## 4 Experimental Results
### Comparison with State-of-the-Art Based on NEU Dataset  
Figure 6 shows the training and testing losses of the level 0 and level 1 models. It can be seen that both networks have a high convergence speed in the first 100 epochs. While comparing the training progress between the level 0 and level 1 models, the testing loss of the level 0 model is much closer to the training loss. This result indicates that the level 1 model contains a higher risk of the overfitting phenomenon owing to less information being provided for the training model. Lastly, the testing loss gradually stabilized after training for 100 epochs, and the experimental results indicate that the testing loss almost remained the same during 200 to 300 epochs. Hence, this result suggests that 300 epochs are suitable for training the models. Furthermore, this section compares the effectiveness of the proposed MRFFN with the state-of-the-art, which includes the ML-based, conventional CNN, and the fusion-based method. In particular, these methods were trained by a relatively larger dataset to better illustrate the performance of the MRFFN under data-limited tasks, and the table of comparison is shown in Table 2. Obviously, the low-level and high-level models obtained different performances, in which the low-level model was 0.27% higher than the high-level model. This result indicates that some representative information was eliminated while applying the Gaussian filter. Thus, the limitation of the Gaussian pyramid  
Figure 5: The examples of the disturbance defect dataset. (**a**) Crazing, (**b**) Inclusion, (**c**) Patches, (**d**) Pitted Surface, (**e**) Rolled-in Scale (**f**) Scratches. should be considered in order to prevent the deterioration of the training progress with limited data. Furthermore, the level 0 model tends to prevail over methods trained by 50 or 150 samples/defect [1, 24, 37, 47]. This result indicates that the fine-tuned structure could better learn the meaningful features from the raw data. Furthermore, the results of the MRFFN shows that the combination of the level 0 and level 1 models can improve the performance of the models. The accuracy of MRFFN is 0.31% higher than the level 0 model and is 0.58% higher than the level 1 model. This shows that both networks are complementary to each other. This result also reveals that the proposed MRFFN yielded the best performance compared with the state-of-the-art [1, 19, 24, 37, 47]. Thus, it is convincing to state that the proposed method is able to generate more meaningful information from the raw data contemporary and to extract the important features effectively. Lastly, the performance of MRFFN increased by 0.14% when applying the image augmentation technique. To investigate the classification results of the proposed MRFFN among six kinds of defects, the confusion matrix is provided in Table 3. From the confusion matrix, the first row represents the ground truth of the defect category, and the value in each column indicates the prediction results of the proposed method. According to the confusion matrix, the proposed MRFFN can easily recognize the patches defect, which yields a perfect precision and recall result. Besides, the MRFFN has achieved high recall (100%, 99.6%, and 100%) \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Training Sample** & **Testing Sample** & **Accuracy** & **Recall** & **Precision** & **F1-Score** \\ \hline [PERSON] et. al. [19] & 210 & 30 & 99.44 & - & - & 99.00 \\ [PERSON] et. al. [47] & 150 & 150 & 97.42 & - & - & - \\ [PERSON] et. al. [1] & 150 & 150 & 98.93 \(\pm\) 0.63 & 97.89 & 97.91 & 97.90 \\ [PERSON] et. al. [24] & 150 & 150 & 99.27 & - & - & - \\ [PERSON] et. al. [37] & 50 & 250 & 99.26 & 99.26 & 100 & 99.63 \\ Level 0 & 50 & 250 & 99.30 \(\pm\) 0.37 & 99.30 & 99.30 & 99.30 \\ Level 1 & 50 & 250 & 99.03 \(\pm\) 0.39 & 99.03 & 99.04 & 99.03 \\ MRFFN & 50 & 250 & 99.61 \(\pm\) 0.23 & 99.61 & 99.61 & 99.61 \\ MRFFN + IA & 50 & 250 & 99.75 \(\pm\) 0.24 & 99.75 & 99.75 & 99.75 \\ \hline \hline \end{tabular}
\end{table}