## 3 Experimental Results and Discussion
### Analysis of the Proposed Insulator Multi-Fault Detection Method  
To verify the importance of the step 2 in the proposed insulator faults detection method (i.e., Section 2.2), an ablation experiment is developed and the results are shown in Figure 8. The average precision rate and the average recall rate are used to exhibit all the experimental results in Section 3.2, and we follow the rounding principle to keep only one digit after the decimal point. \[\left\{ \begin{array}{c}\text{Precision}=\dfrac{1}{n}\sum\limits_{i=1}^{n} \text{Precision (i)}\\ \text{Recall}=\dfrac{1}{n}\sum\limits_{i=1}^{n}\text{Recall (i)}\\ i=1,2,3\ldots,n\end{array} \right. \tag{6}\]  
In formula (6), \(n\) indicates the total image number in a testing set. Precision (i) and Recall (i) show the precision rate and the recall rate when detecting the \(i\)th image, respectively. Precision and Recall indicate the average precision rate and the average recall rate in a testing set, respectively. Based on the observation of Figure 8, it is found that by setting the threshold of the aspect ratio of the contour for interference contour filtering, the precision rate can be increased by 14% and the recall rate by 10.8%. To verify the rationality of the choice of 1:5, different ratios are selected to perform experiments on our dataset. The results are shown in Table 5. It can be seen that the 1:5 is the most appropriate ratio, which achieves precision rate 96.3%, and recall rate 93.3%. Figure 7: Experiments on two UAV-based insulator aerial videos. In (**a**,**b**), the performances of the proposed method in consecutive 9 frames are shown in order from left to right and top to bottom. To verify the performances of the proposed insulator fault detection method, we compare it with methods [11; 20], which are considered to be the state-of-the-art methods. Moreover, for a fair comparison, all the insulator fault images are normalized to the same size of \(800\times 530\) as the way used in the work of [11; 20]. For the insulator one fault detection, some typical images are selected and tested as shown in Figure 9. The first column to the third column depicts the performance of the proposed method, method [20], and method [11], respectively. The detected insulator fault positions are marked with red bounding boxes. It can be observed that the bounding boxes detected by the proposed method are much closer to the real insulator faults, which means that the proposed method yields more accurate results. On the contrary, the methods [11; 20] are quite sensitive to the background interference and result in error detections. In the second row of Figure 8, method [20] does not detect the insulator fault, which leads to a wrong judgment that the working state of the insulators is normal. In the third row of Figure 9, the performance of method [11] is affected by the complex background interferences and part of the power tower is regarded as an insulator fault. To verify the accuracy of the proposed method in the case of insulator multi-fault detection, we choose some typical insulator multi-fault images from our dataset, some examples are shown in Figure 10. Based on the observation of Figure 10, the methods [11; 20] can only detect one insulator fault, while the proposed method can detect not only one insulator fault but also insulator multi-fault. Figure 8: The Ablation experiment. By setting the threshold of the aspect ratio of the contour for interference contour filtering, the Precision rate can be increased by 14% and the Recall rate by 10.8%. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Height/Width** & **1:2** & **1:3** & **1:4** & **1:5** & **1:6** & **1:7** & **1:8** \\ \hline Precision & 65\% & 81.3\% & 89.6\% & 96.3\% & 94.2\% & 93.8\% & 93.8\% \\ Recall & 57\% & 76.5\% & 85.9\% & 93.3\% & 91.9\% & 91.7\% & 92.1\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Different height/width threshold settings. The maximum values are marked in bold. Figure 10: Experimental results in aerial images with insulator multi-fault.