## 1 Introduction  
Wear, corrosion, fatigue, and fracture are some of the many problems that can occur on the surfaces or outermost layers of engineering components [1]. These damages originate from the surface and depend on the characteristics of the component's surface. Consequently, improving the surface quality of the part is crucial. For this purpose, chemical, thermal, thermochemical, and mechanical surface treatments are applied to materials [2, 3]. Thermochemical treatments such as nitriding and boronizing, and mechanical surface treatments such as shot peening, are used to increase the resistance of materials to wear, corrosion, and fatigue. The idea behind the SP method is tossing tiny glass, steel, or ceramic balls onto the machine component. The goal is to enhance the parts' surface properties by creating an incredibly thin, nanoscale layer either on top of or slightly below the surface. In the SP process, the shots hitting the sample surface create CRS on the surface, causing the hardness of the surface to increase. Fatigue crack formation time can be delayed by compressive residual pressure and crack closure stresses occurring after the SP process [4]. In addition, SP causes micro cracks, micro structural changes and changes in the surface roughness of the material. The parameters of this process must be carefully chosen because they have a positive impact on the surface qualities of the material. Poorly chosen process parameters lead to weak compressive residual stress development, worsening of the surface properties, and failure to attain the intended surface properties [5,6]. This has led to many experimental studies on determining the effect of SP process parameters [7, 8, 9, 10, 11]. The main issue with experimental studies is that they need excessive numbers of trials, which adds to the expenses and delays the research process. To address this issue, analytical techniques were employed to identify the ideal parameter [12, 13, 14, 15]. [PERSON] [16] and [PERSON] [17] conducted the initial analytical research for this reason. [PERSON]'s [18] study addressed the relationship between the residual stress after the SP process and the Almen intensity, which is the SP process parameter, with the finite element approach. As a result, it made it possible for the designers to ascertain the ideal process parameter for the forged parts' mechanical behavior. [PERSON] et al. [19], however, transformed a previously experimental work into an analytical one. As a result, the impact velocity, impact angle, and ball diameter, which are SP process parameters, were determined analytically in relation to the residual stress profile. [PERSON] et al. [20] tried to estimate the ideal peening process parameters by using the finite element method, taking into account the surface roughness of the material and compressive residual stress variables. As an alternative to the vibropolishing approach, [PERSON] et al. [21] investigated fatigue life and aerodynamic efficiency utilizing the relatively new vibratory peening method. They set out to create a novel intelligent vibratory SP method; therefore, they carried out a number of experimental operations to validate and describe the part using conventional Almen strips. Their research also sought to forecast the specified pieces and use machine learning to forecast the data gathered from the experiments. When the study results were examined, the properties of the Almen strips were estimated with the Kernel Ridge model at 0.0171 standard deviation and 0.0443 RMSE values. These results were quite consistent with the experimental results. In their study, [PERSON] et al. [22] applied the SP process to (TiB + TiC)/Ti-6 Al-4V composite material and then aimed to estimate the hardness and residual stress distributions depending on the depth of the material. For this purpose, the authors used the deep neural network (DNN) method in their studies.