## 3 Case Study
### Prediction Results Based on EM-ELM, LSTM and CNN before and after Denoising Displacement Data  
Since the partial autocorrelation function (PACF) is a statistical method that directly describes the relationship between time series and their lags, PACF can verify the time correlation of a sequence. Therefore, PACF is utilized to consider the influence of dam deformation self-sequential lag on dam displacement in this paper. Figure 6 plots the PACF before and after denoising. According to Figure 6 (the shaded area is the 95% confidence interval), the PACF of the prototype dam displacement data before denoising presents a 39 th order truncation; accordingly, the data input length before denoising is adopted as 39. Similarly, the data input length after denoising is chosen as 4. The results before and after denoising the data are further analyzed and compared using EM-ELM, LSTM, and CNN models. The indicators of the six models are listed in Tables 3-5, and Figure 7 shows the residual distribution of each model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Subsequences** & **Imf1** & **Imf2** & **Imf3** & **Imf4** & **Imf5** & **Imf6** & **Imf7** & **Imf8** & **Imf9** \\ \hline entropy & 1.0518 & 0.8186 & 0.6306 & 0.5638 & 0.3276 & 0.0669 & 0.0232 & 0.0086 & \(9.7\times 10^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Sample entropy values of IMFs. Figure 5: Comparison of the prototype dam displacement data before and after denoising. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Subsequences** & **Imf1** & **Imf2** & **Imf3** & **Imf4** & **Imf5** & **Imf6** & **Imf7** & **Imf8** & **Imf9** \\ \hline SMSE & 0.0248 & 0.0419 & 0.0622 & 0.0771 & 0.1812 & 7.1408 & 0.1217 & 0.0296 & 36.8884 \\ \hline \end{tabular}
\end{table} 
Table 2: SMSE values of IMFs. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Prediction Days**Algorithm** & **CS-EMELM** & **EMELM** & **CS-LSTM** & **LSTM** & **CS-CNN** & **CNN** \\ \hline First day (mm) & **0.0714** & 0.6207 & 0.1026 & 0.2358 & 0.1241 & 0.6086 \\ Second day (mm) & **0.1969** & 0.6609 & 0.2307 & 0.3315 & 0.2551 & 0.6319 \\ Third day (mm) & **0.3256** & 0.6967 & 0.3526 & 0.4049 & 0.3733 & 0.6709 \\ \hline \end{tabular} Note: The best results are highlighted in boldface.  
\end{table} 
Table 4: Comparison of RMSE of different algorithm test set for different prediction days. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Prediction Days**Algorithm** & **CS-EMELM** & **EMELM** & **CS-LSTM** & **LSTM** & **CS-CNN** & **CNN** \\ \hline First day (mm) & **0.0478** & 0.4598 & 0.0716 & 0.1532 & 0.0934 & 0.4951 \\ Second day (mm) & **0.1388** & 0.4932 & 0.1719 & 0.2382 & 0.1916 & 0.5131 \\ Third day (mm) & **0.2391** & 0.5229 & 0.2683 & 0.3027 & 0.2833 & 0.5458 \\ \hline \end{tabular} Note: The best results are highlighted in boldface.  
\end{table} 
Table 5: Comparison of MAE of different algorithm test set for different prediction days. Figure 6: PACF charts of dam displacement data before and after denoising. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **CS-EMELM** & **EMELM** & **CS-LSTM** & **LSTM** & **CS-CNN** & **CNN** \\ \hline RMSE (mm) & **0.2235** & 0.6602 & 0.2504 & 0.3314 & 0.2707 & 0.6376 \\ MAE (mm) & **0.1419** & 0.4920 & 0.1706 & 0.2314 & 0.1894 & 0.5180 \\ Time(s) & **60.87** & 53.28 & 89.66 & 193.67 & 72.64 & 94.70 \\ \hline \end{tabular} Note: The best results are highlighted in boldface.  
\end{table} 
Table 3: Performance comparison of different algorithms on the test set (predicted three-day average). In order to intuitively verify the effectiveness of the denoising method proposed in this paper, a comparative analysis of the results listed in Table 3 is performed. The results show that, after denoising the prototype dam displacement sequence, the RMSE and MAE of the EM-ELM algorithm on the test set are improved by 66.15% and 71.16%, respectively. The RMSE and MAE of the LSTM algorithm on the test set are improved by 24.44% and 26.27%, respectively.