## 3 Case Study
### Prediction Results Based on EM-ELM, LSTM and CNN before and after Denoising Displacement Data
The RMSE and MAE of the CNN algorithm on the test set are improved by 57.54% and 63.44%, respectively. In summary, the accuracy of the multi-step predictive model can be improved by using the denoising sequence, which suggests that the proposed denoising method can effectively remove redundancy information from the data and thereby increase the prediction accuracy. Furthermore, the statistical indicators in Table 3 are analyzed to verify the applicability and validity of each prediction model. From Table 3, in comparison to the CNN algorithm, the LSTM algorithm improves the RMSE and MAE on the test set by 48.02% and 55.33%, respectively, while the time performance decreases by 51.10%. Compared with the EM-ELM algorithm, the LSTM algorithm improves the RMSE and MAE on the test set by 49.80% and 52.97%, respectively, while the time performance decreases by 72.49%. Regarding the prediction performance after denoising, the CS-EMELM algorithm improves the RMSE and MAE on the test set by 10.74% and 16.82% compared with the CS-LSTM algorithm, respectively, and the time performance improves by 32.11%. With respect to the CS-CNN algorithm, the CS-EMELM algorithm improves the RMSE and MAE on the test set by 17.44% and 25.08%, respectively, and the time performance improves by 16.20%. To summarize the above, without any special denoise processing, the LSTM algorithm illustrates stronger generalization ability compared with CNN and EMELM algorithms, which shows that the LSTM algorithm is capable of capturing the temporal characteristics contained in noise sequences and results in better prediction ability for the redundant prototype data. After denoising the data through the CS algorithm, the performance of all involved approaches has been improved to a large extent, especially the EM-ELM algorithm, which achieves the most significant improvement and results in similar predictive accuracy with the other two models, which demonstrates that by incorporating the CS algorithm, the EM-ELM algorithm can capture and reveal the temporal characteristics of the data and has great predictive accuracy. Moreover, to obtain a reasonable solution, the implementation of LSTM and CNN algorithms is usually complicated, dueto the need to employ optimization algorithms to determine multiple hyperparameters. Hence, taking advantage of combining good accuracy with an affordable computational cost, the CS-EMELM algorithm is utilized as the predictive model in the proposed method. Figure 7: Performance comparison of different algorithms before and after dam displacement denoising on the test set. The prediction results of all involved models under different forecasting days are shown in Figures 8-10, and the values of the evaluation criteria are given in Tables 4 and 5. In comparison to the second-day predicted value, the first-day predicted value of the CS-EMELM algorithm improves by 63.74% and 65.56% in RMSE and MAE, respectively; the first-day predicted value of the CS-LSTM algorithm improves by 55.53% and 58.35% in RMSE and MAE, respectively. The first-day predicted value of the CS-CNN algorithm improves by 51.35% and 51.25% in RMSE and MAE, respectively. Compared with the third-day predicted value, the second-day predicted value of the CS-EMELM algorithm improves by 39.53% and 41.95% in RMSE and MAE, respectively, the second-day predicted value of the CS-LSTM algorithm improves by 34.57% and 35.93% in RMSE and MAE, respectively, the second-day predicted value of the CS-CNN algorithm improves by 31.66% and 32.37% in RMSE and MAE  
Figure 10: Performance comparison of the third day predicted values for each model on the test set (**(a)** EMELM, **(b)** LSTM, **(c)** CNN). Figure 9: Performance comparison of the second day predicted values for each model on the test set (**(a)** EMELM, **(b)** LSTM, **(c)** CNN).