## 2 Materials and Methods
### The Feature Pyramid Network of CSPD-YOLO Model  
In the deep neural networks, the low-level (high-resolution) feature layer contains more detailed information, and the high-level (low-resolution) feature layer contains more semantic information. As the network layer gradually deepens, the detailed information continues to decrease, while the semantic information continues to increase. To achieve multi-scale object detection, the feature pyramid network (FPN) fuses high-level semantic information with low-level detailed information of different layers, which can improve feature extraction capabilities and the detection accuracy of small objects.  
To obtain multi-scale semantic information of insulator faults, motivated by the works of [47; 48; 49], a structure of the feature pyramid network was adopted in this paper, as shown in Figure 5. The multi-scale prediction process of insulator faults is as follows: firstly, the large feature layer (LFL0) 256 \(\times\) 52 \(\times\) 52, medium feature layer (MFL0) 512 \(\times\) 26 \(\times\) 26, and small feature layer (SFL0) 1024 \(\times\) 13 \(\times\) 13 were effective feature layers extracted from the backbone network of the CSPD-YOLO model. Secondly, the feature layer SFL1 was obtained after the convolution operation of feature layer SFL0, and then feature layer SFL1 was fused with feature layer MFL0 via up-sampling to generate feature layer MFL1, while the feature MFL1 was fused with feature layer LFL0 via up-sampling to obtain feature layer LFL1. Finally, feature layer LFL2 was obtained after the convolution operation of feature layer LFL1, and then the feature layer LFL2 was fused with feature layer MFL1 via down-sampling to generate feature layer MFL2, while the feature layer MFL2 was fused with feature layer SFL1 via down-sampling to obtain feature layer SFL2. The feature layers LFL2, MFL2, and SFL2 were connected to three residual units for multi-scale prediction,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Type** & **Filters** & **Size** & **Output** \\ \hline  & Convolutional & 32 & \(3\times 3/1\) & \(32\times 416\times 416\) \\ \hline  & Convolutional & 64 & \(3\times 3/2\) & \\ \multirow{3}{*}{\(1\times\)} & Convolutional & 32 & \(1\times 1/1\) & \\  & Convolutional & 64 & \(3\times 3/1\) & \\  & Residual & & & \(64\times 208\times 208\) \\ \hline  & Convolutional & 128 & \(3\times 3/2\) & \\ \multirow{3}{*}{\(2\times\)} & Convolutional & 64 & \(1\times 1/1\) & \\  & Convolutional & 128 & \(3\times 3/1\) & \\  & Residual & & & \(128\times 104\times 104\) \\ \hline  & Convolutional & 256 & \(3\times 3/2\) & \\ \multirow{3}{*}{\(4\times\)} & Convolutional & 128 & \(1\times 1/1\) & \\  & Convolutional & Residual & & \(3\times 3/1\) & \\ \multirow{3}{*}{Convolutional} & \multirow{3}{*}{\(256\times 3\times 3\)} & Convolutional & 128 & \(1\times 1/1\) \\  & & Convolutional & 32 & \(3\times 3/1\) & \\  & Dense & & & \(256\times 52\times 52\) \\ \hline  & Convolutional & 512 & \(3\times 3/2\) & \\ \multirow{3}{*}{Convolutiona} & \multirow{3}{*}{\(8\times\)} & Convolutional & 256 & \(1\times 1/1\) & \\  & & Convolutional & 32 & \(1\times 1/1\) & \\  & Dense & & & \(512\times 26\times 26\) \\ \hline  & Convolutional & 1024 & \(3\times 3/2\) & \\ \multirow{3}{*}{\(4\times\)} & Convolutional & 512 & \(1\times 1/1\) & \\  & Convolutional & 1024 & \(3\times 3/1\) & \\  & Residual & & & \(1024\times 13\times 13\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The feature extraction network of CSPD-YOLO.  
respectively. Feature reuse was further realized by the top-down and bottom-up feature fusion strategies, which can effectively improve the prediction accuracy of insulator faults. The parameters of three residual units are shown in Table 3.