# Deep Transfer Learning-Based Fault Diagnosis Using Wavelet Transform for Limited Data
## 5 Performance Evaluation
### Diagnosis Performance Analysis
The fault condition of \(l\geq 1\) is the general scenario in which each fault type contains various samples with different severity levels, while \(l=1,6\) shows how the different severity levels affect the overall classification accuracy. Figure 7: Confusion matrix of SVM (**a**), the CNN (**b**), and CNN–TL with various fault types, \(f_{0},\ldots,f_{7}\) (**c**). Let us first consider the general fault condition of \(l\geq 1\) with the mixed severity levels in each fault type. Overall, the classification accuracy of all models improves as the number of training samples increases. While both the CNN and CNN-TL improve the classification accuracy by adding more training data, the classification accuracy of SVM is low, around 0.68, even with the large training data. SVM's performance is fundamentally limited due to the manual feature extraction. Both the CNN and CNN-TL have a good classification accuracy of greater than 0.9 when they have sufficient training samples: \(r\geq 0.4\) and \(r\geq 0.2\), respectively. However, under the strictly limited training samples of \(r=0.1\), the corresponding classification accuracy of the CNN is significantly degraded to 0.75, while that of the CNN-TL is still around 0.87. The gap between the CNN and CNN-TL increases as the number of training data decreases. The classification accuracy of CNN-TL gradually tends to increase with the addition of more training data, while that of the CNN certainly improves for \(r\geq 0.4\). When the training sample is insufficient to train the CNN model, it leads to poor performance due to overfitting. The classification accuracy of the CNN-TL is 0.98 at \(r=0.4\), which is close to that of the one using the maximum training data \(r=0.8\). We note that the average training time of CNN-TL (resp. CNN) increases from 93.5 s to 512.2 s (resp. from 178.5 s to 1202.8 s) with the addition of more training data \(r=0.1,\ldots,0.8\). Different severity levels, \(l=1,6\), significantly affect the classification accuracy. For the severe fault condition of \(l=6\), the classification accuracy of the three classification models is greater than 0.93, even with the small training samples \(r=0.1\). However, when the fault becomes minor, \(l=1\), the performances of the different models varies considerably depending on the training data. CNN-TL still provides a classification accuracy of 0.71, while the CNN has a low accuracy of 0.61 for the small training samples \(r=0.1\). The fault diagnosis with a low severity level is crucial to achieving early fault detection since the impact of the fault is naturally worse due to the fault's propagation over time. This shows the effectiveness of CNN-TL when the training data of the CNN is not enough to learn the hidden features of the minor fault condition. To investigate the impact of the severity level, Figure 9 presents the classification accuracy of the three classification models with different ratios of the training data \(r=0.2,0.6\) as a function of the various severity levels \(l=1,\ldots,9\). Generally, the classification accuracy of the three classification models improves as the fault condition becomes severe due to its significant impacts on the time and frequency domains. Figure 8: Classification accuracy of SVM, the CNN, and CNN–TL with different ratios of the training data, \(r=0.1,\ldots,0.8\). The three classification models perform well for the severe fault condition \(l\geq 8\), while the accuracy trends are considerably different as the fault condition becomes minor. CNN-TL provides better classification accuracy than the other two models for all of the considered ranges of severity levels. Specifically, the worst fifth percentiles of the classification accuracy of SVM, the CNN, and CNN-TL with \(r=0.2\) (resp. \(r=0.6\)) are \(0.55,0.64\), and \(0.73\) (rep. \(0.58,0.75,0.91\)), respectively. Thus, CNN-TL shows a significant benefit when predicting the fault type, even if the fault condition is minor.