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• A novel hybrid prognostic method for remaining useful life prediction is presented. • A new nonlinear health indicator is generated for the training bearings. • The condition monitoring interval of health state is determined by the 3σ criterion. • The degradation and RUL forecasting is achieved based on the nonlinear Wiener process with random effects method. This paper proposes a novel hybrid method aiming at the fault prognosis of bearings. A nonlinear health indicator (HI) is first constructed using Complete Ensemble Empirical Mode Decomposition with Adaptive Noise and Kernel Principal Component Analysis to reflect the health state of a bearing accurately and convincingly. Subsequently, multi-domain features are extracted from vibration signals and the Dual-Channel Transformer Network with the Convolutional Block Attention Module is applied for constructing HIs of the rest bearings. Moreover, the 3σ criterion is employed to establish the condition monitoring interval of health state and detect the First Prediction Time, with which degradation modeling and probabilistic Remaining Useful Life (RUL) prediction are conducted with the assistance of nonlinear Wiener process with random effects. The superior performance of the proposed hybrid prognostic method confirms that the method contributes to the accurate RUL prediction and uncertainty quantification. [ABSTRACT FROM AUTHOR]