# Deep Residual Network Combined with Transfer Learning Based Fault Diagnosis for Rolling Bearing
## 4 Experimental Study
### Classification of CVRUI Datasets  
(1) Dataset: In this section, experiments are conducted using a publicly available dataset from the Bearing Data Center of Case Western Reserve University [39] to verify the robustness of the ResNet34-TL model in terms of diagnostic performance. Its sampling frequency is 12 kHz, the speed is 1797 r/min, no load is applied in the radial direction, and the data of standard bearings and bearings with different types of faults are collected. The fault depth of each kind of faulty bearing is 0.280 mm, and the fault width is 0.178 mm and 0.533 mm. This section selects two fault sizes of the rolling element, two fault sizes of the inner ring, two fault sizes of the outer ring, and the normal condition. The specific dataset description is shown in Table 6. An example of converting the vibration signal collected by the CVRU rolling bearing test bench into a wavelet time-frequency image by overlapping sampling interception is shown in Figure 8.  
Figure 7: Confusion matrix charts of fault diagnosis results obtained by different approaches: (a) ResNet34-TL; (b) MobileNet-TL; (c) ResNet34; (d) MobileNet; (e) CNN.  
(2) Testing Accuracy: Importing the CWRU image dataset converted using CWT into each classification model, the results are shown in Figure 9. It can be seen from the loss error of the training set of the network that the ResNet34-TL model can drop quickly at the beginning of the iteration and eventually stabilize. Moreover, the loss function of the ResNet34-TL model has decreased more quickly. On the other hand, the ResNet34-TL model has achieved more than 90% accuracy since the first generation, and the accuracy has reached 99% in the fourth generation. The accuracy of the diagnostic networks that have been improved by transfer learning is higher than the original diagnostic networks, indicating that the application of transfer learning has led to optimizing the networks.  
The trained models are used for intelligent classification on the test set, and the average of the 10 test accuracies and pre-training times is taken as the final diagnosis result. The results are shown in Table 7, the ResNet34-TL model achieved 99.86% accuracy on the test set, but the required training time was the longest. Although the MobileNet-TL model performed well in terms of time and accuracy, the ResNet34-TL model performed more consistently and robustly in the experiments with different datasets, proving that the ResNet34-TL model is more stable and robust.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & **Fault Size** & **Total** & **Samples in the** & **Samples in the** & **Samples in the** & **Label** \\  & **(mm)** & **Sample Qty** & **Training Set** & **Validation Set** & **Test Set** & **Label** \\ \hline \multirow{2}{*}{ball wear} & 0.178 & 300 & 210 & 60 & 30 & B007 \\ \cline{2-6}  & 0.533 & 300 & 210 & 60 & 30 & B021 \\ \hline \multirow{2}{*}{inner race wear} & 0.178 & 300 & 210 & 60 & 30 & IR007 \\ \cline{2-6}  & 0.533 & 300 & 210 & 60 & 30 & IR021 \\ \hline \multirow{2}{*}{outer race wear} & 0.178 & 300 & 210 & 60 & 30 & OR007 \\ \cline{2-6}  & 0.533 & 300 & 210 & 60 & 30 & OR021 \\ \hline normal bearing & 0 & 300 & 210 & 60 & 30 & NORMAL \\ \hline \hline \end{tabular}
\end{table}
Table 6: Introduction to image data sets.  
Figure 8: Transformed result.  
Figure 9: Experimental results for all models: (**a**) training set loss; (**b**) validation set accuracy.  
In addition, Figure 10 shows a confusion matrix plot of the best test results for all models. The confusion matrix results show that through 20 generations of training, each deep learning model has been able to classify each type of fault on the test set with a relatively high rate of correct classification. In contrast, the ResNet34-TL model can achieve 100% accuracy in each class.  
Figure 10: Confusion matrix charts of fault diagnosis results obtained by different approaches: (**a**) ResNet34-TL; (**b**) MobileNet-TL; (**c**) ResNet34; (**d**) MobileNet; (**e**) CNN.