Optimization of parameters for the best shot peening effect based on surface response and neural network model

To optimize the peening effect of different shot peening process parameters on metal surfaces, the mapping relationship between different shot peening process parameters and metal surface integrity was obtained. In this paper, ABAQUS software was used to establish a DE-FE (Discrete element-Finite element) random multi-shot analysis model to simulate shot peening, then optimize the shot peening process parameters based on the surface response method(RSM), and finally validate it through experiments and BP(back propagation) neural network model. The result shows that when the shot velocity is 70 m s−1, the impact angle of shot is 61.45°, and the shot diameter is 0.78 mm, the shot peening effect is the best, the surface roughness value is reduced by 101.84%, and the arc height value is increased by 54.66%; the error between the predicted results of BP neural network and the results of numerical analysis is less than 8%. Therefore, the optimized process parameters significantly improve the shot peening effect, but also shows that the BP neural network prediction model can more accurately predict the mapping relationship between the input parameters of shot velocity, shot diameter, and impact angle of shot and the output parameters of roughness value and arc height value.


Introduction
Shot peening is one of the most widely used metal surface peening methods [1][2][3].through a large number of particles with high velocities impacting the metal surface, plastic deformation of the metal surface occurs [4], inducing a residual stress layer on the metal surface, which is able to improve the fatigue resistance of the metal, thus improving the service life of metal parts [5,6].Because of its wide range of use, low cost and good strengthening effect, it is often used by enterprises for surface strengthening of metal parts such as aircraft engine blades [7,8], automobile crankshafts [9] and metal gears [10,11].Nonetheless, during the shot peening process, it is imperative not only to consider the degree of surface strengthening but also to evaluate its impact on surface roughness.If the metal's surface roughness exceeds certain limits, the anticipated improvements in fatigue resistance may fail to materialize, thereby compromising the longevity of the metal components.The crux of the matter lies in fine-tuning the shot peening parameters that profoundly influence both the shot peening outcome and surface roughness.Failing to set these parameters optimally could result in the emergence of micro-cracks on the metal surface or the sub optimal fortification of the metal's outermost layer, posing significant safety hazards.
Numerous scholars have devoted their efforts to enhancing shot peening efficacy through the optimization of process parameters.Kim et al [12] proposed a 3D finite element (FE) model to investigate angular shot peening, discovering that the size of surface indentations and residual compressive stresses increase with higher shot peening angles.Their FE results aligned most closely with x-ray diffraction (XRD) experimental data when the angle was set to 60°.Ohta [9] employed particle image velocimetry (PIV) to measure the velocity distribution of compression residuals in AL7075 aluminum alloy.The PIV results exhibited notable consistency with XRD experimental data, revealing that the depth of compressive residual stress increased with shot velocity and reached over 0.5 mm at an air pressure of 0.35 MPa.Furthermore, Wang et al [13] utilized orthogonal experimental methods for parameter optimization to explore the impact of process parameters on shot forming.They concluded that the radius of curvature produced by shot forming increased with nozzle speed and plate thickness, while it decreased with rising air pressure.Despite achieving some optimization effect, their experimental program overlooked the interaction and mutual influence between various process parameters, leading to limitations in its overall effectiveness.Currently, artificial intelligence (AI) finds widespread application across various industries, including the field of shot peening process parameter prediction.Scholars have delved into shot peening through neural networks, seeking to enhance shot peening efficiency.Daoud [14] presented a hybrid approach, employing two prediction models: the second-order model and the feed-forward artificial neural network model.Their study focused on understanding the effects of shot parameters, such as shot diameter, velocity, coverage, and impact angle, on induced residual stress distribution in TRIP780 steel.The results demonstrated consistent predictions from both models concerning the process parameters, rendering them suitable for shot peening parameter optimization due to their responsiveness.Similarly, Huang [15] put forth a numerical prediction framework, integrating the Finite Element Method (FEM) and Artificial Neural Network (ANN) algorithms.Their investigation revealed that the prediction results of the GA-BP-ANN algorithm (Genetic Algorithm Optimized Backpropagation Artificial Neural Network algorithm) closely aligned with FEM simulation results in terms of SP-induced residual stresses, equivalent plastic strains, grain refinement, and surface roughness.Li et al [16] predicted the fatigue life of 25CrMo4 alloy steel notches by micro-shot peening and used a BP neural network to predict the fatigue results, which were within ± 2 error.However, the projectiles in the shot peening model used by M. Daoud and Haiquan Huang were not randomly generated, and they simulated the shot peening process by using the correlation function or by fixing the position and height of the projectile in advance, which is a big gap with the actual shot peening process.
In this paper, an DE-FE random multi-shot analysis model is established to simulate the shot peening process.Firstly, based on the surface response method (RSM) to optimize the response variable arc height (H arc ) and roughness (R a ), and then study the role of the parameters such as shot velocity, shot diameter and nozzle angle and the response variable arc height (H arc ), roughness (R a ) between the relationship between the parameters, and finally verified through experiments and BP neural network, the purpose is to explore the influence of different shot peening process parameters on the integrity of the metal surface, to get the mapping relationship between different shot peening process parameters and surface integrity, to improve the quality and efficiency of the shot peening process.The purpose is to investigate the influence of different shot peening process parameters on the surface integrity of metal, to obtain the mapping relationship between different shot peening process parameters and surface integrity, and to improve the quality and efficiency of the shot peening process.

