## 1 Introduction  
Rolling bearings have the function of reducing friction between components, and they play an important role in modern industrial production [1]. Once a fault occurs, it may have a huge impact on personnel safety and economic benefits. Therefore, it is very important to carry out equipment detection and fault diagnosis on rolling bearings to ensure their safety and reliability [2]. The fault diagnosis method is based on analysis of signals from the structure and fault mechanism of a rolling bearing, and the state of the rolling bearing is judged, artificially, by the monitored information. Of these signals, the vibration signal has been studied the most widely, using methods such as time domain analysis, frequency domain analysis, and resonance demodulation. Such algorithms rely on a great deal of prior experience and require technicians to reserve a great deal of prior knowledge. In the face of increasingly complex mechanical equipment, the diagnosis effect is poor. Data-driven diagnosis methods can classify the condition monitoring data without prior experience. Regarding the traditional rolling bearing fault diagnosis method, two main aspects have been studied: the feature extraction method and pattern recognition selection. With the rapid development of deep learning, more and more new methods are being used to solve various problems in the field of fault diagnosis. The advantages of deep learning are that it avoids the process of artificial feature extraction and that it completes the end-to-end fault classification via automatically mining the hidden nonlinear features of the input signal [3]. In practical engineering applications, the data acquisition conditions for rolling bearing status are complex and diverse due to the influence of speed, noise, load, and other factors. It is inevitable that the data label information is not comprehensive and is different from the information distribution of the training data sample [4]. Although deep learning technology performs well in fault diagnosis, it is difficult to achieve ideal results for mechanical fault diagnosis problems with inconsistent data distribution under different working conditions [5]. To solve the above problems, [PERSON] et al. [6] built a neural network by stacking multiple sets of sparse auto-encoders and used a supervised fault diagnosis method to fine-tune the network. [PERSON] et al. [7] achieved good diagnostic results on three fault datasets by fine-tuning the VGG-16 network's high-level architecture. However, the fine-tuning method does not completely solve the problem of insufficient target domain labels. When facing the problem of label-free target domain data, it is difficult to achieve effective diagnosis by fine-tuning the model alone. Methods to more effectively introduce transfer learning into fault diagnosis have attracted increasing research interest [8]. Researchers use metrics as criteria to increase the similarity between source domain data and target domain data. Metrics determine the outcome. Commonly used measuring methods are Euclidean distance, Markov distance, KL (Kullback-Leibler) divergence, JS (Jensen-Shannon) distance, maximum mean difference, the Pearson coefficient, etc. In order to solve the problem of a mismatched data distribution under different working conditions, adaptive methods of data distribution, such as TCA (transfer component analysis) [9], JDA (joint distribution adaptation) [10], BDA (balanced distribution adaptation) [11], etc., are introduced into the fault field. When the data probability distributions of the source domain and target domain are different, certain methods are used to close the distribution distance between them. The literature [12] takes the MMD (maximum mean difference) as the domain adaptive method and achieves good results in bearing fault diagnosis under different conditions. [PERSON] et al. [13] realized fault diagnosis by improving joint distribution adaptation and using a more comprehensive edge and condition distribution of the source and target domain data.