## 2 Research on Winding Looseness Tests of Power Transformers
### The Basic Structure of ConvNeXt Model  
The ConvNeXt architecture encompasses five distinct variants: ConvNeXt-Tiny, ConvNeXt-Small, ConvNeXt-Base, ConvNeXt-Large, and ConvNeXt-XLarge. As delineated in Table 2, ConvNeXt-Tiny features a streamlined design with fewer layers, while maintaining identical kernel dimensions to its counterparts. This lightweight configuration results in a parameter count just one-third that of ConvNeXt-Base, leading to reduced computational overheads and power consumption--qualities well suited for integration into fault diagnosis hardware. Moreover, its inference speed exceeds 80 FPS, fulfilling the latency requirements of real-time image classification tasks. Through comprehensive evaluation, ConvNeXt-Tiny was selected as the training model for this study. The ConvNeXt model draws on the design concept of transformer and adopts a hierarchical structure to divide the network into five modules. The model block diagram is shown in Figure 10. When the two-dimensional feature map enters the network, the Stem layer's convolution operation conducts an initial extraction of feature information, and the layer normalization operation is utilized to lower the resolution. The ConvNeXt-Tiny model has four stages, each stage contains different numbers of ConvNeXt modules, and there are downsampling operations between the stages. The ConvNeXt blocks in stages 1 to 4 further extract and refine the feature maps output by the Stem layer, and they improve the expression ability of the feature maps by increasing the number of channels. Finally, the feature map output from stage 4 is globally averaged in the spatial dimension, and the feature map of each channel is compressed into a scalar. Then, the feature vector is mapped to the number of categories through a fully connected layer, and the recognition accuracy corresponding to each category is provided as output. As shown in Figure 11, in contrast to the traditional residual module, the ConvNeXt module introduces depthwise convolution. Firstly, a 7 \(\times\) 7 convolution kernel is used for each input channel to perform deep spatial convolution operation. After layer normalization, the influence of internal covariate offset is reduced, and the acceleration model converges. The 1 \(\times\) 1 convolution is applied to fuse the output channels of the deep convolution, which significantly reduces the amount of calculation and maintains a good feature information extraction ability. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & \multirow{2}{*}{**Kernel Size**} & \multirow{2}{*}{**Layers**} & **Parameter** & **Inference** & \multirow{2}{*}{**FPS**} \\
**Variants** & & & **Count** & **Time** & \\ \hline Tiny & 1 \(\times\) 7 \(\times\) 7 & 18 & \(\sim\)29 M & \(\sim\)12 ms & \(\sim\)83 FPS \\ Small & 1 \(\times\) 7 \(\times\) 7 & 24 & \(\sim\)50 M & \(\sim\)20 ms & \(\sim\)50 FPS \\ Base & 1 \(\times\) 7 \(\times\) 7 & 24 & \(\sim\)89 M & \(\sim\)35 ms & \(\sim\)28 FPS \\ Large & 1 \(\times\) 7 \(\times\) 7 & 24 & \(\sim\)190 M & \(\sim\)70 ms & \(\sim\)14 FPS \\ XLarge & 1 \(\times\) 7 \(\times\) 7 & 24 & \(\sim\)290 M & \(\sim\)110 ms & \(\sim\)09 FPS \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameter comparison of ConvNeXt model variants. Figure 10: ConvNeXt-Tiny model block diagram. Gaussian Error Linear Unit (GELU) [38] was picked as the activation function, and the following is its formula:  
\[GELU(x)=x\cdot\frac{1}{2}\bigg{(}1+erf\bigg{(}\frac{x}{\sqrt{2}}\bigg{)}\bigg{)} \tag{11}\]  
In this formula, erf is the error function, defined as follows:  
\[erf(x)=\frac{2}{\sqrt{2}}\int_{0}^{x}e^{-\tilde{x}^{2}}dt \tag{12}\]  
According to Formula (11), the GELU function is a nonlinear smoothing function, and the activation intensity is dynamically adjusted according to the distribution of input values. In the ConvNeXt module, the number of activation functions used is reduced, and only one activation function is added between two \(1\times 1\) convolutions.