## 4 Boom Structure Response Surface Optimization
### Optimization Process and Result Analysis  
We adopted the Central Composite Design (CCD) experimental type and designed 15 groups of design variables. The response surfaces of the maximum time stress and maximum time deformation of the boom structure and its two design variables, with the most substantial influencing factors, were simulated by the genetic aggregation type of response surface, as shown in Figures 15 and 16.  
From Figures 15 and 16, the results indicate that the maximum value of temporal stress in the structural boom increases with L\({}_{3}\) decreasing first and then growing with the rise in L1. The effects show first an increase and then a decrease. The maximum value of the boom structural temporal deformation also increases with L\({}_{3}\) decreasing and then increases with L\({}_{1}\). The changes are slow.  
Figure 14: Sensitivity situation.  
\begin{table}
\begin{tabular}{c c c} \hline
**Input Variable** & **Initial Value/mm** & **Variation Range/mm** \\ \hline L\({}_{1}\) & 1650 & (1555, 1650) \\ L\({}_{2}\) & 1330 & (1200, 1350) \\ L\({}_{3}\) & 17,000 & (16,000, 17,500) \\ \hline \end{tabular}
\end{table}
Table 5: Optimized design variable ranges.  
Through the MOGA (Multi-objective Genetic Algorithm) screening preference method, after 8670 evaluations and the convergence and selection of three candidate points, and after many iterations of calculation, the optimization course curves of the maximum value of time stress, as well as the maximum value of time deformation of the arm structure, were derived, as shown in Figures 17 and 18. The final design point parameter solving was performed to arrive at the optimized design point values and results, as shown in Table 6. A comparison of the first six orders of intrinsic frequencies and modal shapes before and after optimization is shown in Table 7. Compared with the first six orders of modal frequencies before optimization, all the inherent frequencies increase afterward.  
The optimization results show that the maximum value of temporal structural deformation is reduced by about 8.06%, and the maximum value of temporal stress is decreased by about 11.04%. The values of stress and deformation do not exceed the limit of permissible stress and maximum deformation, which indicates that the structure's design is within a reasonable range and that the whole meets the design requirements of the structural arm.  
After optimization, it can be seen that the intrinsic frequency is increased, and the stiffness of the structure is improved, but the vibration energy is not transferred to the overall structure of the boom; the tie rods at the windward side are mainly affected by the wind load, considering that the width of the truss of the structure presents a step-by-step decrease, which leads to vulnerability compared with the tie rods of the distal end, so it is necessary to pay attention to the structural tie rods of the boom when it is carrying out the work. For this towering and long truss structure, the modes are strongly coupled, and the optimization may trigger the coupling of the modal frequencies, resulting in the overall modal frequencies remaining compact. After structural optimization, the first-order mode shapes gradually migrate from the middle vulnerable region of the tie rods to the two ends. Meanwhile, the fourth and fifth section boom joints are still weak after optimization, but their fragility is significantly reduced compared with before optimization. Therefore, focusing on these two positions is essential when working on the net sealer.  
Figure 16: Response surface for the time deformation maximum.  
Figure 15: Response surface for the time stress maximum.