## 4 Case Study
To verify the effectiveness of the optimization results above, the sealing performance indices were simulated in the R-FE model, in which the values of the design variables were the obtained optimum structure parameters. Then, the contact stress contours and contact stress values distributed in the contact interface were obtained (Figures 10 and 11, respectively). Table 3 provides a comparison of the sealing performance indices and the structure parameters before and after optimization. Based on the analysis shown in Table 4, the value of \(\sigma_{m}\) increased by 16.79% and the value of \(S^{2}\) declined by 18.75%, indicating that the sealing performance improved significantly compared to the initial version after VX gasket optimization. Figure 8: The Pareto front and the optimum Pareto solution. Figure 9: A schematic illustration of the Hypervolume (HV) and its concrete value: (**a**) schematic illustration; and (**b**) tendency of the HV value changes with the increased number of interpolations. To demonstrate the advantages of optimization speed in the presented method compared to traditional FE methods, the time required by these two methods was quantified. The time required to simulate the sealing performance indices once was 1.5 h using the traditional FE method. Thus, the total time required to complete the whole optimization process was 3300 h when the optimization algorithm parameters were similar to those followed in the current study (the initial population size F\({}_{0}\) was 44; the number of evolutional generations \(N\) was 50). However, the corresponding time consumption was only 30 h, because the Kriging surrogate model was applied to predict the corresponding sealing performance indices, and it only required 18 simulations to construct the Kriging surrogate model using the time-consuming traditional FE method. This means that the optimization speed of the presented method was enhanced by 99% compared to the traditional FE method. In order to further verify the sealing performance of the optimum structure, the subsea connector engineering prototype was constructed to test the sealing performance of the VX gasket with the optimum structure. The concrete test scheme is illustrated in Figure 12. The working medium, a 90% ethylene glycol/water (v/v) mixture, was injected into the pipeline of the connector using the intelligent pressure testing system, and guaranteeing that the initial pressure of the working medium in the pipeline was 35 MPa. The working medium pressure was then measured every 0.5 h during the whole test process (5 h) using the automatic pressure data acquisition system. Pressure curves were \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Items** & **Initial Value** & **Optimal Value** & **Improvement** \\ \hline \(\alpha\) (\({}^{\circ}\)) & 23 & 25.10 & +9.13\% \\ \(b\) (mm) & 30 & 29.11 & \(-\)2.97\% \\ \(\sigma_{m}\) (MPa) & 466.4 & 544.7 & +16.79\% \\ \(S^{2}\) (10\({}^{2}\)) & 131.72 & 107.02 & \(-\)18.75\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The sealing performance indices and structure parameters of the initial and optimized versions. Figure 11: The values of the contact stress distributed in the contact interface. Figure 10: The contact stress distribution of the VX gasket after optimization. then obtained using statistical methods. On this basis, the VX gasket's sealing performances before and after optimization were tested using this test scheme. The change trend of the inner pressure of the connector is presented in Figure 13.  
The analysis in Figure 13a shows that the inner pressure of the connector continues to decline as the testing time extends until 4.5 h, after which it becomes steady. The final pressure values of the initial and optimal VX gasket were 34.35 MPa and 34.59 MPa, separately. In Figure 13b, the decrease trends of the initial and optimal VX gaskets were almost consistent until 0.5 h. However, the decreasing rate of the initial VX gasket was higher compared to the optimal condition, which finally stabilized at 1.85% after 5 hours.