Research methodology 2.1. Response surface methodology(RSM)
In this manuscript, the Box-Behnke model is chosen, encompassing a comprehensive investigation of 17 groups.The fundamental input parameters considered for our analysis include shot velocity, impact angle of the shot, and shot diameter, which have been meticulously tabulated in table 1.

Establish DE-FE random multi-shot analysis model 2.2.1. Material model and parameters
The Johnson-Cook model is suitable for describing materials with high strain rate deformations and the model has a simple structure and is easy to compute, so the Johnson-Cook principal model was chosen for this paper, as shown in equation (1) [17].
Where A, B, C, m and n are material constants to be determined from deformation tests e  0 and T o is reference values of strain rate and work temperature, respectively e  and T is the strain rate and temperature, respectively.T m is the melting temperature of the material.
The material selected for this paper is SAE1070.The Almen strip used belongs to type-A and has dimensions of 76 mm × 19 mm × 1.29 mm, as depicted in figure 1.The specific parameters of the other materials are detailed in table 2.

Boundary conditions
During the simulation process, the meticulous establishment of accurate boundary conditions emerges as a pivotal determinant influencing the fidelity of our simulation results.Figure 2 visually portrays a quarter Almen strip model, designed with symmetric constraints to enhance the precision of our investigations.To elaborate, at the model's endpoint, rigorous restrictions are imposed on movement along the x, y, and z directions (U x = U y = U z = 0); conversely, at the opposing side of the model, movement along the y direction is constrained (U y = 0); finally, on the lateral side of the model, movement along the x direction is effectively restricted (U x = 0) [19,20].

Numerical simulation process
In accordance with figure 3, This paper has established a random multi-shot model based on DE-FE analysis.[21].This model comprises diverse shot diameters, namely 0.6 mm, 0.7 mm, and 0.8 mm, alongside variable shot velocities of 50 m s −1 , 60 m s −1 , and 70 m s −1 , as well as impact angle of shots set at 60°, 75°, and 90°.The shot ball is treated as a rigid body, and for accurate representation, the friction coefficient between the shot ball and the target plate is thoughtfully assigned a value of 0.3, in order to improve work efficiency, the Almen strip is a 1/4 model, the dimensions of the target plate are specified as 38 mm × 9.5 mm × 1.29 mm, an essential   2. Material parameters used in the Johnson-cook model [18].parameter for precise simulation outcomes.To optimize computational efficiency, this paper adopted the quad grid cell shape type and employed the Structured meshing technique.Almen strip material is SEA1070 with a density of 7800 kg m −3 .

