Gear has been widely used in the modern industry, and the gear reliability is important to the driving system, which makes the residual fatigue life prediction for a gear crucial. In order to realize the residual fatigue life of the gear accurately, a hybrid approach based on the Paris law and particle filter is proposed in this paper. The Paris law is usually applied to predict the residual fatigue life, and accurate model parameters allow a more realistic prediction. Therefore, a particle filtering model is utilized to assess both model parameters and gear crack size simultaneously. As a data-driven method, particle filter describes the dynamical behavior of model parameters updating and gear crack growth, whereas the Paris law, as a model-based method, characterizes the gear's crack growth according to the physical properties. The integration of the Paris law and particle filter is proposed as a hybrid approach, which is suitable for nonlinear and non-Gaussian systems, and can update the parameters online and make full use of the prior information. Finally, case studies performed on gear tests indicate that the proposed approach is effective in tracking the degradation of gear and accurately predicts the residual gear fatigue life.
