# Hybrid Machine Learning Model for Predicting Shear Strength of Rock Joints
## 4 Results and Analysis
### Feature Importance Analysis  
In ML models, feature importance analysis not only helps identify key influencing factors but also uncovers potential relationships among variables [68; 69]. By leveraging advanced algorithms, feature selection can be further performed to eliminate redundant variables and enhance the predictive capability of the ML model [70; 71]. In the field of civil engineering, this approach significantly improves the accuracy of joint shear strength predictions, optimizes design parameters, and ultimately provides a robust scientific basis for engineering decision-making. This section employs feature importance analysis to determine the relative importance of input variables, such as the JRC, normal stress, and Young's modulus, in influencing joint shear strength.  
Feature importance scores quantify the contribution of different input variables in an ML model, with higher scores indicating a greater influence on shear strength. Figure 9 presents the computed feature importance scores, where \(\sigma_{n}\) has the highest score (0.86), followed by JRC (0.16), \(\sigma_{c}\) (0.12), E (0.12), and \(\varphi_{b}\) (0.01). Notably, \(\varphi_{b}\) exhibits the lowest feature importance score (0.01), suggesting that among the five input parameters, it has the least impact on joint shear strength. It is important to note that feature importance scores may vary depending on the dataset and the evaluation method used. Therefore, the ranking of feature importance scores obtained in this paper is specific to the dataset constructed in Section 3.1 and should not be considered a general guideline.  
Feature importance analysis provides clear guidance for the subsequent optimization of ML models, helping to identify key variables that require prioritization or more precise measurement. This facilitates more efficient and targeted experimental design. In practical applications, with the rapid development of big data and artificial intelligence technologies, the prospects for applying feature importance analysis in civil engineering are increasingly promising [72]. Under complex geological conditions, feature importance analysis bridges experimental design with actual needs. This approach offers scientific support for structural design and stability assessment, significantly enhancing the rationality and reliability of engineering solutions [73]. It is worth noting that future work could consider incorporating the SHapley Additive exPlanations (SHAP) method to enhance feature importance analysis. SHAP is an emerging model-agnostic interpretation method based on cooperative game theory, which can consistently quantify the contribution of each input feature to individual predictions. While SHAP was not applied in this study due to practical constraints, its potential to overcome the inherent bias of traditional feature importance techniques is acknowledged. Therefore, in future research, we will prioritize the integration of SHAP to improve model transparency and interpretability in line with recent advances in geotechnical AI modeling [74].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **Dataset** & **RMSE** & **MAE** & **R\({}^{2}\)** & **VAF** \\ \hline SMA-MLP & Training set & 0.01819 & 0.01232 & 0.99863 & 99.864\% \\  & Test set & 0.09699 & 0.0667/7 & 0.96869 & 97.145\% \\ MLP & Training set & 0.03322 & 0.02306 & 0.99583 & 99.583\% \\  & Test set & 0.14861 & 0.12334 & 0.89092 & 89.943\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Prediction performances for each model.