## 1 Introduction
The common external-induced excitation is the problem of cylindrical disturbance, and the pressure pulsation of the in-pipe flow field is only related to the size of the turbulence, so this phenomenon is also called turbulent vibration [17; 18]. In addition, alternatively, shedding the vortex near the cylindrical wake can occur due to the unstable motion of fluid, which also produces the vortex-induced vibration [19]. During the plugging process, due to the obstruction of PIPR, the in-pipe flow field can change violently, which causes turbulent vibration and instability of the plugging operation. In the past few years, research on the flow field characteristics and evolution law has been performed. [PERSON] et al. [20] investigated the pressure fluctuation characteristics using dynamic mesh simulation; the influence of deceleration time, flow velocity, and PIPR's aspect ratio was analyzed, and the optimal parameters were obtained for reducing the pressure fluctuation. [PERSON] et al. [21] analyzed the throttling pressure control flow field of the traction speed regulation and braking mechanism, and the influence of the speed control valve was studied. [PERSON] et al. [22] designed a spoiler device for reducing the pressure difference of the flow field during the plugging process, and different plugging velocities were experimentally investigated to compare the pressure pulsation. [PERSON] et al. [23] simulated the transient pressure behaviors of PIPR in natural gas pipelines, and the implicit and explicit coupled method was developed for the simulation of moving interfaces. In summary, the present relevant research has mainly focused on the mechanical structure and control system. Meanwhile, the turbulent flow field characteristics have been considered to ensure the plugging stability and the structure of PIPR has been optimized to reduce the turbulent vibration [24]. However, the limitations of the investigations reviewed above can be concluded as follows: (1) There are few reports on the influence of the end face's structure on the vibration characteristics of PIPR. (2) Although the size of PIPR's structure is optimized for vibration reduction, such as diameter and length, the size of the end face has not been considered for optimization. (3) The response surface method has been widely used for the structural optimization of PIPR, but this method is limited to nonlinear relationships. In addition, traditional optimization methods are prone to falling into local optimum, such as GA and PSO, which makes it difficult to achieve the global optimum. In this paper, the vibration characteristics and structural optimization are investigated for PIPR under turbulent flow field excitation. The flow field characteristics of the plugging process under different PIPR's end faces are analyzed. An experimental scheme for different end face parameters is designed based on LHSD optimized by greedy strategy. The nonlinear relationship between the end face's parameters and the pressure gradient is established using the BP neural network. In order to minimize the pressure gradient of the flow field, an improved whale optimization algorithm (IWOA) is proposed to determine the optimal parameters of the end face. Finally, an experimental setup is established to verify the superiority of the optimized end face, and the turbulent flow field fluctuation is observed using particle image velocimetry (PIV) technology. This study can provide guidance for ensuring the reliability of plugging operation and provide a reference for the engineering design of PIPR.