## 1 Introduction  
Bearings are widely used in rotating mechanical equipment, such as wind turbines, motor rotations, and rollers. When many rotating machineries operate in harsh environments, their bearings are prone to faults, such as friction, oxidation, wear, pitting, and fracture. A faulty bearing is likely to cause an impact at the fault point, increase friction, and cause damage to rotating mechanical equipment, ultimately leading to shut down and even the overall paralysis of the mechanical equipment system, resulting in huge economic losses. Traditional bearing fault diagnoses mainly analyze the fault features of bearings from the perspective of signal feature extraction and then combine them with classifiers to identify fault types. Common time-frequency analysis methods include empirical mode decomposition [1], and wavelet transform [2, 3]. Common fault identification methods include convolutional neural networks [4], fuzzy neural networks [5], support vector machines [6], and random forests [7]. Empirical mode decomposition is suitable for processing nonlinear and nonstationary signals, but it has stability and computational complexity issues. Wavelet transform is suitable for capturing the time-frequency characteristics of signals, but it has limitations in handling non-stationary signals. Support vector machines and random forests are susceptible to noise. Convolutional neural networks and fuzzy neural networks are prone to computational complexity and long training times. References [8, 9, 10, 11] introduced deep belief networks (DBNs) into bearing fault diagnoses, further improving the accuracy of fault recognition. Unsupervised domain adaptation (UDA) [12; 13; 14; 15] has been applied to fault diagnoses, improving the fault diagnosis of variable working conditions. The maximum mean discrepancy (MMD) [16; 17] has been used to align the data distribution of samples between different domains to achieve UDA, which has attracted much attention from scholars. However, UDA can only globally align the global data distribution between two domains and cannot capture more fine-grained information. Reference [18] proposed local maximum mean discrepancy (LMMD), which can align data distributions of the same category and achieve unsupervised subdomain adaptation (USDA). Reference [19] proposed clustering domain adaptation, which minimizes the nearest neighbor distance between similar samples and maximizes the distance between the cluster centers of samples within the same domain. The adaptive clustering domain further improves the accuracy of fault diagnoses under variable operating conditions [20]. The prerequisite for achieving subdomain adaptation is to obtain reliable labels in the target domain. Reference [21] used feature transferability and output probability similarity to mark the unlabeled target domains with pseudo labels. Reference [22] assisted in achieving USDA by labeling the target domain with pseudo labels. The principle of labeling pseudo labels is to use the classifier trained on the source domain data to label them. The accuracy of pseudo labels is influenced by the discrepancies in data distribution and sample noise. Relying solely on LMMD as the objective function for subdomain adaptation easily leads to local optima and the complexification of the mapping matrix. The implementation of the above methods is an end-to-end model that directly inputs raw data into a neural network for feature extraction and fault type recognition [21]. The end-to-end model utilizes a large-scale neural network to extract abstract features from raw data. However, using neural networks to extract features from raw data requires a significant amount of training time and data and is sensitive to noise. In the industry, the distribution of data is greatly influenced by the degree of damage, bearing type, noise, and variable working conditions. It is difficult to reduce the impact of varying degrees of damage and noise using domain adaptation. The impact will reduce the accuracy of pseudo labels.