# IeALL: Dam Deformation Prediction Model Based on Combination Model Method
## 6 Experiments
### Analysis of Results  
#### 6.3.1 Analysis of EALL  
The dam deformation sequence is predicted using the EALL by setting up reasonable trials, and the efficacy is validated by comparing the experimental results to those of the ARIMA model, the LSTM model, and the conventional combination of ARIMA-LSTM model. The construction and prediction process of EALL is as follows:  
(1) EEMD decomposition of deformation sequence: The dam deformation sequence is decomposed by EEMD. First, the parameters of EEMD are set, and then the number I of adding Gaussian white noise is set to 100, and the standard deviation of Gaussian white noise is 0.05 times. The obtained EEMD decomposition diagram is shown in Figure 6. The original deformation sequence is decomposed into nine IMF components \(imf_{1}(t),imf_{2}(t),\ldots,imf_{9}(t)\), and a trend component \(r(t)\). Where \(imf_{1}(t),imf_{2}(t),\ldots,imf_{5}(t)\) have high frequencies, showing irregular and fluctuating characteristics, which belong to the nonlinear part of the deformation sequence, \(imf_{6}(t),imf_{7}(t),\ldots,imf_{9}(t)\) have low frequencies and show a certain trend, so it can be considered that temperature and aging are the main factors causing the deformation of this part and therefore belong to the linear part of the sequence. (2) Judging the frequency of deformation sequence: after the deformation sequence is decomposed into nine IMF components, the zero-crossing rate approach is used to determine the frequency of each component. According to the experience of dam deformation sequence decomposition, 10% is a suitable definition standard for high and low frequency components [29]. This standard is used in this study to define \(imf_{1}(t),imf_{2}(t),\ldots,imf_{5}(t)\) as high frequency components, and \(imf_{6}(t),imf_{7}(t),\ldots,imf_{9}(t)\) as low frequency components. (3) Prediction of low-frequency series by ARIMA model: ARIMA model is used to predict low-frequency series \(imf_{6}(t),imf_{7}(t),\ldots,imf_{9}(t)\). The other sequences are the same, and \(imf_{7}(t)\) is used as an example in this section. The sequence is first put through the ADF test. If it is determined that the sequence is unstable, the differential operation is performed. The sequence is stable after three differential operations, and the differential order \(d\) is 3. Second, the order of ARIMA modelis determined, the difference order \(d\), autoregressive order \(p\), and moving average order \(q\) are calculated. One of them has been identified as \(d\). AIC criterion is used to identify the parameters of \(p\), \(q\) ranges, and the autocorrelation coefficient diagram (ACF) and partial autocorrelation coefficient diagram (PACF) are used to determine the values of \(p\), \(q\). The parameters \((p,d,\) and \(q)\) of the ARIMA model are determined as \(ARIMA(1,3,2)\) by experiments. The model is then trained to forecast the IMF7 sequence, and its performance is assessed in accordance with the evaluation criteria. The evaluation results are shown in Table 1.  
According to Table 1, it can be seen that the values of RMSE, MAPE, and MAE are relatively small, which indicates that ARIMA has a good prediction effect on the IMF7 sequence and meets the experimental requirements. Similarly, according to the above experimental steps, \(imf_{6}(t),imf_{8}(t),\ldots,imf_{9}(t)\) are predicted, respectively, and the prediction results of all low-frequency series are obtained. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **RMSE** & **MAPE** & **MAE** \\ \hline \(ARIMA(1,3,2)\) & \(9.32\times 10^{-5}\) & 0.7138 & \(8.26\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation results of IMF7 predictive value. Figure 6: Diagram of dam deformation sequence decomposed by EEMD. (4) LSTM model prediction of high-frequency series. The LSTM prediction model is constructed, and the sequence IMF3 is used as the training and prediction sequence.