## 6 Conclusions  
This paper proposes a framework for vibration reduction optimization based on the global POD ROM to address the problem of low efficiency in vibration reduction optimization of complex thin-walled aerospace structures. When the frequency response analysis accuracy of the global POD ROM constructed by the initial reduced basis is insufficient, the CV-Voronoi sequence sampling method is used to adaptively update the global POD ROM until it meets the global accuracy requirements of the design space. In the optimization process, the global POD ROM is used to replace the FOM for frequency response analysis, and an EGO algorithm based on the surrogate model is used to accelerate the optimization process. The conclusions of this paper are as follows:  
Figure 21: Iterative convergence curve for vibration reduction optimization of the PAF (FOM).  
Figure 20: Energy frequency response of the PAF structure before and after optimization.  
1. For the global POD ROM: The calculation accuracy and efficiency of the proposed approach are verified by the vibration reduction optimization examples of the S-shaped curved stiffened shell and PAF. The RMSE of the dynamic response is calculated by random sampling in the design space, which verifies that the global POD ROM has high accuracy in the global design space. Compared with the FOM, the dynamics analysis based on the global POD ROM reduces the single mean calculation time by more than 96.9% and 97.6%, respectively, which has a significant computational efficiency advantage.
2. For vibration reduction optimization: In the S-shaped curved stiffened shell and PAF vibration reduction optimization examples, the optimized result in satisfied mass and first resonance frequency constraint decreased by 79.6% and 31.5% of objective energy, respectively, when compared to the initial results. It shows that this method is effective for vibration reduction optimization in complex thin-walled structures. For the vibration reduction optimization of the S-shaped curved stiffened shell, the optimization results of the global POD ROM are reduced by 58.8% in the same time period compared with the FOM method. For PAF structures, compared with the FOM method, the vibration reduction optimization results of the global POD ROM are reduced by 20.0% in the same time period. It shows that the proposed approach has a stronger optimization ability.  
The subsequent work will carry out a more efficient research method for adaptively updating global POD ROM, including optimizing the add-point strategy and reduced basis updating scheme and using advanced intelligent algorithms for high-dimensional design space to improve the parameter optimization ability on the current basis.  
Conceptualization, Y.S.; Data curation, Z.K.; Formal analysis, Y.S., Z.K. and P.Z.; Funding acquisition, K.T.; Project administration, Z.K., W.S., Q.Y. and K.T.; Supervision, K.T.; Validation, Y.S. and K.T.; Visualization, Z.K., P.Z. and Y.S.; Writing--original draft, Y.S. and Z.K.; Writing--review & editing, K.T., W.S. and P.Z. All authors have read and agreed to the published version of the manuscript.  
This work was supported by National Key Research and Development Program project of China; Grant Number: 2022 YFB3404700. National Natural Science Foundation of China; Grant Number: 11902065. Basic research funds for the central universities of China; Grant Number: DUT21 RC(3)013.  
Not applicable.  
The data and procedures of this study are not uploaded to the public website. The research data can be obtained by contacting the corresponding author of this paper via email.  
The authors declare that there are no conflict of interest.