## 1 Introduction  
Bearings play a vital role in the functioning of rotating machinery to minimize friction between mechanical components. The detrimental effects of bearing damage are especially pronounced in various rotating machinery, often resulting in significant mechanical failures [1]. Therefore, it is very important to ensure the safety and stability of bearings through health monitoring and intelligent fault diagnosis [2, 3, 4]. Researchers have conducted extensive studies on fault diagnosis methods, which include methods based on signal processing, statistical analysis, and machine learning. Methods based on signal processing utilize time-frequency analysis to extract fault characteristic information from vibration signals for fault diagnosis. Common techniques include Short-Time Fourier Transform [5], wavelet transform [6], and mathematical morphology analysis [7], etc. Methods based on statistical analysis monitor and analyze the characteristic values of signals, extracting fault characteristic quantities from the changes produced and comparing them with designed standard values and thresholds to determine the faults. The primary methods include Bayesian theory [8] and multivariate statistical analysis, etc. The method based on machine learning trains the model by collecting normal operation data and fault data so that the model can automatically learn fault characteristics. Compared to the previous two methods, machine learning does not rely heavily on expert knowledge and experience. In fault diagnosis applications, it offers greater flexibility and universality, as well as higher efficiency and accuracy. With the advancement of machine learning algorithms, techniques for bearing fault diagnosis have also made significant progress. Among these techniques, deep learning-based diagnosis methods have gained popularity in recent years, demonstrating superior performance compared to shallow learning methods [9]. One of the main reasons is that deep learning eliminates the part of manual feature extraction, automatically learns internal representation and predict targets from the original input, and realizes an end-to-end system [10]. Numerous deep learning models have been employed in the realm of fault diagnosis, with convolutional neural networks (CNN), recurrent neural networks (RNN), and their respective variants being particularly prominent [11; 12; 13]. [PERSON] et al. introduced the transformer network based on the self-attention mechanism into bearing fault diagnosis, achieving satisfactory diagnostic efficiency and results [14]. [PERSON] et al. integrated generative adversarial networks with deep convolution, utilizing a small amount of labeled data and a large amount of unlabeled data for semi-supervised learning, and attempted to diagnose on unlabeled data with expanded fault types [15]. Typically, fault diagnosis models assume that the training data and the test data follow the same distribution [16; 17]. As a result, the trained models generally achieve high accuracy when evaluated on the test dataset. However, in the actual industry, the working conditions and states of mechanical equipment are not consistent, which will lead to changes in the data distribution under different working states [18]. When a model trained on a dataset from one specific working condition is utilized for diagnosing data from different working conditions, the diagnosis results often prove unsatisfactory, even when the fault type remains the same [19]. For this issue, [PERSON] et al. introduced a probabilistic Bayesian deep network to quantify and analyze the uncertainty of the model's diagnostic results under unknown conditions. The results indicate that the model has a high level of uncertainty in predicting failures under unknown conditions, and the larger the difference between conditions, the greater the uncertainty [20].