## 3 Case Study
### TEP Dataset Analysis
#### 3.1.6 Parameter Sensitivity Analysis for ATASML  
This section investigates the sensitivity of the ATASML model to variations in batch size and learning rate, specifically focusing on the most complex 8-way 5-shot scenario. The choice of this scenario aims to rigorously test the model's performance under demanding conditions, where the complexity of fault classification is significantly higher.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Methods** & **3-way 5-shot** & **3-way 6-shot** & **8-way 5-shot** & **8-way 6-shot** \\ \hline MAML Accuracy & 72.26 \(\pm\) 2.3 & 73.68 \(\pm\) 2.4 & 64.60 \(\pm\) 2.1 & 65.54 \(\pm\) 2.1 \\ GOPML Accuracy & 85.13 \(\pm\) 1.4 & 89.68 \(\pm\) 1.4 & 77.29 \(\pm\) 1.2 & 79.66 \(\pm\) 1.3 \\ ATASML Accuracy & 95.02 \(\pm\) 1.0 & 98.47 \(\pm\) 1.0 & 84.57 \(\pm\) 0.8 & 90.13 \(\pm\) 0.9 \\ MAML F1 & 72.98 \(\pm\) 2.9 & 74.16 \(\pm\) 3.0 & 64.90 \(\pm\) 2.6 & 66.08 \(\pm\) 2.6 \\ GOPML F1 & 86.09 \(\pm\) 1.7 & 89.23 \(\pm\) 1.8 & 75.92 \(\pm\) 1.5 & 79.06 \(\pm\) 1.6 \\ ATASML F1 & 93.12 \(\pm\) 1.1 & 96.50 \(\pm\) 1.2 & 82.88 \(\pm\) 1.0 & 88.33 \(\pm\) 1.1 \\ MAML Precision & 72.66 \(\pm\) 3.6 & 73.54 \(\pm\) 3.6 & 62.72 \(\pm\) 3.1 & 65.22 \(\pm\) 3.2 \\ GOPML Precision & 84.65 \(\pm\) 2.5 & 88.47 \(\pm\) 2.7 & 74.66 \(\pm\) 2.2 & 78.49 \(\pm\) 2.4 \\ ATASML Precision & 92.17 \(\pm\) 1.7 & 95.52 \(\pm\) 1.7 & 82.03 \(\pm\) 1.5 & 87.43 \(\pm\) 1.6 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparative results of fault classification effectiveness on the TEP dataset.  
Figure 7: Training dynamics for the 3-way 6-shot task on the TEP dataset showing Diagnostic Accuracy and Classification Loss.  
The experiments demonstrate that ATASML achieves its best performance with a batch size of 64, particularly as the model approaches 15,000 epochs, as illustrated in Figure 8a. Increasing the batch size has also shown to place a greater demand on GPU resources, reflecting a balance between computational efficiency and model performance. Additionally, the model's learning rate was methodically adjusted across the range from \(1\times 10^{-5}\) to \(1\times 10^{-3}\), with ten iterations conducted at each learning rate to ensure statistical reliability and robustness of the findings. The results, displayed in Figure 8b, indicate that the accuracy stabilizes and peaks at a learning rate of \(5\times 10^{-4}\), achieving an optimal diagnostic accuracy of 84.57%.  
Notably, when the learning rate was increased to \(1\times 10^{-3}\), a subsequent decrease in diagnostic accuracy was observed. This reduction can typically be attributed to the optimizer overshooting the minima during the training process. At higher learning rates, the gradient descent steps become too large, potentially bypassing the optimal solution and leading to less stable training convergence.  
The data from this analysis is crucial for fine-tuning the ATASML model's parameters to ensure maximal efficiency and accuracy in real-world applications. It also offers a framework for future research to explore the impact of other parameter variations on the performance of meta-learning models in fault diagnosis.