# GPR Data Augmentation Methods by Incorporating Domain Knowledge
## 4 Result and Discussion  
### Evaluation Metrics  
The training loss value of YOLOv7 consists of _box_loss_, _cls_loss_, _obj_loss_, and the total loss value is the sum of these three losses (as shown in Equation (5)).  
\[Loss=box\_loss+cls\_loss+obj\_loss \tag{5}\]  
In Equation (5), _box_loss_ denotes the loss of object position, which measures how well the predicted bounding box locates an object. The IoU loss function was used to calculate the _box_loss_. The IoU is the ratio of the intersection and union between the predicted bounding box and the ground-truth box. The _cls_loss_ denotes the loss of object category loss, which measures the probability that the region of interest exists an object. The _obj_loss_ denotes the loss of whether it contains the object, which indicates how well the model can predict the object correctly [39].  
To evaluate the performance of the data augmentation method in this paper, the following evaluation metrics were used, such as precision (\(P\)), recall (\(R\)), \(F\_1\_score\), and the mean average precision (mAP). Additionally, the evaluation metrics can be calculated as follows:  
\[P=\frac{TP}{TP+FP} \tag{6}\]  
\[R=\frac{TP}{TP+FN} \tag{7}\]  
In Equations (6) and (7), \(TP\) is the number of true positives, which means that there is subsurface distress in the ground truth value, and so do prediction. \(FP\) is the number of false positives, it means that there is no subsurface distress in the ground truth value, but it is predicted that there is distress. \(FN\) is the number of false negatives, which is the opposite of \(FP\). \(P\) denotes how well the model in classifying an object as positive, and \(R\) denotes the ability to detect the positive samples.  
\[F\_1\_score=2\cdot\frac{P\cdot R}{P+R} \tag{8}\]  
\[AP=\int_{0}^{1}P(r)\cdot dr \tag{9}\]  
The values of \(F\_1\_score\) combines the result of \(P\) and \(R\) ranges from [0, 1], in which 1 denotes the best output of the model and 0 denotes the worst output of the model. \(AP\) is defined as the area under the \(P-R\) curve, which measures the model's accuracy for each class, and \(P(r)\) refers to the precision value for which the recall is \(r\). \(mAP\) is the average  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Augmentations**} & \multicolumn{2}{c}{**Gain Compensation**} & \multicolumn{3}{c}{**Station Spacing**} & \multicolumn{3}{c}{**Radar Signal Imaging**} \\ \cline{2-10}  & **2 Times** & **4 Times** & **8 Times** & **2 Times** & **4 Times** & **8 Times** & **2 Times** & **4 Times** & **8 Times** \\ \hline The number of cavities & 624 & 1248 & 2496 & 624 & 1248 & 2496 & 624 & 1248 & 2496 \\ The number of cracks & 542 & 1084 & 2168 & 542 & 1084 & 2168 & 542 & 1084 & 2168 \\ The number of images & 1094 & 2188 & 4376 & 1094 & 2188 & 4376 & 1094 & 2188 & 4376 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The statistics of augmented data for training.  
of \(AP\) for all classes. \(mAP\_0.5\) is the mean average precision that the IoU threshold is 0.5. \(mAP\_0.5:0.95\) represents the average \(mAP\) at different IoU thresholds (from 0.5 to 0.95 in steps of 0.05).