## 2 Proposed Method
### Insulator Faults Detection  
As previously mentioned, most of the existing methods can only give good results when detecting one fault in the insulator string, and they cannot detect an insulator multi-fault. To address these challenges, we refer to the work of [11,20], which are considered to be the state-of-the-art insulator one fault detection methods. Then, a novel solution with a systematic analysis is proposed for insulator multi-fault in this section. Figure 4 exhibits the flowchart of the proposed method, and detailed explanations are given as follows. First of all, based on the observations of large numbers of insulator aerial images, three important features of insulators were found, which are listed as follows. First, although the color of the insulators is similar to that of the background, the color between them is still different. Second, the positions of insulator faults are usually random, and these positions are not fixed. Last but not least, the contour sizes of different insulator faults are very similar in an image. Figure 4: Flowchart of the insulator multi-fault detection. Figure 3: Clustering box dimensions on ‘InST_detection’ Dataset. The horizontal axis indicates the number of clusters, and the vertical axis shows the corresponding average IoU. Subsequently, the proposed insulator faults detection method can be divided into the following three steps:  
**# Step 1**: Grab-cut algorithm [57] is adopted to manually segment the insulators region from 300 insulator aerial images in the training set of the InST_detection Dataset. After that, a more proper color distribution of the insulators in RGB color space can be concluded as following. \[\left\{ \begin{array}{c}56\leq R\leq 178\\ 110\leq G\leq 200\\ 30\leq G-R\leq 60\end{array} \right. \tag{3}\]  
Then, the insulators detected by the proposed network is marked by a rectangle bounding box. This bounding box is set to be a RoI. Finally, the color model listed in Formula (3) is applied to segment the insulators from the RoI. **# Step 2**: The adaptive morphology [20] is exploited to fill the gaps between the adjacent insulator pieces, and the insulator string becomes a connected component. Then, the coordinates of the connected component's minimum bounding rectangle are calculated, and the minimum bounding rectangle perform the 'XOR' operation with the connected component. Finally, the contours of the insulator fault candidates are highlighted. It is worth noting that these candidates consist of not only the contours of real insulator faults but also the interference contours. Based on the observation of the contours of the candidates, it is found that some of the interference contours are elongated rectangles. Therefore, parts of the interference contours can be removed by the following rule:  
\[\text{Candidate}= \begin{cases}1&\text{if }height/width\geq\dfrac{1}{5}\\ 0&\text{else}\end{cases}  \tag{4}\]  
In this work, if the aspect ratio of a contour is greater than 1:5, it should be retained in the candidate's sequence; otherwise, it will be regarded as an interference. **# Step 3**: In response to the actual situation, there are two aspects should be considered: (1) The number of the fault candidates is larger than the max number of the real-fault in aerial images of the 'InST_detection' dataset; and (2) the number of the fault candidates is just equal to the max number of the real-fault in the aerial image of 'InST_detection' dataset. In most cases, the number of fault candidates is larger than the real-fault in an image. Moreover, the area of the insulator fault contour is usually much larger than the area of the interference contour. Therefore, on the one hand, if the candidate number is larger than the max number of the real-fault in aerial images of 'InST_detection', the K-means algorithm is applied to cluster the candidate areas into two categories: real fault contours and interference contours. Subsequently, one of the two categories with a larger average area is considered as the real-fault.