# Multi-Scale Rolling Bearing Fault Diagnosis Method Based on Transfer Learning
## 1 Introduction  
Bearing fault diagnosis is a key technology in terms of enhancing the performance, prolonging the lifespan, and ensuring the safe and stable operation of rotating machinery equipment [1, 2]. Bearings, as critical components in rotating machinery, support the load on rotating shafts and ensure smooth operation. Faults or damage in bearings can not only degrade the equipment's performance but also lead to severe accidents and equipment downtime and potentially cause the loss of life and property. Therefore, it is crucial to precisely diagnose bearing faults with modern sensor technology and data analysis methods. This approach not only prevents faults but also optimizes maintenance schedules, improves equipment efficiency, and reduces maintenance costs and downtime [3, 4, 5]. Current bearing fault diagnosis methods encompass those derived from traditional machine learning [6, 7, 8] and deep learning [9, 10, 11]. Among them, deep learning models have been widely studied and applied because of their ability to automatically extract useful features from complex data. [PERSON] et al. proposed a deep learning fault diagnosis methodbased on cyclic spectral coherence diagrams and convolutional neural networks, which improved the identification of rolling bearing faults, but all fault types appeared in the training set [12]. [PERSON] et al. demonstrated the advantages of applying deep learning technology for fault diagnosis in different bearing technologies [13]. Meanwhile, [PERSON] et al.proposed a hybrid deep autoencoder method for bearing fault diagnosis, capable of classifying both existing and new faults, thereby improving the accuracy [14]. However, these studies did not consider the approaches' applicability across different operational conditions. In real industrial environments, the training and testing data may be obtained under different operational conditions, such as varying loads and speeds, leading to domain drift and consequently low fault diagnosis accuracy [15; 16]. In other words, changes in working conditions cause variations in the bearing signal features across the source and target domains, which can affect the reliability of common methods. Moreover, acquiring sufficient vibration signal data and corresponding labels to train models for specific health states is challenging. Thus, bearing fault diagnosis under different working conditions is of significant practical importance. Transfer learning, as a cutting-edge machine learning technique, offers an effective solution for bearing fault diagnosis challenges under varying working conditions [17; 18]. The core idea of this technique is to leverage existing knowledge and data to effectively combine information from both the source and target domains, enabling more precise bearing state diagnosis under new conditions. The advantages of transfer learning are not only reflected in improving the diagnostic accuracy but also in reducing the cost of data collection and labeling and enhancing the efficiency of model training. This is because it allows the transfer of valuable knowledge from the source domain to the target domain, thus better addressing challenges under varying operational scenarios. [PERSON] et al. [19] proposed an efficient transfer learning strategy, fine-tuning the trainable parameters with target domain datasets for domain generalization in mechanical fault diagnosis. [PERSON] et al. [20] introduced a lightweight convolutional neural network that combines transfer learning and self-attention integration for bearing fault diagnosis, highlighting the potential of transfer learning in improving the diagnostic accuracy. [PERSON] et al. [21] utilized a Gaussian prior distribution to construct a common feature space and designed a conditional weighting strategy to quantify the similarity between different source and target domains. [PERSON] et al.