## 2 Materials and Methods
### Methods
#### 2.2.1 Overview
First, the polar coordinate transformation and Gramian matrix methods were used to convert time-series data into two-dimensional images, fully extracting feature information, improving data representation efficiency, and enhancing classification stability. Subsequently, a lightweight front-end encoder, the DWFE, was

Figure 14: Classification results of gearbox fault types and severity levels. (**a**) 23c4s ViT, (**b**) 23c4s RoPE-DWTrans, (**c**) 23c10s ViT, (**d**) and 23c10s RoPE-DWTrans. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Methods**} & \multicolumn{2}{c}{**Evaluated Metrics**} \\ \cline{2-3}  & **Accuracy** & **F1-Score** \\ \hline FFT-SGCN [43] & 0.962 & 0.967 \\ Multireceptive-GCN [50] & 0.971 & 0.968 \\ Attention-TSGNN [51] & 0.975 & 0.976 \\ HHO-MLP [52] & 0.975 & - \\ Ours & 0.981 & 0.978 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of classification performance on MCC5 gearbox datasets. designed. This encoder refined the granularity of feature representation by integrating multi-scale depthwise separable convolution modules, while effectively preserving global structural information, enabling more comprehensive feature representation and more precise feature analysis. Additionally, the self-attention mechanism incorporated the 2D-RoPE, which further enhanced the model's ability to capture temporal dependencies. The introduction of the ReZero mechanism significantly improved the stability and convergence speed of the training process, thus enhancing the performance of the self-attention mechanism in visual tasks. This paper conducted a comprehensive validation of the proposed method using a combined dataset based on the MCC5 and HUST gearbox datasets, with the experimental results presented in Tables 3 and 4. In the 14-class fault classification task, the RoPE-DWTrans model exhibited excellent performance, achieving a classification accuracy of 0.953, a precision of 0.959, a recall of 0.973, and an F1 score of 0.961, significantly outperforming other comparative models. Among these, the classification accuracy of ConvNeXtV2 reached 0.940, slightly lower than that of the RoPE-DWTrans, while the accuracy of InceptionV3 was only 0.859, indicating relatively weaker performance. As the task complexity increased, with fault categories expanding from 14 to 23 classes, the performance of all models declined, with the classification accuracy of the five comparative models decreasing by 10.36%, 4.58%, 14.67%, 3.72%, and 3.15%, respectively. For instance, the classification accuracy of GRU + ShuffleNet and InceptionV3 dropped significantly to 0.831 and 0.733, respectively, while SeNetTrans and ConvNeXtV2 showed classification accuracies of 0.895 and 0.905, indicating notable declines compared to the 14-class task. In contrast, the RoPE-DWTrans model maintained high stability in the 23-class task, achieving a classification accuracy of 0.923, a precision of 0.932, a recall of 0.928, and an F1 score of 0.928, with the smallest performance decline among all models. These results demonstrate that the RoPE-DWTrans model effectively enhances feature representation by transforming time-series data into two-dimensional image forms. Further ablation experiment results (Table 5) validated the effectiveness of the proposed improvements. By progressively removing key modules of the model and analyzing their impact on performance, the results showed that the multi-scale convolution module and 2D-RoPE encoding play pivotal roles in improving classification performance, providing essential support for practical applications in real-world industrial scenarios. The experimental results in Table 6 clearly demonstrate the impact of different feature extraction window lengths on the performance of multi-class classification tasks. In the 14-class classification task, when the feature extraction window was set to 4 s, the model achieved a classification accuracy of 0.953 and a precision of 0.959.