## 2 Materials and Methods
### Experimental Procedure  
Before the experiment, carbon particle samples, epoxy resin boards, and transformer oil were placed in a vacuum drying oven and treated at 80 \({}^{\circ}\)C and 50 Pa for 48 h to meet the insulation oil standards of the CIGRE working group [20; 21]. Subsequently, the carbon particles were mixed with transformer oil to form a suspension of 0.02 g/L and sealed for later use. Before each pour into the container, the suspension was evenly mixed using a magnetic stirrer. The electrode surface was covered with an epoxy resin board and fixed inside the container with bolts. The bolts were then adjusted to keep the distance between the epoxy resin boards at 4 mm. Then, the insulation oil suspension was poured into the container until the liquid level in the oil pillow was above the top of the container. During the experiment, a voltage was applied at a rate of 2 kV/s until the required voltage value was reached. After 10 m, the voltage was stopped. Then, the electrode was removed and placed under a microscope for observation. Twenty areas were randomly selected on the surface of the epoxy resin board for image acquisition. In order to quantitatively analyze the adhesion degree of carbon particles, it is necessary to process the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline Experiment & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ Number & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline Pump voltage (V) & 0.0 & 3.2 & 4.0 & 5.0 & 6.0 & 7.0 & 8.0 & 10.0 & 12.0 \\ Oil flow velocity (mm/s) & 0.00 & 0.29 & 0.96 & 3.30 & 6.19 & 9.19 & 12.03 & 15.67 & 18.40 \\ \hline \end{tabular}
\end{table} 
Table 4: The flow velocity conditions used in the experiment. Figure 6: Calculation results of electromagnetic–fluid–thermal field of the valve-side bushing. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline Experiment & **1** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** \\ Number & 5 & 10 & 15 & 20 & 25 & 30 & 40 & 50 & 60 \\ Electric field & 0.17 & 0.34 & 0.51 & 0.69 & 0.86 & 1.03 & 1.37 & 1.71 & 2.06 \\ intensity (kV/mm) & 0.17 & 0.34 & 0.51 & 0.69 & 0.86 & 1.03 & 1.37 & 1.71 & 2.06 \\ \hline \end{tabular}
\end{table} 
Table 3: The electric field conditions used in the experiment. collected images. Due to the significant color difference between carbon particles and epoxy resin boards, image segmentation methods can be used to distinguish carbon particles in the field of view from the background epoxy resin. Due to the relatively small proportion of total adhesion area of carbon particles in the images collected in the experiment, the calculation of adhesion feature parameters is sensitive to image segmentation errors. Therefore, even if only a small amount of error and noise is generated during image processing, it may still have a significant impact on the calculation results. In order to improve the accuracy of image segmentation as much as possible and reduce the impact of interference factors such as uneven field of view lighting, local impurities, and shadows, this paper uses the two-dimensional moving average variable threshold method for edge recognition. The basic principle is to scan the entire image along the line, calculate a local average threshold separately for each pixel, and distinguish whether the pixel is located at the edge of the particle based on the relationship between its grayscale value and the corresponding local average threshold, as shown in Equation (1). \[g(x,y)= \begin{cases}0&f(x,y)<\lambda_{T}T_{x,y}\\ 1&other\end{cases}  \tag{1}\]  
where \(g(x,y)\) is the value of the pixel located at coordinate \((x,y)\) in the binary image; \(f(x,y)\) is the grayscale value of the pixel in the initial grayscale image; \(\lambda_{T}\) is the segmentation coefficient where the specific value needs to be set according to the overall characteristics of the image; and \(T_{x,y}\) is the local average threshold corresponding to the pixel point. The calculation method is shown in Equation (2).