## 5 Conclusions  
This study focuses on the practical problem of the low fault recognition of deep learning models due to the imbalance between normal and fault samples of rolling bearings, as well as insufficient labeled samples. A sample-expansion method based on GAN and a fault diagnosis method based on transformer were proposed, and the validity and applicability of the methods were confirmed by experimental data. The main conclusions are as follows:  
1. To address the imbalance problem between normal and fault samples of bearings, a CVAE-SKEGAN network is proposed for the expansion of time-frequency image datasets. SKNets and genetic algorithms are introduced in CVAE-SKEGAN, which can adaptively select the convolutional kernel and the loss function to improve the model's feature-learning ability and alleviate the problem of gradient vanishing. The experimental results show that the generated data distribution from CVAE-SKEGAN is closer to the real data distribution, and the information loss of the generated images is less.
2. Aiming at the challenge of inadequate labeled samples, an SSL-VCST network is proposed for bearing fault identification. In SSL-VCST, a variational attention mechanism is introduced to reduce the risk of overfitting and improve the adaptability of the model. The introduction of SSL fully utilizes unlabeled samples to supplement training, avoiding the waste of unlabeled data. The experimental results show that SSL-VCST can adapt to different sample imbalance levels and achieve a more stable accuracy. So, SSL-VCST has better generalization ability and stability.
3. The verification results under three typical operating conditions show that after the powerful balancing effect of the CVAE-SKEGAN, the SSL-VCST network is fully utilized to explore the value of unlabeled data, and the fault diagnosis accuracy achieved is significantly improved compared to other methods. The entire diagnostic scheme described here has strong applicability to multiple operating conditions.  
Due to the high complexity and the high requirements for computing power of GAN, further research is needed to realize adaptive parameter tuning of the network to improve the efficiency of the training model. Of course, these issues cannot eliminate the proposed method from practical application. In addition, the data used for experimental validations come from experimental rigs, which still have a gap from the actual operation data. Further targeted adjustments are needed in subsequent research.  
Conceptualization, X.C.; methodology, Y.L.; software, Y.L.; validation, Y.L., Z.L. and L.Z.; formal analysis, Y.G.; investigation, M.W.; resources, X.C.; data curation, Y.L.; writing--original draft preparation, Y.L.; writing--review and editing, Y.L.; visualization, Y.L.; supervision, Z.L.; project administration, L.Z.; funding acquisition, X.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fundamental Research Funds for the Central Universities, grant number 2024 ZKPYJD02, and the National Natural Science Foundation of China, grant number U1361127.  
Not applicable.  
The original data from the CWRU dataset and the SQV dataset presented in the study are openly available at [[https://engineering.case.edu/bearingdatacenter/welcome](https://engineering.case.edu/bearingdatacenter/welcome)]([https://engineering.case.edu/bearingdatacenter/welcome](https://engineering.case.edu/bearingdatacenter/welcome)) (accessed on 4 January 2024) and [[https://blog.csdn.net/weixin_43543177/article/details/121549538](https://blog.csdn.net/weixin_43543177/article/details/121549538)]([https://blog.csdn.net/weixin_43543177/article/details/121549538](https://blog.csdn.net/weixin_43543177/article/details/121549538)) (accessed on 4 January 2024). The original data regarding the vibrating screen presented in this study are available upon request from the corresponding author due to privacy maintenance.  
The authors declare no conflicts of interest.