Experiment process
As illustrated in figure 4(a), the shot peening and measurement process is depicted.In this study, shot peening experiments were conducted with the chosen parameters of a shot velocity of 60 m s −1 , a shot diameter of 0.8 mm, and an impact angle of 90°, with a projection rate of 42 kg min −1 .The measured arc height value was determined to be 0.331 mmA, while the simulated analysis yielded an arc height value of 0.336 mmA.The average measured surface roughness was found to be 2.895 μm as shown in figure 4(b), whereas the simulated analysis yielded a roughness value of 2.992 μm.The simulation outcomes and experimental results exhibited a robust degree of congruence.

Neural network modeling for shot peening performance prediction 2.4.1. Neural network modeling process
The BP neural network, a widely adopted intelligent algorithm renowned for data fitting and prediction, constitutes the focal point of this study.Specifically, the selected feed-forward neural network architecture encompasses an input layer, hidden layer, and output layer, as detailed in references [22,23].To facilitate effective model training, the input values, namely shot velocity, impact angle of shot, and shot diameter, are meticulously partitioned into training, validation, and test sets, with proportions set at 75%, 15%, and 15%, respectively.Leveraging equation (4) and conducting multiple iterations, the optimal number of hidden neurons was chosen as 10, ensuring the network's aptitude for comprehensive learning.Moreover, the paper has used the Hyperbolic Tangent Tansig Function as the transfer function for the hidden layer, while the Purelin Linear Function is chosen for the output layer, each playing an instrumental role in capturing the intricate relationships within the data.The algorithm type was selected as the Levenberg-Marquardt.
Where, Input, Input 1 and Output 1 , Output 2 are the inputs of the input layers, the output of the implicit layer, and the output of the output layer respectively, f 1 and f 2 are the transfer functions of the implicit layer and the output layer respectively, w 1 is the connection weight of the input layer to the implicit layer, w 2 is the connection weight of the implicit layer to the output layer, b 1 is the connection threshold of the input layer to the implicit layer, b 2 is the connection threshold of the implicit layer to the output layer, k is the number of nodes in the implicit layer, m is the number of nodes in the input layer, n is the number of nodes in the output layer, and a is a constant [25].

Surface morphology and deformation
The size of surface roughness is one of the standards for measuring the quality of metal surfaces after shot peening.Surface roughness has a significant impact on the fatigue performance of parts and directly determines the service life of components.Therefore, research on the surface roughness of parts after shot peening is essential.One of the evaluation parameters for surface roughness is the profile arithmetic mean deviation R , a which refers to the arithmetic mean value of the absolute deviations of each point on the measured profile from the profile centerline within a sampling length L. As shown in figure 6, the surface morphology impacted by different shot peening process parameters can be observed.Under the impact of shot peening, numerous pits are  formed on the surface of Almen strip.This results in different surface roughness under different shot peenting parameters.To obtain the surface roughness value of Almen strip, it is necessary to extract the profile lines in the Z-direction, and the surface roughness values under different shot peening process parameters can be calculated using Formula 6.
As shown in figure 7, it represents the deformation of Almen strip in the Z-direction for different shot peening process parameters.When the projectiles impact the surface of Almen strip, the impacted surface undergoes plastic deformation, resulting in the formation of residual stress layers on the impacted surface.Under the influence of stress, the central part of the Almen strip will deform upward towards the direction of the projectiles.Since this paper employs a 1/4 Almen streip model, it can be observed that the maximum upward deformation occurs at the diagonal, consistent with the actual deformation direction of the Almen strip.Figure 7 reveals that the Almen strip exhibits greater lateral deformation and smaller longitudinal deformation.From figure 7, it can be concluded that when the shot velocity is 60 m s −1 , the peening angle is 75°, and the peening diameter is 0.7 mm, the maximum deformation is 0.5354 mm.When the shot velocity is 60 m s −1 , the peening angle is 75°, and the peening diameter is 0.7 mm, the maximum deformation is 0.7762 mm.When the shot velocity is 70 m s −1 , the peening angle is 75°, and the peening diameter is 0.8 mm, the maximum deformation is 2.093 mm.When the shot velocity is 70 m s −1 , the peening angle is 90°, and the peening diameter is 0.7 mm, the maximum deformation is 1.455 mm.The specific results for roughness values and arc height values are presented in table 3.

