## 5 Experimental Case Planning, Results, and Analysis
### Experimental Case
#### 5.2.2 Case Study 2--AI Model with Limited Data
Analysis of experimental results  
This case study compares the method proposed in this research with typical oversampling and under-sampling models, namely the fine-tuned ResNet50, DCGAN, and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Imbalance Ratio** & **Sampling Techniques** & \multicolumn{2}{c}{**Over-Sampling (Samples)**} & \multicolumn{2}{c}{**Down-Sampling (Samples)**} \\ \cline{3-6}  & **Healthy** & **Faults** & **Healthy** & **Faults** \\ \hline \multirow{2}{*}{Training dataset} & 10:1 & 60 & 60 & 600 & 600 \\ \cline{2-6}  & 20:1 & 30 & 30 & 300 & 300 \\ \hline \multirow{2}{*}{Validation dataset} & 10:1 & 15 & 15 & 15 & 15 \\ \cline{2-6}  & 20:1 & 15 & 15 & 15 & 15 \\ \hline \multirow{2}{*}{Testing dataset} & 10:1 & 500 & 500 & 500 & 500 \\ \cline{2-6}  & 20:1 & 500 & 500 & 500 & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Dataset partition. Figure 8: Training process of residual VGG-based Siamese network. CNN models [23], applied to the across-load fault diagnosis analysis of induction motors with limited data conditions. We investigate the impact of imbalanced training data ratios and different load conditions. At the imbalance ratio of 10:1, the results are shown in Table 7 for induction motors at 50% loading level training--100% loading level testing, and 100% loading level training--50% loading level testing. Whether a five-shot five-way or one-shot five-way, the residual VGG-based Siamese network model achieves an average diagnostic accuracy of 98 to 99%, with STD values ranging from 0.1315 to 1.182. Compared to the fine-tuned ResNet50, DCGAN, and CNN models [23], the method proposed in this research yields an average accuracy of approximately 5% and 25% higher, respectively, with STD values significantly lower than the aforementioned models. Next, to investigate the impact of the data imbalance ratio, we increased the balance ratio to 20:1, with the results shown in Table 8. The residual VGG-based Siamese network model still achieves an average diagnostic accuracy of 98 to 99%, with STD values ranging from 0.2683 to 1.182. Compared to the fine-tuned ResNet50, DCGAN, and CNN models [23], the average accuracy is about 6% and 29% higher, respectively, and the STD value remains much lower than the aforementioned models. Compared with the results in Table 7, where the imbalance ratio is 10:1, the across-load accuracy of the residual VGG-based Siamese network model dropped by less than 1%, but fine-tuned ResNet50 and DCGAN and CNN models [23] decreased by 2%, and 9%, respectively, illustrating the superior performance of the model proposed in this research in across-load fault diagnosis for induction motors. As shown in Figures 9 and 10, which display the confusion matrices of classification results for 50% loading level training--100% loading level testing and 100% loading level training--50% loading level testing, respectively, we can observe the classification results for healthy and four types of faults. The residual VGG-based Siamese network almost achieves effective classification. However, fine-tuned ResNet50, as the pre-trained model, cannot effectively apply the knowledge it has previously learned to the across-load fault diagnosis of induction motors. This model shows more drastic changes in the classification results compared to DCGAN and CNN models [23], indicating the difficulty in training DCGAN, which cannot generate a distribution similar to real samples, leading to a significant decline in the diagnostic performance of the CNN model. Finally, the experimental case results reveal the following points: (1) Even at an imbalance ratio of 20:1 and under five-way one-shot conditions, the method proposed in this research still achieves a diagnostic accuracy of over 98%. (2) Compared to the fine-tuned ResNet50 model, the residual VGG-based Siamese