## 5 Conclusions  
In this study, the vibration characteristics and structural optimization of PIPR under turbulent flow field excitation are investigated. The flow field characteristics of different PIPR's end faces before and after the plugging process are analyzed using numerical simulation. In order to reduce the pressure fluctuation of the flow field, an experimental scheme for optimization of PIPR's end face is designed based on LHSD optimized by greedy strategy. According to the simulation results under different end face parameters, the BP neural network is used to construct the nonlinear model between the end face's parameters and pressure gradient. The WOA improved by GSA is proposed to minimize the average pressure gradient by optimizing the end face's parameters. Finally, an experimental setup is established to observe the turbulent flow field fluctuation and pressure fluctuation. The main conclusions can be summarized as follows:  
1. In-pipe flow field characteristics are different under different PIPR's end faces, and the curved end faces can reduce the vortex-induced vibration and pressure shock on the PIPR.
2. The end face's parameters have different influences on the pressure gradient. The prediction errors of the BP neural network are smaller than those of other methods; the values of MAE, MAPE, and R2 are 23.514, 0.001, and 0.999, respectively.
3. The optimization results of PIPR's end faces optimized by IWOA are the best. Compared with the improved PIPR model before optimization, the average pressure gradient has decreased by 25.11%.
4. The results of the PIV experiment show that the tail flow field of the optimal PIPR's end face is more stable, and the average pressure gradient has decreased by 84.69% and 54.55% before and after the plugging process.  
This study is significant for the structural design of PIPR and ensuring the plugging stability, which can provide guidance for pipeline failure prevention. However, during the plugging operation, in-pipe multiphase flow may influence the flow field characteristics. Consequently, further study will focus on the interaction of transient multiphase flow and PIPR in numerical and experimental tests.  
T.W.: Conceptualization, Methodology, Software, Investigation, Formal Analysis, Funding Acquisition, Writing--Original Draft; X.M.: Methodology, Validation, Data Curation, Supervision, Writing--Original Draft; H.Z.: Conceptualization, Visualization, Investigation, Writing--Review and Editing; L.L.: Formal analysis, Software, Validation, Funding Acquisition; S.L.: Investigation, Validation, Supervision, Project administration. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Henan Provincial Science and Technology Research Project (242102221004), the National Natural Science Foundation of China (Grant No. 52005181).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy of patients.  
The authors declare no conflicts of interest.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**PIPR’s End Face** & **Before the Plugging Process** & **After the Plugging Process** \\ \hline Model 1 & 0.15 Pa/m & 0.30 Pa/m \\ Model 2 & 0.80 Pa/m & 0.94 Pa/m \\ Model 3 & 0.98 Pa/m & 0.66 Pa/m \\ \hline \hline \end{tabular}
\end{table}
Table 9: The average pressure gradient of different PIPR end faces.