## 4 Global Sensitivity Analysis and Optimisation for Structural Parameters of Coupled Systems
### Optimisation of Structural Parameters of Coupled Systems Based on Sensitivity Analysis
\begin{table}
\begin{tabular}{c c c c} \hline
**Names and Symbols** & **Mean Value of Parameters** & **Variance** & **Range of Variations** \\ \hline Mass of upper unit \(m_{1}\) & 46 & 0.46 & \(\mu\pm 30\sigma\) \\ \hline Raft frame quality \(m_{R}\) & 100 & 1 & \(\mu\pm 30\sigma\) \\ \hline Stiffness of upper vibration isolators \(k_{2}\) & \(2.7\times 10^{5}\times(1+0.1\mathrm{j})\) & \(2.7\times 10^{3}\times(1+0.1\mathrm{j})\) & \(\mu\pm 30\sigma\) \\ \hline Stiffness of the lower vibration isolator \(k_{R}\) & \(8.6\times 10^{5}\times(1+0.1\mathrm{j})\) & \(8.6\times 10^{3}\times(1+0.1\mathrm{j})\) & \(\mu\pm 30\sigma\) \\ \hline Spacing of lower vibration isolators \(H_{x}\) & 0.35 & 0.0035 & \(\mu\pm 30\sigma\) \\ \hline Thickness of cylindrical thin shells \(d\) & 0.02 & 0.0002 & \(\mu\pm 30\sigma\) \\ \hline Loss factor for vibration isolators \(\eta\) & 0.1 & 0.001 & \(\mu\pm 30\sigma\) \\ \hline \end{tabular}
\end{table} 
Table 4: Range of values for the design variables of the coupled system parameters optimization. \begin{table}
\begin{tabular}{c c c c c} \hline
**Names and Symbols** & **Values before** & **Optimisation** & **Optimisation** & **Optimisation** \\  & **Optimisation** & **(Method 1)** & **(Method 2)** & **(Method 3)** \\ \hline Mass of upper unit \(m_{1}\) & 46.0 & 47.32 & \(\backslash\) & 47.32 \\ \hline Raft frame quality \(m_{R}\) & 100 & \(\backslash\) & 127 & 127 \\ \hline Stiffness of upper vibration isolators \(k_{2}\) & \(2.70\times 10^{5}\times(1+0.1\mathrm{j})\) & \(\backslash\) & \(2.84\times 10^{5}\times(1+0.1\mathrm{j})\) & \(1.80\times 10^{5}\times(1+0.0996\mathrm{j})\) \\ \hline Stiffness of the lower vibration isolators \(k_{R}\) & \(8.60\times 10^{5}\times(1+0.1\mathrm{j})\) & \(8.32\times 10^{5}\times(1+0.0992\mathrm{j})\) & \(\backslash\) & \(8.32\times 10^{5}\times(1+0.0996\mathrm{j})\) \\ \hline Spacing of lower vibration isolators \(H_{x}\) & 0.35 & 0.295 & 0.299 & 0.254 \\ \hline Thickness of cylindrical thin shells \(d\) & 0.02 & 0.0254 & 0.0254 & 0.0254 \\ \hline Loss factor for vibration isolators \(\eta\) & 0.10 & 0.0992 & \(\backslash\) & 0.0996 \\ \hline \end{tabular}
\end{table} 
Table 5: Comparison of coupling system parameters before and after optimization. According to the above results, all three methods can achieve optimised results in terms of reduced sound radiated power if the minimum sound radiated power is used as the final evaluation criterion. However, in comparison, method 3 has the best optimisation results followed by method 2, and method 1 has the worst results. There are several reasons for this. The first is that the transmitted power flow has a more direct numerical correspondence with the acoustic radiated power according to the analytical conclusions in Section 3.3. The second is that when combining the transmitted power flow and the vibration level dropout for multi-objective optimisation, on the one hand more optimisation variables are covered, and on the other hand the cross effect between some parameters and multiple objective functions may be more fully represented.