## 3 Case Study
### TEP Dataset
#### 3.1.4 Efficacy of Task Sequencing in GOPML  
Task sequencing in GOPML aims to enhance the adaptability of knowledge through a more orderly and systematic learning approach. To validate the effectiveness of task sequencing in GOPML, a comparative analysis was conducted against the baseline algorithm, MAML, which did not incorporate task sequencing. Both algorithms shared a similar internal network architecture, with consistent training strategies and data partitioning. The distinctive factor between the two methods was the integration of task sequencing in GOPML's external meta-learning layer. The classification results of fault diagnosis, illustrated in Table 5, reflected the comparative study by varying the number of categories \(N\) and the samples per category \(K\) across different task setups. It was observed that GOPML surpassed MAML in classification accuracy in all task configurations. Notably, GOPML demonstrated substantial accuracy improvements in the 8-way 6-shot tasks, underscoring its superior learning performance with an increased number of categories and limited samples. This pronounced adaptability in complex few-shot scenarios established GOPML's potential for real-world fault diagnosis applications. In addition to accuracy, precision and F1 score were introduced for a more comprehensive evaluation. Precision measures the proportion of true positives to the sum of true positives and false positives, and the F1 score can be regarded as a weighted average of the model's precision and recall. GOPML surpassed the baseline method on these metrics as well, except in the case of the 8-way 6-shot tasks, where GOPML's performance was slightly lower, which may be due to the increased number of samples per task. Nevertheless, GOPML's F1 score and accuracy remained outstanding when dealing with the 8-way 6-shot tasks. The performance of GOPML reflected its adaptability in complex few-shot scenarios, improving the performance because the ordering of tasks from easy to difficult was more \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Methods**} & **3-Way Accuracy** & **3-Way Accuracy** & **8-Way Accuracy** & **8-Way Accuracy** \\  & **5-Shot** & **6-Shot** & **5-Shot** & **6-Shot** \\ \hline Transfer VGG-11 & 84.20 & 89.84 & 74.14 & 79.78 \\ Transfer Resnet-18 & 87.70 & 92.14 & 75.90 & 80.34 \\ GOPML & 93.53 & 97.48 & 84.01 & 86.59 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fault classification results of the three methods. in line with the acquisition process of meta knowledge. Standardizing the learning process of meta-learning will lead to better learning outcomes, such as making an orderly task-learning step. This step was conducive to the general knowledge representation learned from previous tasks, which helped the model adapt better to later tasks and thus achieve a better generalization performance. During the training process, GOPML exhibited a higher resistance to performance degradation when tuning hyperparameters compared with MAML. Specifically, as training progressed, MAML's accuracy rate rapidly reached saturation and then declined sharply, indicating a failure to achieve optimal training outcomes. In contrast, under identical hyperparameter settings, the training trajectory of GOPML remained stable throughout the training duration. This phenomenon is illustrated in Figure 4, which depicts the training process of both methods in a 3-way 6-shot setting. Notably, the stair-like and progressive nature of GOPML's training process ensured minimal difficulty variance between adjacent tasks. This approach effectively mitigated the risk of significant adverse impacts from earlier learned tasks on the subsequent ones. To further validate this characteristic, an extended experiment was conducted in an 8-way 6-shot scenario. The results, as shown in Figure 5, reinforced the consistency and robustness of GOPML's training performance across more complex task configurations. Figure 4: The 3-way 6-shot accuracy in the outer loop.