## 5 Machine Learning for the Prediction Model
### Results from Machine Learning  
#### 5.3.1 Evaluation of Prediction-Model Performance  
In the regression approach, machine learning and deep learning were utilized to generate the prediction model. The method for evaluating the performance of the prediction models is generally via mean absolute error (MAE), mean-square error (MSE), and root-mean-square error (RMSE) methods. MAE is a concept that adds to the difference of the predicted and real values of the model, which is represented in Equation (5), and can intuitively represent the performance of the model. However, when comparing models with significantly different sizes of average error value, the prediction models favor those with smaller average errors. \[MAE=\frac{1}{n}{\sum}|\hat{y}-y| \tag{5}\]  
where, \(\hat{y}\) is the predicted value, \(y\) is the actual value, and \(n\) stands for the number of input data. Figure 7: Regularization of data dS. MSE is a widely used index in the field of digital-image processing along with machine learning. MSE is calculated to obtain an average value by squaring the difference of the predicted and actual values, divided by numbers of data, as represented in Equation (6). \[MSE=\frac{1}{n}\sum_{i=1}^{n}(\hat{y}_{i}-y_{i})^{2} \tag{6}\]  
RMSE is the square root of MSE that is used to compare the error of the prediction model and determine the error interval of the prediction value, as indicated in Equation (7). \[RMSE=\sqrt{MSE}=\sqrt{\left(\sum_{i=1}^{n}(\hat{y}_{i}-y_{i})^{2}\right)/n} \tag{7}\]  
MAE can represent the performance of the model by the summation of the difference value between the predicted and true values of the model. Upon evaluating the performance of a prediction model using mean error, the result is expressed as a negative number. If the prediction-model value is smaller than the true value, it is utilized to overcome the underestimation of the mean error values. In this study, the evaluation of the prediction model was carried out by RMSE. Figure 8 represents the distribution of prediction models \(\mathbb{S}_{\text{R}}\) from XGB and MLP. When MLP was used compared to XGB, it was predicted to be larger in the 20 to 30 mm section, but smaller in the 50 to 60 mm section. Figure 8: Cont. Each algorithm is schematically illustrated in Figure 9, so that it can be more intuitively analyzed. If test data and prediction data had similar values, the dot was located on the dashed line, and the RMSE values of the prediction model_S\({}_{R}\) derived by XGB and MLP were 2.16 and 2.44, respectively. Figure 8: Distribution of data and prediction model_S\({}_{R}\). Figure 9: Prediction model_S\({}_{R}\). Figure 10 shows the distribution of prediction data derived through XGB and MLP for prediction model_Sp. The section with the highest density (25-30 mm) appeared to be wider in MLP than that in XGB. Figure 11 compares the predicted data and test data of prediction model_Sp derived from XGB and MLP. For the XGB algorithm, the RMSE value was about 1.63, and the MLP algorithm showed an RMSE value of 2.32. Similarly to prediction model_Sp, XGB showed slightly superior performance. Prediction model_dS was derived on the basis of the results of prediction mode_S\({}_{R}\) and prediction model_Sp; data distribution is shown in Figure 12. For XGB, dS values were distributed at the highest density values at 0.0-0.05 intervals. For MLP, the highest density was found at a smaller value. Figure 13 shows a comparison of the prediction data and test data derived using XGB and MLP. The A zone is an area where the \(S_{P}\) value is greater than \(S_{R}\) due to tunnel excavation; the maximal value for XGB was 0.63, and for MLP was 0.64. The B zone is an area where \(S_{P}\) is less than \(S_{R}\) despite tunnel excavation, and the dS value is negative, with a minimal value of \(-0.71\) to 0.60. With the XGB algorithm, the model's RMSE was 0.05, and the MLP showed an RMSE value of 0.07. As in the two previous models, prediction model_dS also showed better performance with XGB.