## 5 Conclusions  
This paper introduces a new method for fault feature extraction in rolling bearings that involves optimizing the parameters of VME with an AOA, and proposes a 1D-MRCNN model with an improved residual structure for the automatic identification of fault types in rolling bearings. Initially, the AOA is employed to optimize the parameters [\(\alpha\), \(\omega\)] of VME, reduce noise in the original vibration signals, and extract fault features. Subsequently, the extracted vibration signals are divided into datasets and input into the 1D-MRCNN for training. Finally, a test is conducted to validate the proposed method's fault classification accuracy, leading to the following conclusions:  
1. In the optimization of the VME parameters with the AOA, weighted correlated kurtosis (WCK) is employed as the objective function. Both simulated and experimental signals demonstrate that this objective function can effectively extract fault information, confirming that this method enhances the accuracy of fault feature extraction in noisy environments. Through comparative analysis with other optimization algorithms, it has been demonstrated that AOA exhibits superior capabilities when addressing complex problems prone to local optimal solutions. This lays a foundation for subsequent fault classification in rolling bearings.
2. A multi-scale residual convolutional neural network is proposed. Compared with the traditional CNN and MSCNN, it can be concluded that a multi-scale convolution kernel can more effectively achieve information complementarity at different scales, a gap layer can reduce the number of network parameters, and an improved residual structure can improve the training speed, and improve the accuracy of fault recognition.
3. Upon comparing parameter-optimized VME with empirical VME, parameter-optimized VMD, EEMD, and unprocessed vibration signals, it is revealed that parameter-optimized VME retains higher recognition accuracy than empirical VME, EEMD, and unprocessed vibration signals in noisy environments. Compared with parameter-optimized VMD, it offers a low computational cost and reduced processing time. This underlines its clear advantages over other algorithms.
4. The computational efficiency of the proposed method, although improved, still poses challenges when deployed in real-time monitoring systems, particularly in resource-constrained environments. Future work will aim to address these limitations by exploring more adaptive signal processing techniques and further refining the network architecture to enhance its applicability and efficiency in a broader range of operational contexts.  
Figure 27: Results for MRCNN model under different signal preprocessing methods.  
**Author Contributions:** [PERSON] analyzed the data, designed the experiments, and wrote the paper; [PERSON] made suggestions and improvements to the paper. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (Grant No. 51906133).  
**Data Availability Statement:** Data is contained within the article.  
**Acknowledgments:** We sincerely thank the reviewers for their constructive comments and the editors for their patient replies.  
**Conflicts of Interest:** The authors declare no conflicts of interest.