## 4 Experiments and Analysis of Results
### Comparison Experiments
#### 4.5.3 Comparison of Different Detector Models  
To comprehensively evaluate PCES-YOLO, comparative experiments were conducted against nine different detector models: Faster R-CNN (FR-CNN), SSD [38], YOLOv5n, YOLOv8n, YOLOv9t, YOLOv10n, YOLOv11n, YOLOv12n, and YOLOv11s. Consistent datasets and parameter configurations were maintained across all experiments. As shown in Table 5, PCES-YOLO achieves a mAP50 of 97.3%, significantly outperforming comparative models. Specifically, it surpasses Faster R-CNN by 11.6%, SSD by 21.0%, YOLOv5n by 3.9%, YOLOv8n by 3.8%, YOLOv9t by 5.2%, YOLOv10n by 5.6%, YOLOv11n by 3.6%, and YOLOv12n by 7.2%. Further, it also obtains consistent accuracy gains across all defect categories and maintains parameter efficiency with a reduced model size relative to YOLOv11n. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Loss Function** & **P/\%** & **R/\%** & **mAP50/\%** & **mAP50–95/\%** \\ \hline CIoU & 96.1 & 89.7 & 93.7 & 62.0 \\ SIoU & 95.7 & 89.4 & 93.5 & 61.8 \\ WIoU & 96.9 & 91.0 & 94.6 & 65.1 \\ Shape-IoU & 97.0 & 92.2 & 94.9 & 62.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative experimental results of different loss functions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Models** & **P/\%** & **R/\%** & **mAP50/\%** & **mAP50–95/\%** \\ \hline YOLOv11n & 96.1 & 89.7 & 93.7 & 62.0 \\ YOLOv11n + C3k2-RFE & 96.4 & 88.2 & 93.2 & 61.9 \\ YOLOv11n + C3k2-PRFE & 96.8 & 90.9 & 94.6 & 64.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative experimental results for different receptive field enhancement modules. Among benchmarked models, only YOLOv9t and YOLOv12n have fewer parameters. However, this reduction corresponds to substantially lower accuracy. Furthermore, YOLOv11n with higher detection accuracy is more suitable as the baseline than YOLOv5n, YOLOv8n, YOLOv9t, YOLOv10n, and YOLOv12n. Compared to YOLOv11s, PCES-YOLO achieves a 1.0% improvement in mAP50, a 5.6% enhancement in mAP50-95, a 0.9% increase in precision, and a 1.1% improvement in recall, thereby reducing false positives and missed detections, despite significant parameter reduction. Consistent accuracy improvements are observed across all defect categories. Tables 6 and 7, and Figure 7a present the training dynamics of PCES-YOLO compared to YOLOv11n, with faster and smoother loss convergence, a much lower loss value, strong training stability, and higher detection accuracy. Figure 7b-d indicate that PCES-YOLO outperforms YOLOv11n in precision, recall, and mAP50. During the initial 0-10 training epochs, PCES-YOLO exhibited a rapid decrease in loss, while its precision, recall, and mAP50 metrics increased rapidly. Its convergence speed was significantly faster than that of YOLOv11n. Between epochs 10 and 290, the performance metrics of PCES-YOLO stabilized, with its stable values surpassing those of YOLOv11n. In the 290-300 epoch phase, both PCES-YOLO and YOLOv11n showed an increase in loss, indicating overfitting to some extent. This phenomenon occurs because the models learn irrelevant features, such as noise, present in the training data. However, as demonstrated by the data in Tables 6 and 7, the severity of overfitting in PCES-YOLO was far lower than in YOLOv11n, demonstrating that it significantly mitigates overfitting risks and effectively suppresses loss fluctuations. The proposed model exhibits faster convergence and fewer training oscillations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Performance** & **50 Epochs** & **100 Epochs** & **150 Epochs** & **200 Epochs** & **250 Epochs** & **300 Epochs** \\ \hline Loss & 0.096 & 0.083 & 0.075 & 0.070 & 0.062 & 0.086 \\ Precision/\% & 96.06 & 98.04 & 98.23 & 98.62 & 98.55 & 98.61 \\ Recall/\% & 91.01 & 93.22 & 94.29 & 94.30 & 94.42 & 94.57 \\ mAP50/\% & 94.69 & 96.44 & 96.87 & 97.04 & 97.16 & 97.34 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of PCES-YOLO during the training process.