## 3 Results and Discussion  
The performance of the constructed ANN models (\(ANN_{14}\)-\(f_{c}\), \(ANN_{14}\)-\(E_{c}\)) in predicting the compressive strength and elastic modulus of RAC with all 14 variables and compared to the models (\(ANN_{6}\)-\(f_{c}\), \(ANN_{6}\)-\(E_{c}\)) using only the \"certainties\" as input variables is shown in Table 4 and Figure 5.  
Figure 4: ANN model constructed for compressive strength or elastic modulus. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sources**} & \multirow{2}{*}{**Mixes**} & \multicolumn{5}{c}{\(f_{c}\) (**MPa**)} & \multicolumn{5}{c}{\(E_{c}\) (**GPa**)} \\ \cline{3-8}  & & **1 Day** & **4 Days** & **7 Days** & **28 Days** & **90 Days** & **28 Days** & **90 Days** \\ \hline T5r50 & 20 & 34.9 \({}^{\text{c}}\) & 41.4 & 49.1 & 54 & 27.39 & 30.13 \\ T5r100 & 18.5 & & 36.5 & 44.7 & 47.4 & 25.69 & 26.15 \\ T10r50 & 19.2 & 37.6 & 42.5 & 50.7 & 52.8 & 26.72 & 28.87 \\ T10r100 & 14.4 & 28.6 & 34.4 & 39.9 & 42 & 24.55 & 25.55 \\ r0 & 21.3 & 42.1 & 48.2 & 51.3 & 30.45 & 33.86 \\ r50 & 20 & 40.2 & 44.1 & 50.3 & 53.6 & 29.58 & 30.35 \\ r100 & 18 & 40.1 & 43 & 49.2 & 51.3 & 26.78 & 27.86 \\ \hline \hline \end{tabular}  
* \({}^{\text{a}}\), \({}^{\text{b}}\), \({}^{\text{c}}\) measured at the age of 5 days, 2 days and 3 days, respectively.  
\end{table} 
Table 3: \(Cont.\)The correlation coefficient \(R^{2}\) of the networks in modeling the compressive strength and elastic modulus reached 0.9984 and 0.9999, respectively, indicating that the correlations between the predictions and the true results were very good. The \(R^{2}\) values of both models were all above 0.994 in the testing and validation sets and these further proved that the constructed models, \(ANN_{14}\)-\(f_{c}\) and \(ANN_{14}\)-\(E_{c}\), had not only good simulating abilities, but also good generalization capabilities. When only the mix proportions and the curing ages were used as the inputs of the networks, the \(R^{2}\) values of \(ANN_{6}\)-\(f_{c}\) and \(ANN_{6}\)-\(E_{c}\) in the training sets were still up to 0.997 and 0.9941. However, the generalization performance (testing and validation sets) of both networks were significantly poorer, with the \(R^{2}\) values reduced to the range of 0.987-0.9931 and the predicted errors _MAPE_ increased by about 50% in both the validation and testing sets. This might explain why many established formulae (based on regression analysis) could not be used for practical applications although they had good correlation coefficients. For compressive strength, Figure 6 shows that the predicted error of the networks (\(ANN_{6}\)-\(f_{c}\)) using only \"certainties\" as inputs was about 8.11%, and the performance of the networks could be enhanced with the addition of each aggregate characteristic to the inputs. It can be found that the predicted error of compressive strength was lower when the water absorption or masonry content of the coarse aggregate were taken into consideration, which was almost close to the model (\(ANN_{14}\)-\(f_{c}\)) with all variables as inputs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sets** & **Model** & \(R^{2}\) & **RMS** & **MAPE (\%)** & **Model** & \(R^{2}\) & **RMS** & **MAPE (\%)** \\ \hline Training & & 0.9984 & 2.067 & 3.531 & & 0.9999 & 0.2825 & 0.73 \\ Testing & \(ANN_{14}\)-\(f_{c}\) & 0.9952 & 3.445 & 5.859 & \(ANN_{14}\)-\(E_{c}\) & 0.9965 & 1.6986 & 4.72 \\ Validation & & 0.9949 & 3.562 & 6.032 & & 0.9968 & 1.563 & 4.399 \\ \hline Training & & 0.997 & 2.764 & 4.743 & & 0.9941 & 0.9558 & 2.641 \\ Testing & \(ANN_{6}\)-\(f_{c}\) & 0.987 & 5.234 & 8.67 & \(ANN_{6}\)-\(E_{c}\) & 0.9931 & 2.3066 & 6.437 \\ Validation & & 0.992 & 4.41 & 7.557 & & 0.9913 & 2.5234 & 7.264 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of ANN models. _MAPE_: the mean absolute percentage error; RMS: root-mean-squared error. Figure 5: Performance of the ANN models constructed. _MAPE_: the mean absolute percentage error; RMS: root-mean-squared error.