## 5 Results and Discussion  
### AOp Model Performance Appraisal Results and Discussion  
The predictive performances of the AOp prediction models generated in this study were appraised using the error metrics listed, and the results are presented in Table 3 for the training and test data, respectively. From Table 3, it is evident that soft computing models such as ANN, SMA-ANN, and MVO-ANN perform better than the empirical predictor and MLR models. Starting with the stand-alone ANN model, the values of MAE, MSE, RMSE, MAPE, RRMSE, and R\({}^{2}\) were 2.881, 12.820, 3.581, 4.350, 0.056, and 0.786 for the training datasets, and 2.303, 10.319, 3.212, 3.418, 0.048, and 0.788 for the test datasets, respectively. The developed SMA-ANN model displayed the smallest MAE, MSE, RMSE, MAPE, and RRMSE and the largest R\({}^{2}\) values of 2.363, 10.803, 3.286, 3.576, 0.051, and 0.809 for the training datasets and 2.102, 8.084, 2.843, 3.245, 0.045, and 0.867 for the test datasets, respectively. For the MVO-ANN model, the MAE, MSE, RMSE, MAPE, RRMSE, and R\({}^{2}\) values for the training datasets are 2.441, 11.712, 3.422, 3.740, 0.053, and 0.805, and 2.254, 8.323, 2.885, 3.380, 0.047, and 0.830, for the test datasets, respectively. The MLR model had the highest error metrics and the poorest performance of all the developed models, with MAE, MSE, RMSE, MAPE, RRMSE, and R\({}^{2}\) values of 5.768, 49.115, 7.008, 8.744, 0.110, and 0.122 for the training datasets and 6.555, 77.281, 8.791, 9.800, 0.128, and 0.044 for the test datasets, respectively. The performance of the USBM empirical predictor commonly used in rock construction excavation blasting is averagely poor, with MAE, MSE, RMSE, MAPE, RRMSE, and R\({}^{2}\) values of 5.272, 43.305, 6.581, 8.011, 0.103, and 0.226 for the training datasets and 6.084, 63.824, 7.989, 9.118, 0.117, and 0.049 for the test datasets, respectively.  
The findings in Table 3 are supported by a graphical representation of the relationship between field measurements and forecasted AOp by the generated models, as shown in Figure 8a-e. The SMA-ANN model fit line was determined to be closer to the perfect fit line, with R2 values close to the perfect R\({}^{2}\) values for both the training and test datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Stage** & **AOp Model** & **R\({}^{2}\)** & **MAE** & **MSE** & **RMSE** & **MAPE** & **RRMSE** \\ \hline \multirow{4}{*}{Training} & ANN & 0.786 & 2.881 & 12.820 & 3.581 & 4.350 & 0.056 \\  & SMA-ANN & 0.809 & 2.363 & 10.803 & 3.286 & 3.576 & 0.051 \\  & MVO-ANN & 0.805 & 2.441 & 11.712 & 3.422 & 3.740 & 0.053 \\  & MLR & 0.122 & 5.768 & 49.115 & 7.008 & 8.744 & 0.110 \\  & USBM & 0.226 & 5.272 & 43.305 & 6.581 & 8.011 & 0.103 \\ \hline \multirow{4}{*}{Test} & ANN & 0.788 & 2.303 & 10.319 & 3.212 & 3.418 & 0.048 \\  & SMA-ANN & 0.867 & 2.102 & 8.084 & 2.843 & 3.245 & 0.045 \\ \cline{1-1}  & MVO-ANN & 0.830 & 2.254 & 8.323 & 2.885 & 3.380 & 0.047 \\ \cline{1-1}  & MLR & 0.044 & 6.555 & 77.281 & 8.791 & 9.800 & 0.128 \\ \cline{1-1}  & USBM & 0.049 & 6.084 & 63.824 & 7.989 & 9.118 & 0.117 \\ \hline \hline \end{tabular}
\end{table}
Table 3: AOp prediction model performance appraisal results.  
Figure 8: _Cont_.