## 1 Introduction
[13] also built a shot peening model and studied the propagation and interaction of stress waves in the treated material. They studied the overlapping ratio between shots by the established high peening coverage model and examined the effects of impact sequence, material strain rate and initial residual stress on the residual stress and the surface deformation. [PERSON] et al. [14] used secondarily development with the ABAQUS single-shot peening model to build a finite element model with multiple randomly distributed shots whose number depends on the accurate number of models calculated under different working conditions and different shot peening coverage. [PERSON] et al. [15] developed a detailed numerical model of dual-shot peening on case hardened gears by considering the variation of material properties through the thickness, various modeling approaches were incorporated to consider the deviation of the impact angle due to geometrical features, and the built model could predict the final distribution of residual stresses and surface roughness. [PERSON] et al. [16] established a random multi-shots model which incorporated dislocation density-based constitutive equations; with the developed model, the effects of peening velocity, peening coverage, and double peening on the surface integrity in terms of the residual stress, surface roughness, and dislocation cell size were analyzed. [PERSON] et al. [17] coupled the Discrete Element Model (DEM)--Finite Element Model (FEM) to predict the process' effects in terms of residual stresses and roughness. [PERSON] et al. [18] combined the finite element method and response surface methodology; the proposed shot peening finite element model could give a reasonable prediction of compressive residual stress field and dimple size, and the shot peening process parameters could be optimized based on the data obtained from shot peening simulation. [PERSON] et al. [19] established a random multiple-shot model to obtain the rough surface profile under the peening parameters, and the rough surface profile was processed by Gaussian filtering to calculate the roughness of the shot peening surface. [PERSON] et al. [20] employed a random-shots finite element model and a new coverage calculation method to study the effect of shot peening coverage on the residual stress field and surface roughness; the validity of the simulation model was verified by experiments. The scholars mentioned above, according to the actual shot peening and based on the research results of single-shot peening, developed the multi-shot peening simulation model. During the modeling process, the surface of the target material is also set as a smooth plane; although the simulation model could predict the residual stress, surface deformation, and other characteristics of the workpiece after shot peening, the models still ignores the effect of initial surface roughness on shot peening. [PERSON] et al. [21] combined the results of shot peening and finite element simulation method and carried out a numerical simulation of residual stress relaxation due to fatigue loading. [PERSON] et al. [22] used a four-point bending rig and grinding to generate the initial stresses, and employed the incremental center hole drilling technique to measure the residual stresses on the bent, ground, shot peened, and bend plus shot peened specimens. After that, they carried out a simulation analysis to compare the redistribution of residual stress caused by different techniques after shot peening, which gave a better understanding of how shot peening residual stresses were redistributed. [PERSON] et al. [23; 24] carried out a simulation and experiment on shot peening and severe shot peening and tested the properties of workpieces after processing. It is found that after grinding, shot peening and severe shot peening have significant effects on the improvement of fatigue life, and the coverage of shot peening could affect the generation of surface compress stress, which could improve the service life of workpieces. [PERSON] et al.