## 2 Methodology
### Adaptive Distribution Normalization  
The adaptive distribution normalization module enables the pavement distress detection model to better adapt to data from different target domains. It further enhances the model's generalization ability across domains. Additionally, besides differences in viewpoint and background, there are other factors such as varying lighting conditions, shadows, and other disturbances in the pavement distress datasets across different domains. These factors can also lead to a decrease in performance when object detection models' transfer application. Therefore, it is necessary to normalize the distribution of images between different domains. Feature normalization is an important step to ensure model stability and convergence for deep learning models. It helps prevent gradient explosions during backpropagation and optimization. Additionally, normalization allows the model to adapt to data of different scales and ranges, thus enhancing its generalization capability. Generally, the formula for normalizing the same batch \(\{x_{1},x_{2}\ldots x_{n}\}\) during training is as follows:  
\[\mu_{B}=\frac{1}{n}{\sum\limits_{i=1}^{n}{x_{i}}} \tag{4}\]  
\[\sigma_{B}^{2}=\frac{1}{n}{\sum\limits_{i=1}^{n}{(x_{i}-\mu_{B})}^{2}} \tag{5}\]  
\[\widetilde{x}_{i}=\frac{x_{i}-\mu_{B}}{\sqrt{\sigma_{B}^{2}}}x \tag{6}\]  
\[y_{i}=\gamma\widetilde{x}_{i}+\beta \tag{7}\]  
where \(\mu_{B}\) and \(\sigma_{B}\) are the mean and variance of the same batch of data, respectively. \(\widetilde{x}_{i}\) represent the normalized results. \(y_{i}\) is the output of the normalization layer. \(\gamma\) and \(\beta\) are trainable neural network parameters. After passing through the normalization layer, the training data can be standardized to a uniform range, which reduces data divergence and lowers the learning difficulty of the network. However, when applying a trained model to real-world testing scenarios, images are typically input one by one rather than in batches. Additionally, the fixed parameters of normalization make it difficult for the model to adjust and adapt to real-world scenarios during the testing phase. Therefore, this paper proposes an adaptive normalization layer, the output of which is as follows:  
\[y_{i}=\gamma\bigg{(}\gamma_{X}\bigg{(}\frac{x_{i}-\mu_{X}}{\sigma_{X}}\bigg{)} +\beta_{X}\bigg{)}+\beta \tag{8}\]  
where \(x_{i}\) represents the test data and \(y_{i}\) represents the result of adaptive normalization for the test data. \(\mu_{X}\) and \(\sigma_{X}\) are the overall mean and variance of the test source domain data, generated by the domain prior knowledge generator. \(\gamma_{X}\) and \(\beta_{X}\) are the normalization parameters of the test source domain data, also generated by the domain prior knowledge generator. \(\gamma\) and \(\beta\) are trainable neural network parameters determined during the training process. This approach allows the domain prior knowledge generator to perform self-supervised learning and induction on the test data, obtaining prior information about the target domain distribution. Subsequently, this prior information is input into the adaptive normalization layer for data normalization, achieving the normalization of test data from different source domains to a unified distribution. This effectively addresses the model transfer issue in pavement distress recognition across different source domains. In the adaptive normalization module, normalization operations can be employed to adjust the data distribution, thereby addressing issues related to varying lighting and style when transferring pavement distress detection models from the source domain to the target domain. By enabling the model to adapt to images in the target domain, better pavement distress detection performance can be achieved. In terms of specific data processing, before inputting the images from the target domain into the pavement distress detection models for distress recognition, the images are first fed into the domain prior knowledge generator.