# Toward a State-of-the-Art of Fly-Rock Prediction Technology in Open-Pit Mines Using EANNs Model
## 6 Results  
Before developing the ANN and EANNs models for predicting FR, the original dataset was divided randomly into two parts: (1) training part (80% of the whole original database); (2) testing part (20% remained). As illustrated in Figure 5, five ANN models were developed first; then, they were combined as a new generation of ANN model (i.e., EANNs model). To avoid the over-fitting of the ANN models, the original dataset was normalized by a min-max scale in the range of [-1, 1]. Finally, five ANN models were selected for predicting FR in the first step, including ANN 5-7-5-1, ANN 5-10-8-1, ANN 5-14-9-1, ANN 5-18-13-1, and ANN 5-21-16-1. An ANN model for predicting FR in this study is illustrated in Figure 6. Subsequently, an ensemble of the five developed ANN models was conducted (i.e., EANNs model). The structure of the proposed EANNs model is shown in Figure 7. Accordingly, the structure of the EANNs model includes three hidden layers (i.e., 5-25-21-15-1); therefore, to have a complete conclusion, the EANNs model was used to train and test the original data (called ANN 5-25-21-15-1 model). The results of the FR predictive models are computed in Tables 2 and 3. Based on the statistical indexes in Tables 2 and 3, the ANN models (six sub-models) performed very well in estimating FR. Their performance is relatively uniform. Notably, the third sub-model (i.e., ANN 5-14-9-1) seems to provide the lowest performance among the six ANN models. For the proposed EANNs model, the high red intensity has revealed that its performance is superior in this study. It should be noted that the EANNs model was developed based on an ensemble of the first five ANN models in Tables 2 and 3, and the sixth ANN model was only developed based on the original database to compare with the EANNs model (with the new database based on the predictions of the first five ANN models). The promising results of the proposed EANNs model were validated through the statistical indexes in Tables 2 and 3. Remarkably, the sixth ANN model (i.e., ANN 5-25-21-15-1) has three hidden layers that have the same structure as those of the proposed EANNs model; however, its performance was lower than those of the proposed EANNs model. Thus, the use of the availableANN models as the sub-models to build a new model (i.e., EANNs model) has led to significant improvement in predicting FR. Figure 8 shows the accuracy of different ANN and EANNs models. Furthermore, a comparison of the proposed EANNs model (on the new database) and an ANN model with the same structure (on the original database) is shown in Figure 9.  
Figure 6: The ANN 5-7-5-1 model for estimating FR. Figure 7: The proposed EANNs model (ensemble of the ANN models) for estimating FR. Figure 8: Accuracy of different ANN and EANNs models in estimating fly-rock. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Model** & **MAE** & **MAPE** & **RMSE** & **VAF** & **R\({}^{2}\)** & **Rank for MAE** & **Rank for MAPE** & **Rank for RMSE** & **Rank for VAF** & **Rank for R\({}^{2}\)** \\ \hline ANN & 3.301 & 0.021 & 6.231 & 97.563 & 0.976 & 6 & 5 & 5 & 5 & 5 \\ ANN & 3.416 & 0.022 & 6.413 & 97.419 & 0.974 & 4 & 4 & 2 & 2 & 2 \\ ANN & 3.26 & 0.021 & 6.122 & 97.648 & 0.976 & 5 & 5 & 6 & 6 & 5 \\ ANN & 3.482 & 0.023 & 6.309 & 97.502 & 0.975 & 3 & 3 & 4 & 4 & 3 \\ ANN & 3.67 & 0.024 & 6.672 & 97.206 & 0.972 & 2 & 1 & 1 & 1 & 1 \\ ANN & 3.695 & 0.024 & 6.361 & 97.460 & 0.975 & 1 & 1 & 3 & 3 & 3 \\ EANNs & 2.908 & 0.019 & 4.954 & 98.464 & 0.985 & 7 & 7 & 7 & 7 & 7 \\ \hline \multicolumn{10}{c}{**Note:** MAE (mean absolute error), MAPE (mean absolute percentage error), RMSE (root-mean-squared error), VAF (variance accounted for), and R\({}^{2}\) (correlation coefficient).