## 5 Results and Discussion
### Model Interpretation  
Figure 11 presents a bee swarm plot that illustrates the distribution of feature contributions alongside the SHAP interaction matrix. The matrix's diagonal elements indicate the independent contribution of each feature to the model's predictions, whereas the off-diagonal elements reflect the interaction effects between pairs of features. The SHAP value is derived by summing the independent contributions of individual features and their interaction contributions. The figure indicates that XB(m) significantly influences the model's predictions, with a notable interaction between XB(m) and E(GPa) enhancing this predictive effect. Conversely, SB demonstrates minimal independent contribution to the model's predictions, and the interaction between SB and BD exhibits a negligible effect on the model's output.  
Figure 12 integrates a local bar plot with a bee swarm plot to provide a comprehensive visualization of feature contributions to the model's predictions. The bars in the local bar plot represent the SHAP values for each feature, illustrating the individual contributions of each. The top x-axis corresponds to the mean SHAP values from the bar plot, while the bottom x-axis represents the SHAP value contributions in the bee swarm plot. In the bee swarm plot, the color coding indicates feature value ranges, with blue signifying low values and red signifying high values. It can be observed that XB plays a significant role in the model's prediction. High values of XB positively influence the predictions, whereas low values have a negative impact. In contrast, SB has minimal influence on the model, with high values of SB contributing slightly positively to the predictions.  
Figure 10: Scatter plots of the models during the testing phase: (**a**) TPE-ET model, (**b**) TPE-GB model, and (**c**) TPE-RF model.  
Figure 13 employs a scatter plot with a LOWESS fit curve to provide an intuitive understanding of how the range of feature values influences the model's predictions. The LOWESS curve (the red curved line) represents a weighted regression curve that smooths out non-linear trends in the data. Figure 13 shows the fitted curves for all the features in the dataset. The horizontal dotted line displays SHAP values at zero (y = 0), whereas the vertical blue dotted line shows where the feature value intersects it. This intersection signifies the threshold at which the feature's contribution to the prediction shifts from negative to positive or vice versa. For instance, for XB, values less than 1.19 negatively impact the model's predictions, whereas values greater than 1.19 positively influence the predictions. There are two intersections in the case of E, at 10.29 and 41.66. The predictions are negatively affected by values less than and between 10.29 and 41.66, and positively affected by values  
Figure 11: A bee swarm plot of the SHAP interaction matrix.  
Figure 12: A combination of a local bar plot and a bee swarm plot of feature importances.  
above this range. However, the exact intersection values are difficult to discern in Figure 13, which prompted the use of Figure 14, which provides a clearer depiction of these critical points. For the SB, HB, TB, and Pf features, the intersections are at 1.11, 2.47, 1.29, and 1.28, respectively. This study developed a novel rock fragmentation prediction model and subsequently a user-friendly web interface through cloud deployment. The web interface overcomes the limitations of requiring software downloads on computers or mobile devices, offering seamless accessibility for rock fragmentation prediction applications. The following is the link to the web application accessed on 15 October 2024: [[https://rockfragmentation.streamlit.app/Data_statistics](https://rockfragmentation.streamlit.app/Data_statistics)]([https://rockfragmentation.streamlit.app/Data_statistics](https://rockfragmentation.streamlit.app/Data_statistics)).  
Figure 13: LOWESS fit curve with SHAP scatter plot of each feature.