# CPDet: Circle-Permutation-Aware Object Detection for Heat Exchanger Cleaning
## 4 Results
### Experimental Results  
In this experiment, this work used the \(mAP_{50}\), \(mAP_{90}\), and \(mAP_{50:95}\) as the evaluation metrics for heat exchanger circle detection. The mAP values were calculated using Equation (22). By comparing the experimental results of the YOLO series and the improved method, it can be inferred that our method is better than the YOLO series in detecting circles in the HE dataset, and the modules proposed in this paper can be plug-and-play  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**YOLOv8s Backbone**} & \multirow{2}{*}{\(mAP_{50}\)} & \multirow{2}{*}{\(mAP_{90}\)} & \multirow{2}{*}{\(mAP_{50:95}\)} \\ \hline
**IPE + IPF** & **PSA** & & & \\ \hline  & & 81.63\% & 77.49\% & 77.13\% \\ ✓ & & 82.92\% & 81.94\% & 79.33\% \\  & ✓ & 84.33\% & 84.12\% & 80.34\% \\ ✓ & ✓ & **86.87\%** & **85.23\%** & **82.65\%** \\ \hline \hline \end{tabular} The \(\checkmark\) represents the module that takes this column, and the **bold** indicates the highest value for this column metric.  
\end{table}
Table 6: Ablation experiments on different modules.  
Figure 9: The circle domain and background domain under varying trimming rates.  
in the YOLO series shown in Table 7; also note that CPDet(v3) represents the test results with YOLOv3 as the backbone and the same applies to CPDet(v5) and CPDet(v8). On our self-collected heat exchanger dataset, conducting a visual comparative analysis of detection results using different algorithms, as shown in Figure 10, demonstrates that the approach has avoided most of the error detections compared to other methods and has also significantly reduced the rate of false negatives. In the HE dataset, the heat exchangers are the same type; therefore, the number of circle holes on the end face is constant. Therefore, we tallied the total number of objects in the dataset to further calculate the True Positive Rate (TPR), False Positive Rate (FPR), and False Negative Rate (FNR), shown in Equations (19)-(21), which can intuitively display the performance gains of the model in actual scenarios.  
\[Precision =\frac{TP}{TP+FP}, \tag{15}\] \[Recall =\frac{TP}{TP+FN},\] (16) \[AP =\sum_{n=1}^{N}Precision_{n}\times\Delta Recall_{n},\] (17) \[mAP =\frac{\sum_{i=1}^{k}AP_{i}}{k},\] (18) \[F1 Score =2\times\frac{Precision\times Recall}{Precision+Recall},\] (19) \[TRP =\frac{TP}{TNO},\] (20) \[FNR =\frac{FN}{TNO},\] (21) \[FPR =\frac{TNO-TP}{TNO}, \tag{22}\]  
where \(TP\) (True Positive) represents the correctly detected positive samples, \(FP\) (False Positive) represents the incorrectly classified negative samples as positive, and \(FN\) (False Negative) represents the incorrectly predicted positive samples as negative. TNO (Total Number of Objects) represents the total number of objects to be detected in each image in the dataset. \(Precision_{n}\) represents the precision at the \(n\)th recall threshold. \(\Delta Recall\) denotes the interval between the recall threshold at the \(n\)th point and that at the preceding point.  
Figure 10: The actual comparative gains of our method compared with the baseline method, where the red box indicates successful reduction of the False Positive results, and the blue box indicates successful reduction of the False Negative results; moreover, the gray box indicates a failed reduction of the False Negative results.  
In the conducted experiments, the performance of the improved model was evaluated using a test set from the heat exchanger dataset, as shown in Table 8. The areas highlighted in blue represent the outcomes achieved by augmenting the baseline approach with the proposed method. It can be seen from the ablation experiment that our method can better focus on the detection of circles and greatly improved the YOLO method detection performance.