# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 4 Results and Discussion
### Models Performance Comparison  
To validate whether the improved LSSVM model performed better, it is necessary to compare the prediction accuracy of the model before and after improvement. To examine the effectiveness of traditional pillar classification methods, safety factor analysis was also employed. The pillar safety factor evaluation involves assessing the stability level of an object by calculating the ratio of the pillar's own strength \"\(\sigma\),\" to the actual load \"\(\sigma\)\" it bears, denoted as \(\mathrm{K}=\sigma_{\mathrm{p}}/\sigma\), where \(\mathrm{K}\) represents the safety factor index. According to  
Figure 8: Result of balancing the M-3 feature combination dataset (red part means failed samples, yellow part means unstable samples, and green part means stable samples). (**a**) Default, (**b**) Smote, (**c**) Adasyn, and (**d**) Tomek–Smote. commonly used stability rating criteria, the pillar cases can be classified into three states: K\({}_{\rm z}\geq 2\) indicates a stable state, 1.2 \(\leq\) K\({}_{\rm z}\) < 2 signifies an unstable state, and K\({}_{\rm z}\) < 1.2 corresponds to a failure state. From the statistical Table 3, it can be observed that the average accuracy of SABO-LSSVM in the five datasets improved by 18.99% compared to that of LSSVM. It also showed improvements of 30.32% and 16.78% compared with the SVM and ELM models, respectively. Therefore, the original model, after parameter optimization with the SABO algorithm, can effectively enhance the accuracy of pillar state prediction. The classification results of the pillar cases using the safety factor (SF) method showed significantly lower accuracy compared to other machine learning methods. Specifically, with parameter combinations M-1 and M-2, the SABO-LSSVM model achieved accuracy rates 35.36% and 35.95% higher, respectively, than the safety factor method. Additionally, to compare the effectiveness of SABO with that of other optimization algorithms, a horizontal comparison of the optimization algorithms is required. From the results in the statistical Table 4, it can be observed that for datasets composed of different indicator combinations, the SABO-LSSVM model had the highest average prediction accuracy of 83.75%. The PSO-LSSVM and GWO-LSSVM models followed, with average accuracies of 82.94% and 82.54%, respectively. The models optimized using GA, WOA, and KOA showed slight improvements over the initial model, but their average accuracies were all below 80%, which is significantly lower than that of the top three models. In order to further evaluate the prediction results exhibited by the LSSVM models optimized by different algorithms, this study presents the overall distribution of the prediction results from six optimization models in the form of cumulative distribution curves, the results are shown in Figure 9. These curves provide a visual representation of the concentrated distribution areas of prediction accuracy on the test set for each model. The closer the curve is to the bottom-right corner, the more concentrated the results are in the high-accuracy range [43], indicating a more stable and accurate prediction capability of the model. Origin was used to plot the curves, and the Boltzmann nonlinear fitting function was employed to fit the cumulative distribution curves. Orthogonal distance regression was used as the iteration algorithm, resulting in a good fit of the processed curves.