## 4 Case Study
### Results and Discussion
#### 4.5.4 Performance of Different Prediction Periods Based on the Proposed Model  
In summary, the proposed model has the smallest RMSE and MAE values and the largest R\({}^{2}\) value, and the prediction performance of the model is satisfactory. However, in the DD prediction, in addition to the prediction accuracy, the length of prediction period is also important to guide the normal and stable operation of a dam. In this section, we mainly discuss the influence of different prediction periods (1-, 4- and 7-day ahead) on the prediction performance of the proposed model. The specific implementation process for different periods is shown in Figure 11. The prediction results and performance evaluation indicators for each period are shown in Figure 19, where the bar graph of performance evaluation indicators for each model is shown on the left and the curves of prediction results is shown on the right. It is clear from Figure 19 that the VMD-SE-ER-PACF-ELM model is the most effective when the prediction period is one day, followed by the next best when the prediction period is four days, and the worst when the prediction period is seven days. Figure 19: Comparison of prediction results for different periods. Figure 18: Taylor diagram of the prediction performance of each model. * Blue contours represent Pearson correlation coefficient; black contours represent standard deviation of the simulated pattern; and green contours represent centered RMS error in the simulated field. To further compare the impact of prediction periods on the results, Table 7 presents the performance evaluation indicators of the predicted results for the corresponding periods. Their RMSE values are: 0.2755 (1d), 0.4198 (4d) and 0.4547 (7d). The RMSE values of one-day prediction period are reduced by 34.37% and 39.41%, respectively, compared to the other two periods. Meanwhile, the values of MAE are: 0.2087 (1d), 0.3140 (4d) and 0.3063 (7d). The MAE values of one-day prediction period are reduced by 33.54% and 31.86%, respectively, compared to the other two periods. The above results are consistent with the relatively high R\({}^{2}\) values (0.8912 for 1d, 0.8130 for 4  
are as follows: (1) The VMD algorithm is used to decompose an original deformation sequence into a number of subsequences with good characteristics to improve the prediction performance. (2) The SE method is used to quantify the complexity of each subsequence in order to select the appropriate decomposition modulus. (3) The secondary VMD decomposition of the ER enables the prediction value to be closer to the actual deformation characteristics. (4) The PACF method is used to analyze the characteristics of each subsequence to extract the input variables. (5) The ELM models are used to predict the subsequences and their combination is the final prediction result. Meanwhile, the prediction performance of the VMD-SE-ER-PACF-ELM model is compared with those of Arima, PACF-ELM, HST-ELM, VMD-PACF-ELM, and VMD-SE-PACF-ELM models with RMSE, MAE, R\({}^{2}\), and Taylor diagrams as performance evaluation indicators. The results show that the proposed VMD-SE-ER-PACF-ELM model has the best prediction performance among all prediction models. It can effectively predict nonstationary and nonlinear time series and significantly improve the prediction accuracy. In addition, we have also analyzed its performance under different prediction periods. The results show that the length of the prediction period is inversely proportional to the prediction accuracy, which can provide a priori knowledge for the normal operation and early warning of the dam projects. Although the proposed method has good prediction results, there are still certain prediction errors. In this paper, the uncontrolled errors due to the randomness of the ELM model is the main cause of the prediction errors, which needs to be addressed in our future research. In addition, the idea of spatial relationships between the measurement points [51] will be introduced into the prediction to analyze the overall deformation effect of dams.