# Dam Deformation Monitoring Model Based on Deep Learning and Split Conformal Quantile Prediction
## 3 Case Study
### Model Construction and Deformation Feature Selection  
In order to eliminate the influence of different dimensionalities between variables and to improve the learning speed of the neural network, the training and test samples are first subjected to Min-Max Normalization before being inputted to the model, calculated as follows:  
\[x_{norm}=\frac{x-\min(x)}{\max(x)-\min(x)} \tag{22}\]  
For AI-based models, hyperparameter selection is a crucial part of the modeling process and can directly affect the performance of the prediction model. All model hyperparameter choices involved in this study were derived by trial-and-error and grid search methods. First, we used the trial-and-error method to identify the approximate range of specific parameters. This process involved manually testing various parameter combinations and recording the fluctuations in model performance. Subsequently, grid search was employed to determine the optimal hyperparameter combination, ensuring that the model's performance met the expected standards. Take the proposed Bi-SCQLSTM as an example. The number of bidirectional LSTM layers was set as 3, and the number of neurons was 128, 64, and 32, respectively. To prevent overfitting, a dropout layer was provided between the bidirectional LSTM layers, and the probability of each layer was selected as 0.35. The number of epochs was set to 3000; the batch size was 100; the Adam optimized learning rate was set to 0.003. The size of the sliding time window was 6, meaning that the data from the previous 6 days are used to predict the deformation of the subsequent day. In addition, considering the required accuracy of dam deformation prediction, the _PINC_ in this study was specified for 95%.  
Generally speaking, the causes of dam deformation can be divided into three main categories: deformation caused by hydrostatic pressure \(Y_{H}\); deformation caused by temperature stress \(Y_{T}\); and deformation caused by ageing \(Y_{t}\). For horizontal deformation, the deformation caused by hydrostatic pressure \(Y_{H}\) shows a linear relationship with the upstream water level \(H\), \(H^{2}\), \(H^{3}\), and \(H^{4}\). Thus, \(Y_{H}\) can usually be expressed as a quadratic  
Figure 8: Historical monitoring of the water level of the arch dam.  
Figure 9: Historical monitoring of the air temperature of the arch dam.  
polynomial in terms of the upstream water level. The horizontal deformation \(Y_{t}\) due to the time effect can usually be expressed as a combination of the monitoring date \(t\) and a function of its corresponding logarithm. Notably, [PERSON] et al. (2020) verified that the deformation lag due to temperature effects in dams is better captured by actual historical temperature measurements, resulting in more physically explanatory dam deformation prediction [38]. Therefore, the deformation input features used in this study are based on the improved HTT statistical model:  
\[\begin{split}\text{deformation input factors}=&\Big{\{}x^{water level},x^{temperature},x^{time}\Big{\}}\\ =&\{H,H^{2},H^{3},H^{4},T_{0},T_{1-2},T_{3-7},T_{8-15},T_{16-30},T_{31-60},T_{61-90},T_{91-120},T_{121-180},\delta,\ln\delta\}\\ &\text{where }T_{0}\text{ denotes the mean air temperature on the initial deformation monitoring date;}\\ T_{a-b}&\text{ is the mean air temperature from days }a\text{ to }b\text{; and }\delta\text{ is the cumulative number of days from the initial deformation monitoring date.}\\ \end{split} \tag{23}\]