## 3 Case Study
### Validation Effect after Eliminating Gross Errors  
According to the data in Table 4, utilizing the LMS-IGG-ELM method to establish the dam safety monitoring model after eliminating outliers for the four methods, and making a prediction according to water pressure, temperature and aging component from 21 May 2018 to 30 December 2018, proves the final generalization ability of the model (see Figures 7-11). It can be seen from Figure 7, after eliminating outliers by using the LMS-IGG-ELM method, the fit values of the model basically coincide with the actual measured values in the fitting and validation segment, so the fitting effect is quite good; and it can be seen from the scatter arrangement of the predicting segment that the change trend of dam radial displacement follows the change law of the fitting segment, which indicates that the method has good prediction accuracy and good generalization ability.  
Figure 8: Dam monitoring model after eliminating gross errors by the DBSCAN clustering algorithm.  
Figure 7: Dam monitoring model after eliminating gross errors by the LMS-IGG-ELM method.  
Mean absolute error (_MAE_), root mean square error (_RMSE_) and coefficient of determination (\(R^{2}\)) are selected as evaluation indicators for comparison, which are defined as follows and are shown in Table 6, thus verifying the influence of gross errors identification effect on the accuracy of subsequent dam safety monitoring.  
\[MAE=\frac{\sum\limits_{i=1}^{n}\left|y_{i}-\overset{\wedge}{y_{i}}\right|}{n} \tag{24}\]  
Figure 11: Effect comparison chart of the dam validation segment after eliminating gross errors by the four methods.  
Figure 10: Dam monitoring model after eliminating gross errors by the \(3\sigma\) method.  
Figure 9: Dam monitoring model after eliminating gross errors by the Romanovsky criterion.  
\[RMSE=\sqrt{\frac{\sum\limits_{i=1}^{n}\left(y_{i}-\hat{y_{i}}\right)^{2}}{n}} \tag{25}\] \[R^{2}=\frac{\sum\limits_{i=1}^{n}\left(\hat{y_{i}}-\bar{y_{i}} \right)^{2}}{\sum\limits_{i=1}^{n}\left(y_{i}-\bar{y_{i}}\right)^{2}}=1-\frac{ \sum\limits_{i=1}^{n}\left(y_{i}-\hat{y_{i}}\right)^{2}}{\sum\limits_{i=1}^{n} \left(y_{i}-\bar{y_{i}}\right)^{2}} \tag{26}\]  
In the equation \(\bar{y_{i}}\) represents the average of the dam monitoring data, \(\hat{y_{i}}\) represents the result of the model fitting, \(y_{i}\) represents actual measured values of dam deformation and \(n\) represents the number of deformation monitoring data points.  
It can be seen from Table 6, in the dam radial displacement verification after eliminating outliers, \(R^{2}\) for all four methods is above 0.85, and \(MAE\) and \(RMSE\) of the validation segment are all below 1, which indicates that the LMS-IGG-ELM method is reasonable and accurate. \(MAE\), \(RMSE\), and \(R^{2}\) of the fitting segment and validation segment after eliminating gross errors by the LMS-IGG-ELM method are 0.0890, 0.1261, 0.9998 and 0.3284, 0.4101, 0.9720, which are the set of data with the smallest errors and the strongest correlation among the four methods. In conclusion, we show that the LMS-IGG-ELM method eliminates the highest proportion of gross errors, and the monitoring effect of the subsequent dam radial displacement is also the best.