# IeALL: Dam Deformation Prediction Model Based on Combination Model Method
## 4 Dam Deformation Prediction Model Based on IEALL
### EALL Algorithm  
The EALL algorithm is implemented as follows:  
1. Collection and preparation of data. Gather and arrange the pertinent temperature, water level, and dam deformation data, as well as the data needed for preprocessing, reduction, and other activities. 2. EEMD decomposes deformation data. Figure 1: Optimization diagram of composite model. Figure 2: Overall framework diagram of IEALL. The dam deformation sequence is decomposed into \(m\)\(IMF\)\((IMF_{1},IMF_{2},\ldots,IMF_{m})\) component sequences by EEMD decomposition algorithm, and then the frequency is judged one by one. If the number of high-frequency sequences in \(m\)\(IMF\) components is \(i\), then the high-frequency sequence are \(imf_{1}(t),imf_{2}(t),\ldots,imf_{i}(t)\) and the low-frequency sequence are \(imf_{i+1}(t),imf_{i+2}(t),\ldots,imf_{m}(t)\); the decomposition process is described in Section 3.1. Construct the ARIMA model. First, the ADF criterion is used to measure the stationarity until the sequence is stable and the parameter \(d\) is obtained, and then the values of \(p,q\) are determined by AIC criterion and autocorrelation and partial autocorrelation to complete the model order determination. The linear portion of \(imf_{i+1}(t),imf_{i+2}(t),\ldots,imf_{m}(t)\) in the sequence of dam deformation is predicted using \(ARIMA(p,d,q)\). If the sequence is \(imf_{k}(t),k\in i+1,\ldots,m\), the current sequence prediction value \(L_{k}\) can be calculated using the Equation (11). Similarly, the \(\hat{L}_{t}\big{(}\hat{L}_{i+1},\ldots,\hat{L}_{m}\big{)}\) outcome of the linear prediction:  
\[\hat{L}_{k}=arima(imf_{k}(t),(p,d,q)),k\in i+1,\ldots,m \tag{11}\]  
4. Construct the LSTM model. The LSTM model is used to predict the nonlinear part in the deformation sequence, and it is built on top of the RNN by using three gate structures (i.e., forget gate, input gate, and output gate) to control the information flow, forgetting, and updating at different time steps, thereby solving problems such as gradient explosion in long-term dependencies, and making it better at predicting time series with large time spans. Assuming the original sequence is \(x_{t}\), the process of using the LSTM model for prediction can be mainly divided into the following steps:  
Data preprocessing and normalization. The feature sequence of the most correlated influencing factors (temperature, water level, age) is added to the training data as the training sample of the LSTM model. Then, the training data are normalized and divided into a training set and a validation set. Specifically, the expression for the displacement component of the dam body affected by temperature \(\delta_{T}\) is given in Equation (12) [27]:  
\[\delta_{T}=\sum_{i=1}^{n}(b_{1i}\sin\frac{2\pi it}{365}+b_{2i}\cos\frac{2\pi it }{365}) \tag{12}\]  
where \(b_{1i}\) and \(b_{2i}\) are the regression coefficients of the temperature factor, \(n\) is generally a value of 1 or 2, and \(t\) is the cumulative number of days from the monitoring day to the measurement day. When \(i\) is 1, the period is one year, and when \(i\) is 2, the period is half a year. The water level factor \(\delta_{H}\) is the expression of the displacement component generated by the dam under the action of water pressure and the gravity of the reservoir, as shown in Equation (13) [27]:  
\[\delta_{H}=\sum_{i=1}^{m}a_{i}H^{i} \tag{13}\]  
where \(a_{i}\) is the regression coefficient for the water pressure factor, \(m\) is generally 3 for gravity dams, and \(H^{i}\) is the water level of the reservoir. The time-dependent component of the dam deformation is expressed as Formula (14) [27], which is denoted as \(\delta_{\theta}\):  
\[\delta_{\theta}=cIn(\theta) \tag{14}\]  
In Equation (10), \(c\) represents the regression coefficient of the time effect factor, and \(\theta\) is the accumulated number of days from the observation day to the measurement start day divided by 100.