# Damage Evaluation in Tempered Vacuum Glazing via Multivariate Statistical Methods
## 3 Results
### PCA Process and Results  
To standardize data in Table 8, average values and standard deviations were calculated at first (see Table 9). After that the data were standardized using the normalization method. The results can be seen in Table 10.  
PCA was performed afterwards on the data from Table 10 using Statistical Product and Service Solutions (SPSS) software, and the results are shown in Table 11. Six components were selected from the initial solution. The total variance of the original variables was calculated, giving the cumulative contribution rate of 100%. Two components with \(\lambda\) exceeding one (2.607 and 1.314) were selected as the most informative, whose contribution rates were found to be 43.455% and 21.906%, respectively, resulting in the cumulative contribution rate of 65.361%. In this case, PCA is satisfactory because most of the information about the parameters of the samples could be successfully extracted.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(\mathbf{z_{1}}\) & \(\mathbf{z_{2}}\) & \(\mathbf{z_{3}}\) & \(\mathbf{z_{4}}\) & \(\mathbf{z_{5}}\) & \(\mathbf{z_{6}}\) \\ \hline
1 & 1.74111 & 1.09545 & 0.52623 & 1.21529 & \(-\)0.40967 & 0.40967 \\
2 & \(-\)0.92176 & 0 & \(-\)0.61394 & 1.21529 & 0.92176 & 1.74111 \\
3 & \(-\)0.92176 & 0 & \(-\)1.75412 & \(-\)0.10127 & 0.92176 & 0.40967 \\
4 & 0.40967 & 1.09545 & 0.52623 & \(-\)0.10127 & 0.92176 & \(-\)0.92176 \\
5 & 0.40967 & 0 & \(-\)0.61394 & \(-\)1.41784 & \(-\)0.40967 & \(-\)0.92176 \\
6 & \(-\)0.92176 & \(-\)1.09545 & \(-\)1.75412 & \(-\)1.41784 & \(-\)1.74111 & \(-\)0.92176 \\
7 & 0.40967 & 1.09545 & 1.66641 & \(-\)0.10127 & \(-\)0.40967 & 0.40967 \\
8 & \(-\)0.92176 & \(-\)2.19089 & 0.52623 & \(-\)0.10127 & \(-\)0.40967 & \(-\)0.92176 \\
9 & \(-\)0.92176 & \(-\)1.09545 & 0.52623 & \(-\)1.41784 & 0.92176 & 0.40967 \\
10 & \(-\)0.92176 & 0 & \(-\)0.61394 & \(-\)0.10127 & \(-\)1.74111 & \(-\)0.92176 \\
11 & 0.40967 & 0 & 0.52623 & \(-\)0.10127 & 0.92176 & 1.74111 \\
12 & 0.40967 & 1.09545 & 0.52623 & 1.21529 & 0.92176 & \(-\)0.92176 \\
13 & 1.74111 & 0 & 0.52623 & 1.21529 & \(-\)0.40967 & 0.40967 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Standardized results of sample parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sample** & \(\mathbf{Z_{1}}\) & \(\mathbf{Z_{2}}\) & \(\mathbf{Z_{3}}\) & \(\mathbf{Z_{4}}\) & \(\mathbf{Z_{5}}\) & \(\mathbf{Z_{6}}\) \\ \hline
1 & 9 & 9 & 8 & 9 & 7 & 8 \\
2 & 7 & 8 & 7 & 9 & 8 & 9 \\
3 & 7 & 8 & 6 & 7 & 8 & 8 \\
4 & 8 & 9 & 8 & 7 & 8 & 7 \\
5 & 8 & 8 & 7 & 5 & 7 & 7 \\
6 & 7 & 7 & 6 & 5 & 6 & 7 \\
7 & 8 & 9 & 9 & 7 &The coefficients of elements 1 and 2 were afterwards calculated using the regression method in SPSS software. The results are available in Table 12, where \(z_{1}\) and \(z_{2}\) components account for a major proportion. This means that surface stress and vacant pillars exert a significant influence on the TVG damage, which agrees with a practical situation.  
According to the data in Table 12 and Formula (1), the new variables were determined as follows:  
\[\left\{\begin{array}{l c c}p_{1}=0.424z_{1}+0.347z_{2}+0.288z_{3}+0.255z_{4}-0. 076z_{5}-0.085z_{6}\\ p_{2}=-0.184z_{1}-0.046z_{2}-0.012z_{3}+0.138z_{4}+0.556z_{5}+0.565z_{6}\end{array}\right. \tag{8}\]  
In turn, the scores of two principal components were generated by calculating the standardized values from Table 10 using Formula (8). The results can be found in Table 13.