## 6 Sensitivity Analysis of Influencing Factors  
According to the above simulation results, the change value of each influence parameter is selected as the comparison matrix \(X\), and the displacement \(Y_{a}\), velocity \(Y_{b}\), and acceleration \(Y_{c}\) under the corresponding conditions are taken as the reference matrix. The comparison matrix and reference matrix are established, and the grey correlation degree of  
Figure 26: The law of mid\(-\)span peak value changing with vehicle mass (**a**) displacement, (**b**) velocity, and (**c**) acceleration. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Vehicle Mass (kN)**} & \multicolumn{1}{c}{**Displacement (mm)**} & \multicolumn{1}{c}{**Velocity (mm\(\cdot\)s\({}^{-1}\))**} & \multicolumn{1}{c}{**Acceleration (mm\(\cdot\)s\({}^{-2}\))**} \\ \hline
20 & 12.3189 & 2.4217 & 21.8611 \\
40 & 12.3193 & 2.4283 & 21.9722 \\
60 & 12.3251 & 2.4395 & 22.1111 \\
80 & 12.3336 & 2.4505 & 22.2778 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of peak displacement, velocity, and acceleration at the mid\(-\)span measuring point when the vehicle mass changes. Figure 25: Peak value variation rule of different measuring points when the vehicle mass changes (**a**) displacement, (**b**) velocity, and (**c**) acceleration. the influencing factors of civil air defense construction vibration caused by vehicle vibration is calculated. \[X= \begin{pmatrix}X_{1}\\ X_{2}\\ X_{3}\\ X_{4}\\ X_{5}\\ X_{6}\end{pmatrix} = \begin{pmatrix}32.5&34.5&36.0&37.0\\ 3&4&5&6\\ 1750&1800&1850&1900\\ 1&3&5&7\\ 15&30&45&60\\ 20&40&60&80\end{pmatrix}  \tag{15}\]  
\[Y_{a}= \begin{pmatrix}Y_{a1}\\ Y_{a2}\\ Y_{a3}\\ Y_{a4}\\ Y_{a5}\\ Y_{a6}\end{pmatrix} = \begin{pmatrix}12.3189&12.2768&12.2477&12.2293\\ 12.3189&11.3611&10.1895&8.7635\\ 26.6230&27.3133&28.0004&28.6927\\ 81.4519&27.3133&16.6250&12.0389\\ 12.2992&12.3147&12.3175&12.3189\\ 12.3189&12.3193&12.3251&12.3336\end{pmatrix}  \tag{16}\]  
\[Y_{b}= \begin{pmatrix}Y_{b1}\\ Y_{b2}\\ Y_{b3}\\ Y_{b4}\\ Y_{b5}\\ Y_{b6}\end{pmatrix} = \begin{pmatrix}2.4217&2.405&2.395&2.3883\\ 2.4217&2.1867&1.9557&1.6773\\ 5.1417&5.2883&5.4267&5.57\\ 15.4133&5.2883&3.27&2.37\\ 1.8479&2.2667&2.3813&2.4217\\ 2.4217&2.4283&2.4395&2.4505\end{pmatrix}  \tag{17}\]  
\[Y_{c}= \begin{pmatrix}Y_{c1}\\ Y_{c2}\\ Y_{c3}\\ Y_{c4}\\ Y_{c5}\\ Y_{c6}\end{pmatrix} = \begin{pmatrix}21.8611&21.6667&21.5833&21.5278\\ 21.8611&18.4167&16.275&13.9222\\ 31.1389&31.9167&32.5278&33\\ 56.3889&31.9167&25.4722&21.9722\\ 12.1545&19.1111&20.8906&21.8611\\ 21.8611&21.9722&22.1111&22.2778\end{pmatrix}  \tag{18}\]  
According to Equations (5) and (6):  
\[X^{\prime}= \begin{pmatrix}0&0.4444&0.7778&1\\ 0&0.3333&0.6667&1\\ 0&0.3333&0.6667&1\\ 0&0.3333&0.6667&1\\ 0&0.3333&0.6667&1\\ 0&0.3333&0.6667&1\\ 0&0.3333&0.6667&1\\ \end{pmatrix}  \tag{19}\]  
\[Y^{\prime}_{a}= \begin{pmatrix}1&0.5301&0.2054&0\\ 1&0.7306&0.4011&0\\ 0&0.3335&0.6655&1\\ 1&0.2201&0.0661&0\\ 0&0.7868&0.9289&1\\ 0&0.0272&0.4218&1\\ \end{pmatrix}  \tag{20}\]  
\[Y^{\prime}_{b}= \begin{pmatrix}1&0.5&0.2001&0\\ 1&0.6843&0.3739&0\\ 0&0.3424&0.6654&1\\ 1&0.2237&0.0690&0\\ 0&0.7298&0.9296&1\\ 0&0.2310&0.6185&1\end{pmatrix}  \tag{21}\]\[Y^{\prime}{}_{b}= \begin{pmatrix}1&0.5&0.2001&0\\ 1&0.6843&0.3739&0\\ 0&0.3424&0.6654&1\\ 1&0.2237&0.0690&0\\ 0&0.7298&0.9296&1\\ 0&0.2310&0.6185&1\end{pmatrix}  \tag{22}\]  
The discernibility matrix is obtained from Equation (7):  
\[\Delta_{a}= \begin{pmatrix}1&0.0857&0.5724&1\\ 1&0.3973&0.2656&1\\ 0&0.0002&0.0012&0\\ 1&0.1132&0.6006&1\\ 0&0.4535&0.2622&0\\ 0&0.3061&0.2449&0\end{pmatrix}  \tag{23}\]  
\[\Delta_{b}= \begin{pmatrix}1&0.0556&0.5777&1\\ 1&0.3510&0.2928&1\\ 0&0.0091&0.0013&0\\ 1&0.1096&0.5977&1\\ 0&0.3965&0.2629&0\\ 0&0.1023&0.0482&0\end{pmatrix}  \tag{24}\]  
\[\Delta_{c}= \begin{pmatrix}1&0.0277&0.6111&1\\ 1&0.2328&0.3703&1\\ 0&0.0846&0.0796&0\\ 1&0.0444&0.5650&1\\ 0&0.3834&0.2333&0\\ 0&0.0666&0.0667&0\end{pmatrix}  \tag{25}\]  
where \(\Delta_{max}=max(\Delta_{ij})\); \(\Delta_{min}=min(\Delta_{ij})\), the resolution coefficient is generally taken \(\zeta=0.5\).