# Deep Neural Network for Predicting Ore Production by Truck-Haulage Systems in Open-Fit Mines
## 3 Methods
### Experimental Setup for DNN Model Training  
To optimize the DNN models to predict the morning and afternoon ore productions efficiently, the DNN models were trained with different settings for the number of hidden layers and the number of nodes within them. Table 4 describes the number of hidden layers and the number of hidden layer nodes set for DNN model training by experience. The number of hidden layers was varied from three to five, and the number of hidden layer nodes varied from 30 to 50 in increments of 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multicolumn{3}{c}{**Ore Production (M 1)**} & \multicolumn{3}{c}{**Ore Production (A 2)**} \\ \cline{2-7}  & \multicolumn{3}{c}{**Dump Truck Type**} & \multicolumn{3}{c}{**Dump Truck Type**} \\ \cline{2-7}  & **45 tons** & **60 tons** & **84 tons** & **45 tons** & **60 tons** & **84 tons** \\ \hline Average number of dispatched trucks & 4 & 2 & 4 & 3 & 2 & 4 \\ Average utilization ratio (DA \({}^{3}\)DB \({}^{4}\)) & 0.51:0.49 & 0.34:0.66 & 0.27:0.73 & 0.45:0.55 & 0.30:0.70 & 0.21:0.79 \\ \hline Average stay time (min) & DA & & 2.25 & & & 2.29 & \\  & DB & & 3.65 & & & 2.64 & \\ \hline Average travel time (min) & DA & & 11.08 & & & 11.51 & \\  & DB & & 10.39 & & 10.47 & \\ \hline \hline \end{tabular}  
* Morning, 2 Afternoon, 3 Dumping zone A, 4 Dumping zone B.  
\end{table} 
Table 2: Results of statistical analysis of training data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Ore Production during Morning Operation Time** & **Ore Production during Afternoon Operation Time** \\ \hline
**Input Variables** & **PCC 1** & **Input Variables** & **PCC 1** \\ \hline Interval between operation times & 0.77 & Interval between operation times & 0.81 \\ Relative operation end time & 0.43 & Relative operation end time & 0.40 \\ Number of dispatched 60 tons trucks & 0.41 & Number of dispatched 60 tons trucks & 0.37 \\ Number of dispatched 84 tons trucks & 0.31 & Number of dispatched 84 tons trucks & 0.33 \\ Dumping zone A utilization of 60 tons trucks & 0.22 & Dumping zone B utilization of 84 tons trucks & 0.17 \\ Number of dispatched 45 tons trucks & 0.22 & Number of dispatched 45 tons trucks & 0.17 \\ Average staying time of trucks in dumping zone B & \(-0.19\) & Dumping zone A utilization of 84 tons trucks & \(-0.10\) \\ Relative operation start time & \(-0.33\) & Relative operation start time & \(-0.40\) \\ \hline \hline \end{tabular}  
* Pearson correlation coefficient.  
\end{table} 
Table 3: Pearson correlation coefficient values obtained between different input variables and ore production during the morning and afternoon operation times. A 5-fold cross validation was conducted five times to evaluate prediction performance of DNN models with different hidden layer configurations. The 5-fold cross validation randomly shuffles the data set and divides the data set into five sets. One set is used for validation set and the other four sets are used for training set. Five experimental validations are executed at one round. After one round of cross-validation, random shuffling process of the whole data set is repeated again. That is, totally 25 experimental runs are used for the performance evaluation on the DNN model. To evaluate the prediction error of the DNN models, the values of the coefficient of determination (\(R^{2}\)) and mean absolute percentage error (MAPE) between predicted and observed values were evaluated. Equation (9) defines the evaluation of the coefficient of determination, wherein \(n\) denotes the number of datasets; \(y_{i}\) denotes the observed value of the ith training data; \(\hat{y}_{i}\) denotes the predicted value of the ith training data; and \(\overline{y}\) denotes the mean observed value. Equation (10) describes MAPE evaluation.