## 3 Data Preparation and Experiments Setup
### Dataset Augmentation and Experimental Setup  
Deep learning target detection always needs a large number of images to prevent model over-fitting. Since there is no public infrared image data set of high-temperature  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Air thermal conductivity/W-m\({}^{-1}\)\({}^{\circ}\)C\({}^{-1}\) & 0.0807 \\ 8 YSZ thermal conductivity/W-m\({}^{-1}\)\({}^{\circ}\)C\({}^{-1}\) & 2.43 \\ Topcoat temperature/\({}^{\circ}\)C & 1212 \\ Substrate temperature/\({}^{\circ}\)C & 844 \\ Horizontal velocity of upper boundary fluid/m-s\({}^{-1}\) & 23 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Calculation parameters of the numerical model.  
TBCs, and the simulation samples are relatively limited, a series of operations were carried out to expand the dataset. The size of the dataset can be augmented through certain geometric transformations and size transformations of the image, such as rotation, flip, clipping, scaling transformation, and so on. Clipping did not work well since the method of crop and mix often does not meet the characteristics of coating heat conduction, and will make the infrared image very unnatural. Although the scale of coating cracks may change, the pores of the coating are often fixed, so changing the scale to enhance the data is also ineffective. Rotation and flip are adopted and proved useful in this paper. The original image dataset is enhanced to 1083 images. In order to make full use of the dataset, a 5-fold cross validation is conducted. The specific steps are as follows: the initial sampling is divided into 5 sub samples, a single sub sample is retained as the data of the validation model, and the other 4 samples are used for training. The cross validation is repeated 5 times, and each sub sample is verified once. The results of 5 times in total are used to obtain the estimation result.  
The code is implemented in the TensorFlow framework. TensorFlow is an end to end software library developed by the Google brain team for machine learning. It contains various open source tools and libraries, enabling developers to build and deploy applications supported by deep learning. Adaptive momentum (ADAM) is chosen as the optimizer. Adam is an adaptive moment estimation gradient descent algorithm. Its super parameters are well interpretable, and can generate adaptive learning rates for different network parameters, so that the gradient update is more stable and natural, and efficient convergence can be achieved. The mini-batch size of the RPN stage and classification stage is 8. The initial learning rate of the first 35,000 iterations is 0.0001 while the learning rate of the subsequent 5000 iterations is 0.001 to increase the training speed. The maximum iterations are set to 40,000. The momentum is 0.9 and the weight decay is 0.0001.  
In the stage of RPN, various shape and scale parameters of anchors are set, as well as the thresholds of anchors and true cracks to select positive and negative samples. In training the RPN network, when the overlap between the ground truth and the anchors meets the conditions, the anchors can be used to train the RPN network. Figure 2 shows the training curve of the MSE-Faster R-CNN. In this figure, Loss_cls represents the loss of classification, which refers to the difference between the predicted class and the actual class through the Softmax layer. Loss_bbox represents the loss of crack location, which refers to the difference between the predicted anchor location and the actual anchor location during the training stage by calculating the most fit anchor box after NMS. In the training phase, these two loss functions are minimized to achieve higher accuracy. From the figure it can be seen that both the loss of classification and the loss of regression converge after 40,000 iterations, decreasing from 90% of the initial iteration to less than 15%.  
Figure 2: Training curves of MSE-Faster R-CNN.