## 3 Parameters Studies and Discussions
### Orthogonal Design Test
#### 3.2.3 Selection of Active Factors  
The results calculated during the simulation for the observation parameters listed in Table 2 are adopted as observation vectors for Equation (3) for evaluation. Table 3 shows the mean square errors of analysis factors under different observation parameters. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**No.** & \(\mathbf{x_{1}}\) & \(\mathbf{x_{2}}\) & \(\mathbf{x_{3}}\) & \(\mathbf{x_{4}}\) & \(\mathbf{x_{5}}\) & \(\mathbf{x_{6}}\) & \(\mathbf{x_{7}}\) & \(\mathbf{x_{8}}\) & \(\mathbf{x_{9}}\) & \(\mathbf{x_{10}}\) & \(\mathbf{x_{11}}\) & \(\mathbf{x_{12}}\) & \(\mathbf{x_{13}}\) & \(F_{x}\) (\(\mathbf{kN}\)) & \(F_{y}\) (\(\mathbf{kN}\)) & \(A_{c}\) (\(\mathbf{mm^{2}}\)) \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 2: Twenty-seven experiment samples and the corresponding observation values. (1) \(H\) statistic value  
For the \(H\) statistic, in this paper, it is supposed that the effect is 0 for at least two columns of values in Table 2, i.e., \(s=2\). In addition, the given global significance level of this paper is \(\alpha=0.05\). According to Equation (11) regarding calculation of \(l\), the \(l\) values obtained corresponding to the four observation para meters are: \(l=10\) for \(F_{z}\), \(l=12\) for \(F_{x}\), \(l=11\) for \(F_{y}\) and \(l=6\) for \(A_{c}\). Table 4 shows the \(H\) statistic values of all analysis factors calculated according to Equation (10). Figure 11 shows the \(H\) statistic positions of the observation parameters corresponding to different analysis factors in contrast with those of the critical value. As shown in Figure 12, for \(F_{z}\), the \(H\) statistic values of 3 analysis factors are higher than the critical value, namely \(x_{1}\), \(x_{2}\) and \(x_{13}\) are the significant influence factors of \(F_{z}\). Similarly, \(x_{13}\) is the significant influence factor of \(F_{x}\) and \(F_{y}\), \(x_{4}\), \(x_{10}\) and \(x_{12}\) are the significant influence factors of \(A_{c}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{6}{c}{**\(H\) Statistic Values**} & \multirow{2}{*}{**Critical Value**} \\ \cline{2-2} \cline{5-8}  & \(F_{z}\) & & & \(F_{x}\) & & \(F_{y}\) & & \(A_{c}\) \\ \hline \(x_{7}\) & 0.06469 & \(x_{1}\) & 0.02988 & \(x_{6}\) & 0.17214 & \(x_{9}\) & 0.14598 & 5.505 \\ \(x_{4}\) & 0.14401 & \(x_{10}\) & 0.03287 & \(x_{5}\) & 0.18075 & \(x_{7}\) & 0.18981 & 5.505 \\ \(x_{6}\) & 0.16229 & \(x_{9}\) & 0.11743 & \(x_{11}\) & 0.25236 & \(x_{11}\) & 1.05385 & 5.505 \\ \(x_{11}\) & 0.25897 & \(x_{11}\) & 0.15806 & \(x_{8}\) & 0.31184 & \(x_{13}\) & 1.06055 & 5.505 \\ \(x_{10}\) & 0.56367 & \(x_{12}\) & 0.17824 & \(x_{3}\) & 0.41736 & \(x_{6}\) & 1.42821 & 5.505 \\ \(x_{9}\) & 0.60404 & \(x_{3}\) & 0.18985 & \(x_{12}\) & 0.49595 & \(x_{8}\) & 1.62203 & 5.505 \\ \(x_{3}\) & 0.65548 & \(x_{5}\) & 0.37128 & \(x_{7}\) & 0.50449 & \(x_{1}\) & 3.16670 & 5.505 \\ \(x_{5}\) & 0.66202 & \(x_{8}\) & 0.80207 & \(x_{9}\) & 0.79891 & \(x_{3}\) & 3.93523 & 5.505 \\ \(x_{12}\) & 0.70907 & \(x_{6}\) & 1.12715 & \(x_{1}\) & 1.11541 & \(x_{2}\) & 4.77114 & 5.505 \\ \(x_{8}\) & 1.16509 & \(x_{7}\) & 1.24410 & \(x_{10}\) & 1.15407 & \(x_{5}\) & 5.24434 & 5.505 \\ \(x_{13}\) & 5.89688 & \(x_{4}\) & 2.22188 & \(x_{4}\) & 1.81392 & \(x_{10}\) & 5.61736 & 5.505 \\ \(x_{1}\) & 8.81897 & \(x_{2}\) & 2.40877 & \(x_{2}\) & 3.77904 & \(x_{12}\) & 5.99169 & 5.505 \\ \(x_{2}\) & 10.78661 & \(x_{13}\) & 10.03983 & \(x_{13}\) & 10.67472 & \(x_{4}\) & 6.76578 & 5.505 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: \(H\) statistic values of 13 analysis factors.