## 5 Results and Discussion
### Prediction of Tool Wear on PHM2010 Dataset  
Table 4 demonstrates the performance comparison results of the STAGCN and all baselines on the PHM2010 dataset. To avoid randomness of the results, the final values of two evaluation metrics are the average of five experiments. Based on the results, the following conclusions can be obtained:  
1. Transformer-based models outperform traditional deep learning approaches primarily due to the effectiveness of the attention mechanism. Unlike RNN-based architectures such as GRU and LSTM, which process sequences sequentially and suffer from vanishing gradient issues, transformer-based models dynamically focus on key parts of the input sequence. This flexibility allows them to capture long-range dependencies more effectively, ensuring better modeling of complex temporal patterns in tool wear progression. 2. The STAGCN achieves the best overall performance by integrating an AGCN and Bi-Mamba for spatial-temporal feature extraction. Traditional graph-based models, such as a GCN, rely on a fixed adjacency matrix, which limits their adaptability to \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Window size T & 60 \\ Initial learning rate & 0.001 \\ Batch size & 32 \\ Training epoch & 100 \\ Dropout rate & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The detailed hyperparameters. dynamically evolving sensor relationships. In contrast, an AGCN enables dynamic learning of sensor dependencies, adjusting the graph topology based on real-time sensor interactions. This adaptability is particularly beneficial in scenarios where sensor measurements are affected by changing cutting conditions and wear patterns. 3. The MTLA mechanism further enhances the STAGCN by refining feature selection across different timescales. Unlike conventional attention mechanisms that primarily focus on individual time steps, MTLA enables hierarchical feature aggregation, ensuring that both short-term fluctuations and long-term degradation trends are effectively captured. This is particularly crucial in predictive maintenance, where wear progression may follow nonlinear trends that require flexible time-dependent modeling. Furthermore, the predicted tool wear for each task is shown in Figure 10, from which it can be concluded that in the initial and steady wear stages, the estimated wear values are very close to the true wear, and the wear progresses linearly with a relatively low and stable wear rate. In the severe wear stage, although the error significantly increases, the proposed STAGCN can still achieve high prediction accuracy. The performance difference between the initial and severe wear stages is mainly due to three factors: (1) The initial wear stage follows a more stable and gradual progression, making it easier for the model to learn consistent patterns, whereas the severe wear stage exhibits rapid and nonlinear deterioration, increasing prediction difficulty. (2) As tool wear intensifies, sensor data become noisier due to increased vibrations and surface roughness, reducing prediction accuracy. (3) Since the training data are primarily composed of early