## 3 Result and Discussion
### Model Optimization and Generalization Performance  
To select the best model, the hyper-parameter set should be optimized. This process is the essential step because the performance of a model varies significantly depending on the hyper-parameter set. The procedure of optimizing a model is divided into five stages: (1) a hyper-parameter tuning space is specified; (2) an arbitrary hyper-parameter set within a given range is chosen using random-search method. Here, random-search is the method sampling hyper-parameter set randomly in the range of specified tuning space; (3) a model is built for the training set with a given hyper-parameter set and is  
Figure 9: The changes of the damage for cumulative AE parameters such as **(a)** amplitude, **(b)** hit, **(c)** count, **(d)** rise time, **(e)** absolute energy, and **(f)** initiation frequency. Although 10 granite specimens were extracted from the same borehole in RG-2 section, the curves for each input showed different trends. This phenomenon seems to be due to the difference of properties such as rock strength, stiffness, and Poisson’s ratio and indicates that predicting the degree of rock damage using only one or two AE parameters is a difficult problem. evaluated through cross-validation. Here, the cross-validation is the one of validation methods used for selecting the optimum hyper-parameter set in the given space. The principle of cross-validation is to divide a training set into k-folds, and then one fold is used as the validation data for the model which is fitted by the rest of folds. This process is repeated k times and all the outputs are evaluated through evaluation metric; (4) after repeating the stage 3 several times, only the hyper-parameter set with the best value of evaluation metric is chosen; (5) based on the hyper-parameter set selected from the stage 4, the stages 1-4 are repeated until the hyper-parameter set converges to the optimum set. From the process, final hyper-parameter space and optimum set selected are summarized in Table 4. As for an evaluation metric, the RMSE was selected and the equation can be expressed as Equation (8);  
\[\text{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}} \tag{8}\]  
where \(y_{i}\) is the actual output and \(\hat{y}_{i}\) is the corresponding predicted output. The RMSE history for the final cycle of stage 5 according to the models such as random forest (RF), linear and nonlinear support vector regression (\(\text{SVR}_{\text{Linear}}\), \(\text{SVR}_{\text{BBF}}\)) are shown in Figure 10. Here, the vertical axis indicates the result of the sorted root mean squared error (RMSE) in descending order. The results show that the RMSE for \(\text{SVR}_{\text{Linear}}\) and \(\text{SVR}_{\text{BBF}}\) were 0.182 and 0.104, respectively. In other words, the performance of \(\text{SVR}_{\text{BBF}}\) showed about 1.8 times higher than that of the \(\text{SVR}_{\text{Linear}}\). This result implies that the relationship between the AE parameters and the degree of damage is a complex and nonlinear problem. As for comparison between two different nonlinear models, the RF (RMSE = 0.048) showed 2.2 times higher optimizing performance than the \(\text{SVR}_{\text{BBF}}\) (RMSE = 0.104).