## 4 Engineering Example Application
### Analysis of the Predicted Results  
In the regression sequence prediction model, several measures are used to evaluate the prediction accuracy, including the mean absolute error, mean square error, root mean square error, and mean absolute percentage error. To compare the accuracy of different models, we used the root mean square error \((RMSE)\), mean absolute error \((MAE)\), the coefficient of determination \((R^{2})\), and mean absolute percentage error \((MAPE)\) as the accuracy error. The following equation shows the standard for these measures:  
\[RMSE=\sqrt{\frac{1}{N}\sum_{i=1}^{n}\left(y_{i}-\overset{\wedge}{y}\right)^{2}} \tag{19}\]  
\[MAE=\frac{1}{n}\sum_{i=1}^{n}\left|\left(y_{i}-\overset{\wedge}{y_{i}}\right)\right| \tag{20}\]  
\[R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-\overset{\wedge}{y}\right)^{2}}{\sum_{ i=1}^{n}\left(y_{i}-\overline{y}\right)^{2}} \tag{21}\]  
\[MAPE=\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{y_{i}-\overset{\wedge}{y_{i}}}{ \overset{\wedge}{y_{i}}}\right| \tag{22}\]  
where \(y_{i}\) represents the actual value; \(\overset{\wedge}{y_{i}}\) represents the predicted value; \(\overline{y}\) represents the mean of the true value, and \(n\) is the number of samples.  
To further verify the generality and credibility of the IESSA-LSSVM algorithm, the LSSVM, SSA-LSSVM, and GWO-LSSVM algorithms were selected to build models for the analysis and prediction of the two slopes--xtGXT1 and xtGXT3--in Xin Tan and the Yangtze River. The number of populations was set to 30, the number of iterations was set to 100, and the dimension was set to 2.  
Figures 10 and 11 show the simulation results of the four algorithms, LSSVM, SSA-LSSVM, GWO-LSSVM, and IESSA-LSSVM, over a period of 60 months. The IESSA-LSSVM algorithm resulted in a prediction graph that was much closer to the engineering-measured graph, indicating higher prediction accuracy and better results. Table 3 presents the model error evaluation indicators \(MAPE\), \(MAE\), \(R^{2}\), and \(RMSE\) derived from the four algorithms.  
Figure 10: Comparison of xtGXT1 slope displacement algorithm prediction.  
From the table above, it is evident that the error evaluation index values of the IESSA-LSSVM model are better than the other three models, and the error evaluation parameters \(RMSE\) and \(MAPE\) of the IESSA-LSSVM model are significantly lower than the other three. In the xtGTX1 slope test sample, the IESSA-LSSVM model exhibited a decrease of 6.33568 and 2.89598 in \(RMSE\) compared to the SSA-LSSVM and GWO-LSSVM models, respectively. Furthermore, there was a decrease of 0.276801% and 0.2214031% in \(MAPE\) and a decrease of 4.084511% and 3.21711% in \(MAE\). Moreover, the \(R^{2}\) tended to be more toward 1.  
As can be seen from Table 4, in the xtGXT3 slope test sample, the IESSA-LSSVM model has much smaller values for \(RMSE\), \(MAE\), and \(MAPE\) than for the remaining three models; meanwhile, \(R^{2}\) is closest to 1, indicating that the model has a small prediction error and a high degree of fit when studying the slope displacements. Therefore, the EEMD-IESSA-LSSVM model proposed in this paper is highly versatile and has high prediction accuracy. However, with the gradual complexity of the algorithm, the model may introduce some errors, but these errors are negligible compared to the model's accuracy. This model and method can serve as a reference for slope displacement prediction and related forecasting.