## 3 Result and Discussion
### Parameter Analysis  
To capture an insight for the RF model, not only predictive performance but also model interpretability should be accompanied simultaneously. The Shapley additive explanations (SHAP) proposed by [PERSON] and [PERSON] (2008) is the integrated framework for interpreting the model's prediction, which can express each parameter importance for a specific prediction to magnitudes and directions. The SHAP value is based on Shapley values originated from coalitional game theory and a local interpretable model agnostic explanation (LIME) that gives insights for local interpretability. The LIME value has a limitation of being unfair in terms of collaborative game theory. To complement this shortcoming, the SHAP value improved this unfairness of LIME by employing the Shapley value. A detailed explanation and theory of SHAP can be found in ([PERSON] and [PERSON], 2018). In this study, SHAP analysis for the RF model was performed (Figure 12). In this graph, an individual point represents the SHAP value of each dataset. The higher the SHAP value, the higher the positive contribution to the damage value. On the other hand,  
Figure 11: Actual damage versus the damage predicted by (**a**) SVR\({}_{\text{RBF}}\) and (**b**) RF for the testing set. The solid line indicates the relationship \(y_{\text{predicted}}=y_{\text{Actual}}\). Data points for a good prediction would lie close to the solid line. In Figure 11, some data points far from the solid line seem to have increased the prediction error. On the other hand, the data points in Figure 11 were overall close to a solid line, which indicates that RF is higher generalization performance compared with SVR\({}_{\text{RBF}}\). the lower the SHAP value, the higher the negative contribution to the damage value. The degree of 'high' and 'low' values for the parameter can be distinguished by colors'red' and 'blue', respectively. As shown in Figure 12, the degree of contribution to the damage value for the cumulative absolute energy strongly increased when the cumulative absolute energy increased. In general, the cumulative energy is related to the energy released by the crack growth of the rock [39] and is known to be directly proportional to the actual energy of the rock [27]. The result suggests that AE absolute energy is still the main parameter that has a major influence on the degree of damage even under the condition considering various AE parameters. The cumulative initiation frequency also contributed to the damage value positively when this value also increased. The distribution of frequency is known to be concerned with the stress level including rock type and the degree of fracturing [40]. Based on the result, an AE frequency seems to be definitely associated with the degree of damage, but it is unsuitable to use alone due to the low importance relatively. In addition, since the value varies with the type of AE sensor and the adhesion condition to rock [41], AE frequency should be considered with several AE parameters. For a better understanding of these results, we plotted the force plots for specific data points corresponding to a high and low damage level, respectively (Figure 13). In the case of a data point belonging to the high level of damage (0.99), it was confirmed that the cumulative absolute energy and initiation frequency strongly give a positive contribution to the damage value (Figure 13a). In the opposite case at which the damage value is 0.02, the above two parameters strongly offered a negative contribution to the damage value (Figure 13b). Figure 14 shows the absolute average of the SHAP values for each parameter. The result showed that the average value of the cumulative absolute energy is 0.152, which is the highest value among the several AE parameters. This result is in good agreement with several studies [15,42,43]. Obviously, other parameters also contribute to the prediction of rock damage. These results provide rationality for considering various AE parameters for predicting the degree of rock damage.