Analysis of variance and regression model for roughness 3.2.1. BBD (box-behnken design) procedure and variance analysis
As indicated by table 4, the quadratic regression model demonstrates an F value of 15.28 and a corresponding P-value of 0.0008, signifying the model's significance.Consequently, the model aptly fits within the entirety of the regression domain, showcasing commendable fit.The R 2 (adj) value of the model, measuring 0.8893, indicates the model's capacity to account for a notable 88.93% of the variation in response values.Similarly, the R 2 value of 0.9516 underscores that the model can elucidate 95.16% of the data set, rendering it highly suitable for model analysis and predictive assessment of roughness values.Through comparative evaluation of the P-values, it is evident that shot velocity wields the highest significance, followed by shot diameter, and lastly, impact angle of shot.Further deduced from the magnitudes of F-values presented in table 5, the hierarchical impact of each response variable on roughness is established as follows: A (shot velocity) > C (shot diameter) > B (impact angle of shot).An in-depth regression fitting analysis of the data in table 4 culminates in a quadratic regression equation model formula that adeptly encapsulates the interplay of shot velocity, impact angle of shot, and shot diameter.
Where R a is the predicted roughness, and A, B, and C are the response values for shot velocity, impact angle of shot, and shot diameter, respectively.

Response surface analysis of roughness values
The response surface method overcomes the limitation of orthogonal experiments in not providing intuitive visualizations.Contour plots are created based on the quadratic regression equation model formula, and these contour plots visually depict the degree of interaction effects on response values.The more curved the contour lines, the stronger the interaction between the two factors.In this study, the independent variables were shot velocity (A), nozzle angle (B), and peening diameter (C), while the response variable was the roughness value.
Response surface plots and contour plots were generated.From figure 8, it can be observed that by comparing the curvature of the plots, the order of the magnitude of the impact of interaction on roughness is determined as follows: AB > BC > AC.This conclusion aligns with the results obtained from the analysis of variance (ANOVA) based on the F-values.

Analysis of variance and regression model for arc height 3.3.1. BBD design procedure and variance analysis
As evidenced from table 5, the quadratic regression model exhibits an F value of 54.94, with a P-value less than 0.0001, signifying the model's utmost significance.This demonstrates that the model fits the entirety of the regression domain.The R 2 (adj) value of the model, standing at 0.9681, illuminates the model's ability to account for a substantial 96.81% of the variation within response values.Correspondingly, the R 2 value of 0.9860 underscores that the equation can elucidate a remarkable 98.60% of the dataset, solidifying its suitability for model analysis and predictive evaluation of arc-height values.Through meticulous scrutiny of the P-values and comparative assessment, it is evident that shot velocity and shot diameter exhibit the most pronounced significance.Deduced from the magnitudes of F-values presented in table 6, it can be discerned that the hierarchical influence of each response variable on arc-height values is as follows: A (shot velocity) > C (shot diameter) > B (impact angle of shot).Subsequent regression fitting analysis of the data in table 6 culminates in a quadratic regression equation model formula that accurately encapsulates the interplay of shot velocity, impact angle of shot, and shot diameter, the formula is shown in equation (8).where H arc is the predicted arc height value, and A, B, and C are the values of shot velocity, impact angle, and shot diameter, respectively.

Response surface analysis of the arc height values
Contour plots primarily illustrate the influence of each pair of factors on the corresponding variable.These contour plots are generated through fitting the quadratic regression equation model.From figure 9, it can be deduced that, by comparing the curvature of the response surface plot and contour plots in figure 9, the order of the magnitude of the impact of interaction on arc height values is determined as follows: AC > BC > AB.This conclusion is consistent with the judgment based on the F-values in table 5.

