# Research on Hard Rock Pillar Stability Prediction Based on SABO-LSSVM Model
## 4 Results and Discussion
### Models Performance Comparison
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **SABO** & **PSO** & **GWO** & **GA** & **KOA** & **WOA** & **Average** \\ \hline M-1 & 84.74 & 82.93 & 81.93 & 73.28 & 78.92 & 79.30 & 80.18 \\ M-2 & 85.33 & 83.46 & 83.53 & 73.82 & 79.29 & 79.52 & 80.82 \\ M-3 & 85.58 & 84.28  
From the impact of different indicator combinations on various models, the M-3 combination, after excluding \(\rm C_{pav}\) and \(\rm\sigma_{p}\), resulted in an overall average accuracy of 81.23% (as shown in the boxplot), which was slightly higher than that of the M-1 and M-2 combinations, which had average accuracies of 80.18% and 80.82%, respectively. Thus, the accuracy of the model improved slightly. However, when the number of features was further reduced, the average accuracy of the models began to decrease significantly. From the statistical table, it can be observed that the M-4 combination, which removed pillar height, H, from the M-3 combination, experienced a decrease in average prediction accuracy by 1.93%. When pillar width, W, was also removed, the average accuracy decreased by 3.79% compared to that of M-3. Figure 9: _Cont._  
Looking at the response of each model, both the LSSVM and the six optimized LSSVM models exhibited similar changes in their results during the feature selection process, following the overall trend of the average values. The ELM model showed relatively low sensitivity to these manipulations, with fluctuating overall trends, and parameter combination M-2 achieved the highest accuracy. However, the SVM model demonstrated a gradually increasing trend in prediction accuracy when redundant features were removed, contrary to the trends observed in the other models. This indicates a strong correlation between the aspect ratio, K, and C\({}_{\rm paw}\), as well as between the uniaxial compressive strength (UCS) and \(\sigma_{\rm p}\), when used as input for the models. The removal of redundant features can effectively improve the predictive ability of some models. Although pillar height and pillar width exhibited only slight correlations during the correlation analysis, removing either of them during the actual model prediction weakened the model's performance to varying degrees. Therefore, it was necessary to consider the inclusion of both W and H as features when constructing the dataset. There is a relationship between the aspect ratio, K, W, and H, but W and H represent the dimensional characteristics of the pillar and K represents the shape characteristic of the pillar, and they together constitute the pillar dataset as distinct fundamental features. Therefore, when eliminating redundant features, the aspect ratio, K, cannot be disregarded. From the graph, it can be observed that for the M-1, M-2, and M-3 combinations, the SABO-LSSVM model performed the best, followed closely by the PSO-LSSVM and  
Figure 9: Cumulative distribution curves and boxplots of different optimization models’ results of predicting pillar stability under various parameter combinations (%). (**a**) Performance of different models under the M-1 parameter combination. (**b**) Performance of different models under the M-2 parameter combination. (**c**) Performance of different models under the M-3 parameter combination. (**d**) Performance of different models under the M-4 parameter combination. (**e**) Performance of different models under the M-5 parameter combination. GWO-LSSVM models. The GA-LSSVM, KOA-LSSVM, and WOA-LSSVM models had lower prediction accuracies, indicating that the SABO-optimized model outperformed the baseline model and other optimization models in the first three parameter combinations. The overall performance of the models in the M-4 and M-5 combinations declined compared with the first three combinations, with the most significant decline observed in the M-5 combination.