## 3 Experiments Results and Discussion
### Quantitative and Qualitative Analysis  
In this paper, to test and verify the feasibility of the CSPD-YOLO model for insulator fault detection, experiments were conducted on YOLO-v3, the model in the literature [38] (two Dense blocks were added to the backbone network of YOLO-v3), YOLO-v4, and the CSPD-YOLO model. To perform a fair comparison, the four network models were trained and tested on the dataset 'InSF-detection'. In the field of machine learning, four common types are used to evaluate binary classification model, including true positive (TP), false positive (FP), true negative (TN), and false negative (FN), which are defined in Table 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Ground Truth** & **Predicted** & **Definition** \\ \hline Positive & Positive & TP \\ Positive & Negative & FP \\ Negative & Positive & TN \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The definition of TP, FP, TN, and FN. Figure 7: The clustering results on dataset ‘InSF-detection’. The average precision (AP), precision (P), recall (R), F1 score, and running time are employed to evaluate performances of the compared networks: YOLO-v3, method in the literature [38], YOLO-v4, and CSPD-YOLO model. The precision (P), recall (R), and F1 score are defined in Formulas (7)-(9), respectively. The P-R curve is composed of precision (P) and recall (R), taking recall (R) as the x-axes and precision (P) as the y-axis. AP is the closure area of the P-R curve, which is defined in Formula (10). \[P =\frac{\text{TP}}{\text{TP}+\text{FP}} \tag{7}\] \[R =\frac{\text{TP}}{\text{TP}+\text{FN}}\] (8) \[\text{F1} =\frac{2\times P\times R}{P+R}\] (9) \[\text{AP} =\int_{0}^{1}P(R)dR \tag{10}\]  
The experimental effects of different networks for insulator fault detection are listed in Table 7, and the P-R curves of the proposed network and the compared networks (YOLO-v3, the model in the literature [38], and YOLO-v4) are shown in Figure 8, which were conducted on the testing set of 'InSF-detection'. Specifically, the average precision (AP) values of the four network models were YOLO-v3 (93.31%), the literature model [38] (95.07%), YOLO-v4 (96.38%), and the CSPD-YOLO model (98.18%), and the AP of the CSPD-YOLO model was 4.9%, 3.1%, and 1.8% higher than that of YOLO-v3, the literature model [38], and YOLO-v4, respectively. The precision (P) values of the four network models were YOLO-v3 (94%), the literature model [38] (97%), YOLO-v4 (98%), and the CSPD-YOLO model (99%), and the precision (P) of the CSPD-YOLO model was 5%, 2%, and 1% higher than that of YOLO-v3, the literature model [38], and YOLO-v4, respectively. The recall (R) values of the four network models were YOLO-v3 (94%), the literature model [38] (95%), YOLO-v4 (95%), and the CSPD-YOLO model (98%), the recall (R) of the CSPD-YOLO model was 4%, 3%, and 3% higher than that of YOLO-v3, the literature model [38], and YOLO-v4, respectively. The F1 score values of the four network models were YOLO-v3 (94%), the literature model [38] (96%), YOLO-v4 (97%), and the CSPD-YOLO model (99%), and the F1 score of the CSPD-YOLO model was 5%, 3%, and 2% higher than that of YOLO-v3, the literature model [38], and YOLO-v4, respectively. Based on the values of average precision (AP), precision (P), recall (R), and F1 score, it is proved that the proposed CSPD-YOLO model is superior to the compared networks. The running times of the networks were YOLO-v3 (0.01 s), the literature model [38] (0.011 s), YOLO-v4 (0.01 s), and the CSPD-YOLO model (0.011 s), and it can be concluded that the proposed CSPD-YOLO model can run in real time. Consequently, as it achieves a good trade-off between average precision (AP), precision (P), recall (R), F1 score, and running time, the proposed CSPD-YOLO model may be more advantageous than YOLO-v3, the literature model [38], and YOLO-v4.