# Concrete Dam Deformation Prediction Model Research Based on SSA-LSTM
## 3 SSA-LSTM Based Dam Deformation Prediction Model  
### Selection of Feature Factors and Model Parameters  
According to the dam engineering principle, the displacement \(\delta\) generated at any point of the dam under the effect of water pressure and temperature can be divided into three components according to the cause [24; 25], which are the water pressure component \((\delta_{H})\), the temperature component \((\delta_{T})\), and the aging component \((\delta_{\theta})\), with the formula:  
\[\delta=\delta_{H}+\delta_{T}+\delta_{\theta} \tag{13}\]  
Depending on the type of dam, the components of Formula (13) are slightly different, and this paper focuses on the deformation of any point on the gravity dam. According to the structural characteristics of the gravity dam and the actual condition of the project, under the effect of the upstream reservoir, the horizontal displacement on the gravity dam is linearly related to the water depth \(H\), \(H^{2}\), \(H^{3}\), which can be expressed by Equation (14). The temperature at any point within the concrete of the dam can be approximated by a periodic function, assuming that the temperature displacement is linearly related to the concrete temperature, and the harmonic sine function can be chosen as a factor, i.e., the displacement caused by the temperature effect for a gravity dam can be expressed by Equation (15). The aging component of the dam reflects the creep, plastic deformation of the concrete and bedrock, as well as the compression deformation of the bedrock geological structure. During normal operation, the time-dependent displacement of the dam typically exhibits a sharp change at the beginning and gradually stabilizes towards the end. For concrete gravity dams, the aging component can be expressed by Equation (16). In summary, there are nine initial input variables to the model, namely \(H\), \(H^{2}\), \(H^{3}\), \(\sin 2\pi it/365\), \(\cos 2\pi it/365\), \(\sin 4\pi it/365\), \(\cos 4\pi it/365\), \(\theta\), and \(ln\theta\). The specific calculation formula is:  
\[\delta_{H}=\sum_{i=1}^{3}a_{i}H^{i} \tag{14}\]  
\[\delta_{T}=\sum_{i=1}^{2}\left(b_{i}\sin\frac{2\pi it}{365}+c_{i}\cos\frac{2 \pi it}{365}\right) \tag{15}\]  
\[\delta_{\theta}=d_{1}(\theta-\theta_{0})+d_{2}(\ln\theta-\ln\theta_{0}) \tag{16}\]  
where \(H\) represents the upstream reservoir level; \(a_{i}\), \(b_{i}\), \(c_{i}\), \(d_{1}\), and \(d_{2}\) represent the corresponding linear coefficients; \(t\) is the number of days from the initial date of dam observation to the current observation date; \(t_{0}\) is the number of days from the initial date of the dam observation to the initial date of the modeling; \(\theta\) is \(t/100\); and \(\theta_{0}\) is \(t_{0}/100\). In LSTM networks, parameters such as training rate, number of training epochs (Epoch), batch size, number of neurons in the first layer1 (units1) and number of neurons in the first layer2 (units2) are the key indicators affecting the prediction accuracy, and these parameters directly determine the network structure of the LSTM model. Therefore, the SSA optimization algorithm is used to automatically optimize the five parameters of the LSTM model. The training rate refers to the step size of the parameter update in each iteration of the model. The size of the training rate affects the convergence speed and  
Figure 2: SSA algorithm flowchart. stability of the model, usually by back propagation, which calculates the gradient of each parameter against the loss function and then updates the model parameters based on the gradient and the training rate. The number of training epochs is the number of iterations of the model over the entire training dataset. The size of the training epochs affects the model's ability to fit and generalize. In each iteration, the model performs a forward and backward propagation using all the samples in the training dataset and then updates the model parameters. Batch size is the number of samples processed simultaneously in a training session.