## 3 Results and Discussion
As shown in Table 5, the performance of the networks (\(ANN_{8}\)) with the combinations of two aggregate characteristics added as inputs of \(ANN_{6}\)-\(f_{c}\) was not necessarily better than those with only one aggregate characteristic added to the inputs. This was mainly due to the fact that the degrees of influence related to these aggregate characteristics were inconsistent, which may have misled the correlation of the inputs and outputs. However, the results demonstrated that the use of seven combinations (italics) of aggregate characteristics as inputs to \(ANN_{6}\)-\(f_{c}\) could improve the predicted capability of the networks; these combinations were \(SG_{\text{SSD}}\) and \(W_{\text{a}}\), \(SG_{\text{SSD}}\) and TFV, \(W_{\text{a}}\) and \(\delta\), \(W_{\text{a}}\) and TFV, FM and TFV, m and \(\delta\), and m and \(M_{\text{c}}\). Then, these combinations of two characteristics were used to examine whether they could form new combinations of three or four characteristics that could further improve the prediction of the networks. The results listed in Table 6 show that the error of networks could be reduced to 5.43-5.91 when the following combinations of aggregate characteristics, together with \"certainties\", were adopted as the inputs of networks: \(SG_{\text{SSD}}+W_{\text{a}}+\delta\), \(SG_{\text{SSD}}+m+TFV+M_{\text{c}}\), \(SG_{\text{SSD}}+W_{\text{a}}+TFV\) and FM + m + TFV + \(M_{\text{c}}\). Moreover, the further combinations of these factors was no longer useful to reduce the error of prediction of the networks (Table 7). Figure 6: Influence of each uncertainty on the properties of RAC relative to models (\(ANN_{6}\)) with only “certainties” as inputs—Stage a. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Factors** & \(SG_{\text{SSD}}\) & \(W_{\text{a}}\) & \(FM\) & \(M_{\text{c}}\) & \(\delta\) & \(m\) & \(TFV\) & \(ACV\) \\ \hline \(SG_{\text{SSD}}\) & **6.44** & 5.94 & 6.95 & 7.12 & 6.8 & 7.63 & 6.11 & 6.54 \\ \(W_{\text{a}}\) & & **6.03** & 6.6 & 6.99 & 5.76 & 6.89 & 5.92 & 6.55 \\ FM & & & **7.36** & 7.34 & 7.48 & 6.91 & 6.55 & 8.02 \\ \(M_{\text{c}}\) & & & & **7.7** & 5.84 & 5.99 & 6.99 & 7.25 \\ \(\delta\) & & & & & **7.07** & 6.88 & 8.09 & 7.23 \\ m & & & & & & **6.16** & 8.32 & 6.64 \\ TFV & & & & & & & **6.94** & 6.87 \\ ACV & & & & & & & **6.42** \\ \hline \hline \end{tabular} For Tables 5–8, each figure represents the mean absolute percentage error (_MAPE_) value of the networks with “certainties” and the uncertain factors indicated in the 1 st row and 1 st column as inputs; the bold figures represent the _MAPE_ value of the networks with “certainties” and the uncertain factors indicated either in the 1 st row or 1 st column as inputs; the underlined figures are _MAPE_ values lower than those of the corresponding bold letters.  
\end{table} 
Table 5: The errors of networks for compressive strength with different input variables—Stage b (%). To sum up, the addition of any one of the eight aggregate characteristics to \(ANN_{6}\)-\(f_{c}\) could help achieve a better prediction of the compressive strength of RAC. When these characteristics were added to the input variables of \(ANN_{6}\)-\(f_{c}\) alone, water absorption contributed to the largest reduction in the error of networks, from about 8.11% to only 6.03%. The use of some combinations of these eight characteristics could further decrease the error of networks, even lower than that of \(ANN_{14}\)-\(f_{c}\). The network error was only 5.43% when a combination of \(\mathrm{SG}_{\mathrm{SSD}}\), \(W_{\mathrm{a}}\), \(\delta\), and the \"certainties\" (mix proportions and curing ages) were used as the input variables. The case was slightly different for the elastic modulus. As shown in Figure 5, the error of the networks (\(ANN_{6}\)-\(E_{c}\)) with only the mix proportions and the curing ages as inputs was about 6.73%.