## 3 Application Results and Discussion  
### Selection of the Input Variables Using the PCA Technique  
In this paper, to propagate the most effective combination of inputs for the simulation matrix of the mechanical characteristics, principal component analysis (PCA) based on dimensionality reduction was performed. The predictor variables affecting mechanical characteristics of RCCP of different ages are described as bellow:  
\[f_{c}=f(CA,FA,C,SCM,B,\ W,\frac{W}{C},\frac{W}{B},\frac{SCM}{B},\frac{CA}{FA}) \tag{11}\]where \(CA\) (Kg/m\({}^{3}\)), \(FA\) (Kg/m\({}^{3}\)), \(C\) (Kg/m\({}^{3}\)), \(SCM\) (Kg/m\({}^{3}\)), \(B\) (Kg/m\({}^{3}\)), \(W\) (Kg/m\({}^{3}\)), \(W\)/\(C\), \(W\)/\(B\), \(SCM\)/\(B\), and \(CA\)/\(FA\) are the coarse aggregate content, fine aggregate content, cement content, supplementary cementitious material content, binder content, water content, ratio of water to binder, ratio of supplementary cementitious material to binder, and ratio of coarse to fine aggregate, respectively. Table 1 reports the results of analysis consisting the contribution of 10 inputs to 10 PCs, the explained variance (EV) of each PC, and the cumulative sum (CS) of EV. PC1 represents 51.3% and the first four PCs represent 99.1% of total variance. The optimal input combinations are made bold in the table. The higher the EV, the better the combination of inputs. The optimal combination of mixture proportions is calculated using Equation (11) using the PCA technique, as presented in Table 1. Five predictors provided the majority of the explained variance. Table 1 presents the values of the PCs and their variances. In Table 1, it can be seen that the volumetric and weighted forms of the experimental variables of \(CA\), \(FA\), \(SCM\), \(W\), and \(B\), based on PC1, are the most effective independent predictor variables. Therefore, this combination of simulation variables along with age of specimens (\(AS\)) is used to construct the models to predict the mechanical characteristics of the concrete. The descriptive measures of the best combination of inputs for simulation of the mechanical characteristics of RCCP are presented in Table 2. The correlation coefficients of the selected independent variables for development of the proposed models are presented in Figure 2. According to the matrix, there are no significant relationships between the developed matrix \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Variable** & **PC1** & **PC2** & **PC3** & **PC4** & **PC5** & **PC6** & **PC8** & **PC9** & **PC10** \\ \hline
**CA** & **0.262** & \(-\)0.942 & 0.187 & 0.086 & \(-\)0.028 & \(-\)0.001 & 0.000 & 0.000 & 0.000 \\
**FA** & **\(-\)0.959** & \(-\)0.244 & 0.054 & 0.113 & \(-\)0.065 & \(-\)0.007 & 0.000 & 0.000 & 0.000 \\
**C** & 0.011 & 0.168 & 0.777 & 0.151 & 0.108 & 0.007 & 0.003 & 0.000 & 0.001 \\
**W/B** & 0.000 & 0.000 & 0.000 & \(-\)0.001 & 0.000 & 0.007 & \(-\)0.113 & \(-\)0.993 & 0.019 \\
**SCM** & **0.046** & \(-\)0.043 & \(-\)0.546 & 0.600 & 0.069 & 0.004 & \(-\)0.002 & 0.000 & \(-\)0.002 \\
**W** & **0.072** & 0.082 & 0.081 & 0.187 & \(-\)0.971 & \(-\)0.056 & \(-\)0.003 & 0.000 & 0.001 \\
**B** & **0.057** & 0.125 & 0.231 & 0.750 & 0.178 & 0.011 & 0.001 & \(-\)0.001 & \(-\)0.001 \\
**W/C** & 0.000 & 0.000 & \(-\)0.003 & 0.001 & \(-\)0.004 & 0.001 & 0.986 & \(-\)0.115 & \(-\)0.117 \\
**SCM/B** & 0.000 & 0.000 & \(-\)0.002 & 0.001 & 0.000 & 0.000 & 0.118 & 0.006 & 0.993 \\
**CA/FA** & \(-\)0.003 & 0.000 & 0.000 & 0.000 & \(-\)0.058 & 0.998 & 0.000 & 0.007 & 0.000 \\
**EV** & 0.513 & 0.326 & 0.098 & 0.054 & 0.008 & 0.000 & 0.000 & 0.000 & 0.000 \\
**CS** & 0.513 & 0.839 & 0.937 & 0.991 & 1 & 1 & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Principal component analysis results to select optimal input combination.