## 3 Experimental Results and Discussion
### Analysis of the Proposed Network  
The experiments are conducted on a PC with an Intel quad-core i7-7700, 3.6 GHz CPU, 32 G of RAM, and a NVIDIA GeForce TITAN XP (12 GB). The proposed network is trained on Dark-net framework [55] and it takes 28 h to obtain its final model. After that, the final model and the source code of the proposed insulator faults detection method are evaluated on the Visual studio framework. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Image Number** & **Training Set** & **Testing Set** & **Image Size** & **Insulator String Number** \\ \hline
4031 & 2675 & 1356 & 416 px \(\times\) 416 px & 9609 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The InST\(\_\)detection dataset. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Image Number** & **One-Fault** & **Multi-Fault** & **Image Size** & **Fault Number** \\ \hline
120 & 60 & 60 & 800 px \(\times\) 530 px & 228 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The insulator faults dataset. To evaluate the effectiveness of the proposed network, the 'InST_detection' dataset is divided into the training set and the testing set. The training set consists of 2675 images and the testing set is composed of 1356 images, approximately 2:1. We compare the proposed network with four existing networks: YOLOv3, YOLOv2, YOLOv3-tiny, and ResnetV2. Specifically, YOLOv3 and YOLOv2 are considered to be the state-of-the-art one-stage object detectors that can achieve good performances and run in real-time. YOLOv3-tiny is the abbreviated version of YOLOv3, which runs faster than YOLOv3. ResnetV2 takes the Resnet50 as the backbone and adopts the header layer of YOLOv2 as the detection layer. For a fair comparison, both the compared networks and the proposed network are trained and tested on the 'InST_detection' dataset. Moreover, three measurements: AP, running time, and Memory usage, are introduced to validate the effectiveness of the proposed network quantitatively. \[\left\{ \begin{array}{c}\text{Precision}=\frac{\text{TP}}{\text{TP}+\text{FP }}\\ \text{Recall}=\frac{\text{TP}}{\text{TP}+\text{FN}}\end{array} \right. \tag{5}\]  
Specifically, AP indicates the area under each Precision-Recall curve (i.e., PR-curve); the better the network, the higher the AP value. The definitions of Precision and Recall are given in Formula (5). Specifically, True Positive (TP) indicates the number of insulators that have been correctly detected. False Positive (FP) and False negative (FN) indicates the number of background regions that are marked as insulators and the insulators that are incorrectly identified, respectively. We calculate the AP values for different networks after conducting on the testing set of the 'InST_detection' dataset, as shown in Figure 5, where the horizontal axis shows different recall values, and the vertical axis gives the corresponding precision values. Moreover, the running times and memory usages of different networks are also exhibited in Table 4. Based on the observation of Figure 5, it is found that the AP value of the proposed network (89.96%) is higher than that of the YOLOv2 (89.83%), the ResnetV2 (85.92%), and the YOLOv3-tiny (52.78%), while is only a little smaller than that of the YOLOv3 (90.05%), which means that the performance of the proposed network is almost consistent with that of the state-of-the-art object detection networks (i.e., YOLOv3 and YOLOv2) and is superior to the ResnetV2 and YOLOv3-tiny. When considering the running times and the memory usages, both the proposed networks, YOLOv3 and YOLOv2, can run in real-time, while the memory usage of the proposed network is 14.5% and 21.5% less than that of the YOLOv3 and the YOLOv2, respectively. Therefore, the proposed network is more advantageous when been deployed on embedded devices. Figure 5: The Precision-Recall curves (PR-curves) of the proposed network and the four compared networks. Figure 6: Experiments in different aerial scenes. First row: sky. Second row: mountain. Third row: building and road. Fourth row: forest. Fifth row: farmland.