## 1 Introduction  
As a critical technology to guarantee the reliability and safety of equipment, prognostics and health management (PHM) has made plenty of theoretical achievements and has been broadly used in the last few decades [1]. PHM aims to maximize the availability of engineering assets, reduce maintenance losses and improve system reliability and security. RUL prediction has been regarded as the foundation and core of PHM technology for a long time. Rolling element bearings are significant mechanical components in rotating machinery, which is a common cause of operation failures [2]. The precise RUL estimation of the bearings can obviously improve the reliability and operation safety of the rotating machinery and avoid accidents. RUL prediction methods are broadly divided into model-based and data-driven methods. Model-based methods use prior knowledge of equipment degradation and failure mechanisms to mathematically model equipment degradation and failure behavior and then estimate model parameters based on the collected data [3]. However, the establishment of a physical model to describe the degradation trend depends on thoroughly understanding the failure mechanism of the system. With the increasing complexity of the equipment, it is generally difficult to obtain the failure mechanism of the equipment, or the cost of obtaining the failure mechanism is too high. With the rapid development of modern industry, data-driven methods have been developed rapidly. Data-driven methods rely on historical run-to-failure data to estimate the RUL by different machine learning methods. In recent years, a variety of data-driven algorithms have been proposed and made good achievements. [PERSON] et al. [4] developed a bearing performance degradation model using an artificial neural network and successfully predicted the bearing RUL. [PERSON] et al. [5] used the artificial neural network and Weibull theory to predict the bearing RUL. The experimental analysis shows that the predicted results of the artificial neural network are consistent with the actual results. In order to predict the RUL of industrial equipment precisely, [PERSON] et al. [6] proposed a multivariate grey RBF hybrid model which combines the grey model and RBF neural network's strong-point, effectively ensuring the prediction accuracy and has practical value in engineering application. [PERSON] et al. [7] used multiple signal features and support vector regression (SVR) to make bearing RUL predictions. [PERSON] et al. [8] used a relevance vector machine to train and predict the battery capacity and, at the same time, used the Kalman filter (KF) to optimize the predicted results online, thereby achieving the RUL prediction of the battery. Although data-driven methods are feasible in many cases, their main challenge is to extract effective representative features from the unprocessed data. However, the performance defects of traditional machine learning models significantly limit their ability to learn advanced features. In recent years, Deep Learning (DL) has made great breakthroughs in computer vision, natural language processing and other fields. Deep learning is characterized by a deep network structure with multiple layers stacked in the network, which can automatically and accurately construct high-level features from low-level features to learn a hierarchy of features [9]. A convolutional neural network (CNN) is a classic deep learning model that can automatically learn high-dimensional abstract features from the raw data, effectively establish the relationship between the degradation trend of mechanical properties and the measured data and reduce the dependence on prior knowledge and physical knowledge. Research on CNN-based RUL predictions started in 2016. [PERSON] et al. [10] proposed a CNN model for RUL prediction, which has two convolutional layers and two pooling layers to extract the characteristics of the original signal, and combined it with a multilayer perceptron (MLP) to achieve bearing RUL prediction. [PERSON] et al.