## 4 Sensitivity Analysis of RPC-FST
### Sensitivity Analysis of the RPC-FST  
Based on a numerical example provided in Section 3, 20 sample groups are selected to establish the Kriging surrogate model. The accuracy of the Kriging surrogate model needs to be verified, so 10 groups of data obtained by numerical calculation are used as verification groups and standard values. Absolute error \(E_{\text{A}}\) and relative error-index \(\beta_{\text{R}}\) are critical parameters for evaluating the response surface. The design of the experiment is shown in Table 9. The Bayesian method can update the coefficient of variation based on samples. It should be pointed out that coefficients of variation can be obtained in large-scale tests [44]. The distribution of random variables is shown in Table 10. These numerical examples are tested on a personal computer with Intel i7-9700 and 16 GB memory. The analysis structure of the relative error-index is shown in Table 11. The data shows that the error fluctuates within an acceptable range. It confirmed that the derived Kriging surrogate model could predict the displacement of the RPC-FST accurately. The Kriging surrogate model constructed by the limit state function is used for calculation. Furthermore, \(10^{6}\) MCS is used to calculate the reliability sensitivity prognosis of the RPC-FST system [45].  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Distribution** & **Mean** & **Variable Coefficient** & **Unit** \\ \hline \(W\) & normal & 225 & 0.01 & kg \\ \(L\) & normal & 1500 & 0.001 & mm \\ \(D\) & normal & 400 & 0.01 & mm \\ \(t\) & normal & 15 & 0.1 & mm \\ \(H\) & normal & 2500 & 0.001 & mm \\ \hline \hline \end{tabular}
\end{table}
Table 10: Distribution of random variables.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variable** & **Distribution** & **Mean** & **Variable Coefficient** & **Unit** \\ \hline \(W\) & normal & 225 & 0.01 & kg \\ \(L\) & normal & 1500 & 0.001 & mm \\ \(D\) & normal & 400 & 0.01 & mm \\ \(t\) & normal & 15 & 0.1 & mm \\ \(H\) & normal & 2500 & 0.001 & mm \\ \hline \hline \end{tabular}
\end{table}
Table 11: Testing results based on testing samples.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Variable** & **Lower Bound** & **Upper Bound** & **Unit** \\ \hline TNT weight \(W\) & 150 & 300 & kg \\ Distance of TNT \(L\) & 1000 & 2000 & mm \\ Diameter of RPC-FST \(D\) & 300 & 500 & mm \\ Thickness of steel tube \(t\) & 10 & 20 & mm \\ Height of RPC-FST \(H\) & 2000 & 3000 & mm \\ \hline \hline \end{tabular}
\end{table}
Table 9: Design of experiment.  
From Figure 8a, it is obvious that the overall maximum displacement of RPC-FST has a greater correlation with the five variables of steel tube thickness, RPC-FST column height, TNT weight, TNT distance, and RPC-FST section diameter. However, the positive and negative correlations of the five variables with RPC-FST maximum displacement are different. The maximum displacement risk of RPC-FST increases with the increase of TNT weight and RPC-FST column height (positive correlation) and increases with the decrease of RPC-FST section diameter, steel tube thickness, and TNT distance (negative correlation). This can be concluded from Figure 8b.  
To compare the efficiency of the three models (the modified HJC model, the modified K&C model, and the Kriging surrogate model) in calculating the maximum displacement, we selected four sets of data for analysis, as shown in Table 11. The results show that the updated Kriging surrogate model in this paper can significantly improve the sensitivity analysis efficiency of the RPC-FST system under explosion load, as shown in Table 12.