## 3 Experiments
### Evaluation Criteria  
Extensive studies associated with object detection have confirmed that indicators including Precision, Recall, Average Precision (AP), and mean Average Precision (mAP), can jointly describe the performance of a learning model. Usually, the higher values of these indicators represent better performance. The indicators can be formalized as below:  
\[Precision=\frac{TP}{TP+FP}\times 100\%\;, \tag{8}\]  
\[Recall=\frac{TP}{TP+FN}\times 100\%\;, \tag{9}\]  
where \(TP\), \(FP\), and \(FN\) indicate the number of true positives, false positives, and false negatives, respectively. _Precision_ is defined as the fraction of relevant instances among all retrieved instances. _Recall_, sometimes referred to as Sensitivity, is the fraction of retrieved instances among all relevant instances. To identify the surface defects on an arc magnet, the _Recall_ indicator for a category of defects should reach 100% to ensure that the category can be completely identified.  
\[AP=\frac{1}{M}\Sigma_{i=1}^{M}\rho_{interp}(r_{i})\;, \tag{10}\]  
\[mAP=\frac{1}{N}\Sigma_{i=1}^{N}AP_{i}\;, \tag{11}\]  
where \(\rho_{interp}(r_{i})\) is the precision corresponding to the \(i\)-th _Recall_ (\(r_{i}\)); \(M\) refers to the number of _recall_s associated with all interpolated points; \(N\) refers to the number of object categories; \(AP_{i}\) denotes the average precision for the \(i\)-th class of objects.  
According to the actual manufacturing needs, the surface defect identification of arc magnets is particularly concerned with the other accuracy indicator, named \(A_{D}\), which refers to the correct identification rate of all defective samples. Unlike _Precision_ and _Recall_, which correspond to the quantitative identification accuracy for identifying a certain category of surface defects from all samples, \(A_{D}\) is the qualitative indicator for determining whether each sample is defective, regardless of the category. An increase in \(A_{D}\) indicates that a sample that has defects can be determined more accurately. It is worth noting that in  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multicolumn{6}{c}{**Basic Data**} & \multicolumn{6}{c}{**Expanded Data**} & \multirow{2}{*}{**Total**} \\ \cline{2-2} \cline{4-9}  & **Free** & **Blowhole** & **Break** & **Crack** & **Fray** & **Uneven** & **Stained** & **Unfilled** & **Scratched** \\ \hline Validating set & 200 & 203 & 248 & 215 & 219 & 200 & 206 & 200 & 200 & 1891 \\ Testing set & 200 & 201 & 217 & 217 & 224 & 200 & 212 & 200 & 200 & 1871 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._the case of high-quality arc magnet manufacturing, \(A_{D}\) should be strictly 100% to ensure the absolute reliability of the product quality. The indicator can be defined as follows:  
\[A_{D}=\frac{\Sigma_{i=1}^{N}TP_{i}}{\Sigma_{i=1}^{N}(TP_{i}+FN_{i})}\times 100 \%\,, \tag{12}\]  
where \(TP_{i}\) and \(FN_{i}\) are the numbers of true positives and false positives for the \(i\)-th category of surface defects, respectively.  
To further analyze the model performance in detail, additional indicators, including the total number of network parameters (TNNP), floating-point operations per second (FLOPS), model size (MS), and average inference time consumption for one image (AITC), were also considered as evaluation metrics in our study. These additional indicators are frequently utilized to quantify model complexity, computing power burden, and runtime speed.