## 4 Experiments Results and Discussions
### Large Scale Crack Detection Experiments and Discussion  
In the real gas turbine operation process, it is difficult to detect cracks on global scope due to the limitation of shooting resolutions. Under such conditions, if the detection of large cracks (between 100 \(\mu\)m to 260 \(\mu\)m) can be realized on global scope, it can effectively avoidthe occurrence of major risks. Therefore, in this section, the detection of cracks between 100 \(\upmu\)m and 260 \(\upmu\)m in a large coating model will be discussed.  
Figure 3 shows the detection results for different coating porosity and length of large scale cracks. The upper row is the temperature distribution of the coating with internal cracks. The temperature distribution here is intercepted by the numerical model in the state of heat exchange convergence, that is, it can be regarded as the final image surface temperature distribution. The temperature legend attaching the input image is generated based on the maximum and minimum temperature of the color temperature map, which will make the quality of the image reach the best possible level. The middle row is the feature visualization result, which maps the features in the convolution process to the pixel space to realize visualization, so as to observe the abstract process more intuitively. Since the model network is deep, an obvious convolution characteristic diagram is given. The correlation between the convoluted object and the convolution kernel can be calculated by the convolution kernel. The stronger correlation between the corresponding parts and the convolution kernel, the greater the convolution result will be. It can be seen from the figure that the deeper convolution layer makes the crack contour information fuzzy, but it can still show the area where the crack appears well. The bottom row is the detection results. The results show that cracks have been correctly detected with bounding boxes by using the detection scheme.  
\begin{table}
\begin{tabular}{c c c} \hline
**Models** & **Location Accuracy** & **Detection Accuracy** \\ \hline Alexnet & 0.711 & 0.662 \\ VGG-16 & 0.781 & 0.729 \\ VGG-19 & **0.814** & **0.733** \\ Resnet-50 & 0.732 & 0.725 \\ Resnet-101 & 0.778 & 0.732 \\ \hline \end{tabular}
\end{table}
Table 2: Accuracies of different baseline network models.  
Figure 3: Examples of large scale crack detection results of using MSE-Faster R-CNN. (**a**) Porosity = 5%, Crack length = 260 \(\upmu\)m; (**b**) Porosity = 20%, Crack length = 220 \(\upmu\)m; (**c**) Porosity = 15%, Crack length = 180 \(\upmu\)m; (**d**) Porosity = 10%, Crack length = 140 \(\upmu\)m; (**e**) Porosity = 25%, Crack length = 100 \(\upmu\)m.  
Figure 4 presents the confusion matrix of large-scale crack detection using the proposed algorithm. The confusion matrix is an analysis tool to measure the classification and prediction ability of the model. The rows of the confusion matrix represent the real value of each class and the columns represent the actual number of the predicted value of each class. The form of the confusion matrix is:  
\[C=C\big{[}c_{ij}\big{]},i,j=1,2,\ldots,K \tag{14}\]  
In Equation (14), \(C\) is the confusion matrix, \(K\) is the total classification number, \(c_{ij}\) represents the number of prediction results of classifying the class \(i\) samples represented by row \(i\) into the class \(j\) samples represented by column \(j\). Therefore, the main diagonal elements (\(i=j\)) in the confusion matrix indicate that the classification is correct, and other non-main diagonal elements are miss-predictions. From the figure it can be seen that the overall accuracy of the proposed method is 84.95%. With the increase of crack length, the detection accuracy increases; especially when the crack length is more than 260 \(\upmu\)m, the accuracy is more than 92%. This is because the longer crack has a greater influence on the whole region, which is more easily captured by the RPN network of MSE-Faster R-CNN in the training stage and regressed in the \(L_{1}\) smooth stage.