# Predicting Compressive Strength of
## 4 Results and Discussion  
To validate and test the proposed DCNN model, a 10-fold cross-validation approach was used. The training and validation process of the proposed model is presented in Figure 8.  
As shown in Figure 8, the model--which is designed to be validated every 428 iterations to ensure that the network was not overfitting--starts to fit the data early in the process. The final root mean square error (RMSE) in the training process is approximately 1.39. To measure the prediction accuracy of the proposed DCNN, variable \(\alpha\) was set to represent the gap between the predicted and the actual values. \(\alpha\) is assumed to be an acceptable margin of error; for example, if \(\alpha\) is set at 0.5 and the actual value of one sample is 1.7, this prediction would be accepted as correct if the predicted value was in the range \(1.7\pm 0.5\). In this work, the prediction accuracy is measured using various \(\alpha\) values. The prediction accuracy and its corresponding \(\alpha\) value are presented in Table 2. The final prediction accuracy was calculated by averaging the accuracy of all folds. Figure 7: The architecture of the proposed deep convolutional neural network (DCNN) model. Figure 8: The training process of the proposed DCNN model. As can be seen in Figure 9 and Table 2, the prediction accuracy starts to be acceptable (accuracy \(>\)50%) when \(\alpha\) is assigned to be greater than 0.8 of the tested \(\alpha\) values. Moreover, if it is recalled that the minimum compressive strength of the CSRE samples was 3.41 MPa and the maximum was 13.97 MPa, then \(\alpha\) = 2 might be considered as an acceptable error threshold. Then a reasonable prediction accuracy of 84% is achieved. The accuracy of the prediction is proportional to the margin of error; however, the margin of error cannot be significantly increased to claim a higher prediction accuracy. Therefore, other measures such as the RMSE can be used to acquire a better understanding of the prediction system's performance [37]. Furthermore, to provide more information about the predictions of the proposed deep learning model, the covariance and correlation coefficient are calculated as results of the experiments. Table 3 demonstrates the correlation coefficient and the covariance for each fold separately. As it can be observed in Table 3, the correlation is close to 0.9, which statistically means that the predictions and the actual values have a very strong relationship between them. Moreover, the covariance shows that these sets of data have a positive relationship. \begin{table}
\begin{tabular}{c c} \hline \hline \(\alpha\) & **Prediction Accuracy** \\ \hline
0.4 & 0.31 \\
0.6 & 0.46 \\
0.8 & 0.57 \\
1 & 0.64 \\
1.2 & 0.71 \\
1.4 & 0.75 \\
1.6 & 0.79 \\
1.8 & 0.81 \\
2 & 0.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Prediction accuracy of the proposed DCNN with their \(\alpha\) values. Figure 9: Prediction accuracy of the proposed DCNN as a function of \(\alpha\) value. In addition to the prediction, which is based on regression, the proposed DCNN can offer deep features that can be used by another regression method to obtain the prediction results. Two more regression methods are used: the random forest and linear regression features. In the case of calculating the prediction accuracy of the DCNN, the RMSE is one of the important measures that is usually used to measure the performance of a prediction system [37]. The number of deep features obtained by the proposed DCNN was quite large (4096 features); therefore, a principal component analysis (PCA) was used to reduce the number of features [25; 38; 39], keeping 95% of the data variance to attain only 572 features.