Ensuring the safety and reliability of key components, such as bearings, is crucial in machinery systems. Therefore, academia and industry have long tried to develop prognostic and health management technology. In particular, it is necessary to carry out methods to predict the remaining useful life (RUL) of the bearing, which can reduce economic losses and significantly prevent safety accidents. To overcome the deficiency of current investigations on bearing RUL prediction, a new method based on acoustic emission signals and a physics-informed neural network (PINN) is proposed in this paper. A new health index is constructed by developing an improved diffusion entropy, which outperforms current time-domain features. Four different labeling functions are compared to demonstrate that the exponential function has the best capacity to represent the bearing degradation process. The physical knowledge in this paper is derived from reliability engineering, that is, the failure procedure described via the Weibull distribution, and this knowledge is incorporated into a long short-term memory neural network to construct the PINN model by developing a Weibull-loss function. Moreover, this knowledge integration can improve prediction performance and help circumvent some obstacles, including poor quality or limited historical data and the obscurity of the underlying processes. Finally, the effectiveness and superiority of the proposed method are validated through experimental results and comparison with other existing methods.
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