## 6 Sensitive Analysis
### RF Model  
Machine learning models are frequently regarded as enigmatic \"black boxes,\" impeding their interpretability. To unravel the core features influencing a model's predictions, the utilization of explainable machine learning techniques has emerged. Among these techniques, the SHAP (SHapley Additive exPlanations) method [93] has garnered substantial attention for its effectiveness. SHAP feature importance offers a conceptual framework to elucidate the predictions generated by a machine learning model. This approach provides an intuitive means of comprehending the significance of features in prediction outcomes, gauged based on the magnitude of feature attributions. Substantial absolute Shapley values stand as the most pivotal indicators. SHAP values quantify the impact of each feature on a specific prediction compared to a baseline prediction. These values are computed using game theory concepts to distribute the contribution of each feature fairly among the features. The quantification of SHAP feature importance (FI) adheres to the methodology outlined in [48]. The significance of input parameters on the output can be determined at both local and global levels [94]. Global SHAP analysis provides an overall understanding of feature importance across the entire dataset. This involves summarizing the SHAP values for each feature across all instances. Visualizations like SHAP summary plots showcase the distribution of feature contributions, allowing us to identify which features consistently  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Input Variable**} & \multicolumn{3}{c}{**Outcome**} \\ \cline{2-5}  & **Relative Importance** & **Relative Importance (\%)** & **Rank** \\ \hline \(T_{s}/T_{1}\) & 17.352 & 45.234 & 1 \\ \(\xi_{s}\) & 8.155 & 21.258 & 2 \\ Floor & 7.046 & 18.367 & 3 \\ Soft-story level & 5.432 & 14.162 & 4 \\ Excitation direction & 0.376 & 0.980 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 19: Five-story models—relative importance of input parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Output.**} & \multicolumn{6}{c}{\(w_{HO}\) (Hidden–Output Neuron Weights)} \\ \cline{2-10}  & **N1** & **N2** & **N3** & **N4** & **N5** & **N6** & **N7** & **N8** & **N9** & **N10** \\ \hline CDAF & 0.48 & \(-1.58\) & \(-4.07\) & 0.60 & \(-0.45\) & 3.07 & \(-3.56\) & 1.07 & 9.82 & 1.68 \\ \hline \hline \end{tabular}
\end{table}
Table 18: Ten-story models—hidden and output neuron weights.  
have the most impact on predictions. Local SHAP analysis focuses on explaining individual predictions. For a chosen instance, SHAP values reveal how each feature contributes to the prediction. This information helps in understanding why a specific prediction was made and whether it aligns with domain knowledge or expectations. In conclusion, the global SHAP analysis approach is more advantageous when we seek to comprehend the collective impact of features on model predictions. This approach empowers us to make informed decisions based on an understanding of the overall model behavior, guiding feature engineering and enhancing model transparency. Illustrated in Figure 18, the SHAP feature importance plot is a representation of the RF model's feature impact. Notably, the tuning ratio (\(T_{s}/T_{1}\)) emerges as the most influential feature, exerting its effect across all predictive outcomes. Conversely, the feature related to excitation direction appears to have negligible influence on the CDAF.