# IeALL: Dam Deformation Prediction Model Based on Combination Model Method
## 4 Dam Deformation Prediction Model Based on IEALL
### EALL Algorithm
According to the above formulas, the appropriate influencing factors are selected as: \(H\), \(H^{2}\), \(H^{3}\), \(\sin\frac{2\pi it}{365}\), \(\cos\frac{2\pi it}{365}\), \(\sin\frac{4\pi it}{365}\), \(\cos\frac{4\pi it}{365}\), \(\theta\), and \(In\theta\), to construct the LSTM model input feature sequence. At the same time, they are combined with the deformation sequence to construct the input of the training set, as follows:  
\[rainX=\left( \begin{array}{cccccccc}x_{1}&x_{2}&\cdots&x_{4}&d_{1}&d_{2}&\cdots& d_{4}\\ x_{2}&x_{3}&\cdots&x_{5}&d_{2}&d_{3}&\cdots&d_{5}\\ \cdots&\cdots&\cdots&\cdots&\cdots&\cdots&\cdots&\cdots\\ x_{n-4}&x_{n-3}&\cdots&x_{n-1}&d_{n-4}&d_{n-3}&\cdots&d_{n-1}\end{array}  \right),trainY=\left( \begin{array}{c}x_{5}\\ x_{6}\\ \vdots\\ x_{n}\end{array} \right) \tag{15}\]  
The formula shows that the training set input of the LSTM model is constructed by combining the deformation sequence and the feature sequence that considers factors such as temperature, water level, and aging, where \(n\) is the length of the training sequence, and \(x_{1},x_{2},\ldots,x_{n}\) represent the deformation sequence of the training set, and \(d_{1},d_{2},\ldots,d_{n}\) represent the feature sequence composed of factors such as temperature, water level, and aging, which are added to the training in the form of features. This can effectively improve the recognition of influencing factor features by the LSTM model and achieve more accurate predictions. (b) Parameter initialization. Parameter initialization is an important step in training a deep learning model such as LSTM. The batch size, number of neurons (or units), and learning rate (\(\eta\)) are parameters that need to be initialized when setting up the LSTM model. (c) LSTM Model Training. Train the LSTM model using the parameters initialized in step 2, using the Adam algorithm instead of the original gradient descent algorithm in the LSTM model. The Adam algorithm updates the neural network weights iteratively based on the training data, achieving efficient computation and better performance. At the same time, set the training parameters such as the number of training epochs, batch size, etc. (d) Model prediction. Read the trained model from step 3 to make predictions on the validation set and check the prediction performance of the model. If the error is large, adjust the parameters and retrain. If the error meets the requirements, save it as the predicted value of the LSTM model. Firstly, the LSTM is used to predict the nonlinear part \(imf_{1}(t),imf_{2}(t),\ldots,imf_{i}(t)\) in the dam deformation sequence, and the sequence is set as \(imf_{k}(t),k\in 1,2,\ldots,i\) and the lstm() is set as the functional relationship determined by the LSTM model to obtain the predicted value \(\hat{N}_{t}(\hat{N}_{1},\ldots,\hat{N}_{i})\) of the nonlinear part:  
\[\hat{N}_{j}=lstm\left(inf_{j}(t)\right),\ j\in 1,2,\ldots,i \tag{16}\]  
Finally, an LSTM model is constructed to fit the linear and nonlinear prediction results. Assuming the functional relationship determined by the second LSTM is \(lstm^{\prime}\), the final prediction result of the combination model is:  
\[\hat{y}_{t}=lstm^{\prime}\left(\hat{L}_{t},\hat{N}_{t}\right) \tag{17}\]