nonlinear closed-loop systems considering stochastic Gaussian and non-Gaussian uncertainties. The proposed approach is based on the use of the particle filtering technique for estimating the system states and outputs. From these estimations, the residual signals would be generated through a mathematical filtering and augmentation technique, allowing the incipient fault estimation that is evaluated using the designed fixed and adaptive thresholds that consider system uncertainties. In this way, the fault detection performance is improved but also the false detection and false alarm problems are comprehensively addressed. Moreover, the augmented Gauss–Newton identification method is used for the incipient fault trend prediction. Finally, to evaluate the effectiveness of the proposed approach, the incipient fault diagnosis in the heat transfer unit built in the nonlinear closed-loop continuous stirred-tank reactor (CSTR) system is used. Besides, the confusion matrix is employed to assess the results from a quantitative point of view.