Optimization results
Table 6 contains a total of 4 sets of data, with two sets being selected data, and the other two sets being the optimization group and the actual simulation group.If a comparison between two variables is needed, one should look for a set with similar parameters and keep them constant while comparing the other set of parameters.From table 6, it can be observed that in the 8th set and the optimization group, the roughness values are approximately the same, so we compare their arc height values.Similarly, in the 8th set and the optimization group, the arc height values are approximately the same, so we compare their roughness values.To ensure data rigor, the 'optimal group' in figure 10 represents the actual data from the FEM group.From figure 10, it can be seen that the roughness value decreased by 101.81%, the arc height value increased by 54.66%, and the feasibility of the experiment is 0.669.

Shot peening BP neural network prediction results
As illustrated in figure   0.94952, respectively.Furthermore, the combined R-value reaches 0.98949.This indicates that the model has excellent predictive accuracy.

The result of the neural network prediction
As shown in figure 12, in order to make the predictions of this model more representative, groups 1, 8, 14, and the optimized group were selected for model validation.This selection was made because the shot velocity in groups 1, 8, and 14 ranged from 60 to 70 m s −1 , the nozzle angle ranged from 60 to 75°, and the shot diameter ranged from 0.7 to 0.8 mm.These parameter ranges are the closest to the optimized parameters.The results obtained from the model predictions closely matched the results obtained from simulation analysis.This  indicates that the BP neural network model exhibits good predictive accuracy for both roughness values and arc height values.

Conclusion
In this paper, the DE-FE random multi-shot analysis model is established to simulate the shot peening process.Firstly, the response variables roughness value (R a ) and arc height value (H arc ) are optimized based on the surface response method (RSM), and then the relationship between the three parameters mainly affecting the peening effect of shot peening, such as shot velocity, shot diameter, and impact angle of shot, and the response variables roughness value (R a ) and arc height value (H arc ) are studied and finally verified by experiments and BP neural network.The following conclusions are obtained: (1) Based on surface response experiments, the study investigated the influence of shot angle, shot velocity, and peening diameter on the comprehensive shot peening effect on metal surfaces.It was determined that the optimal shot peening parameters are a velocity of 70 m s −1 , a nozzle angle of 61.45°, and a peening diameter of 0.78 mm, resulting in the best shot peening enhancement effect.The roughness value decreased by 101.84%, and the arc height value increased by 54.66%.This indicates that the optimized process parameters significantly improved the shot peeing enhancement effect on the metal surface.
(2) A prediction model for shot peening surface integrity parameters based on a neural network was established.
The training set, validation set, test set, and overall R-values of the BP neural network were 1, 0.99919, 0.94952, and 0.98949, respectively.This indicates that the well-trained model has excellent prediction accuracy, and the predictive accuracy meets the requirements of engineering projects.
(3) A comparison between the roughness and arc-height values forecasted by the BP neural network model and those gleaned from simulation analysis reveals a remarkable concordance between the two sets of outcomes.This salient alignment underscores the BP neural network model's aptitude for predictive precision in forecasting roughness and arc height values.Moreover, the model effectively elucidates the intricate mapping relationship between the input parameters encompassing shot velocity, shot diameter, and impact angle of shot, and the ensuing output parameters involving roughness and arc height.

Figure 3 .
Figure 3.The DE-FE multi-shot impact analysis mode for Almen strip and parameters.

Figure 8 .
Figure 8.The interaction effects of different shot peening parameters on the value of roughness.

Figure 9 .
Figure 9.The interaction effects of different shot peening parameters on the value of roughness.

Figure 10 .
Figure 10.Simulated and tested results with optimal parameters.

Figure 11 .
Figure 11.BP neural network model training regression analysis diagram.

Figure 12 .
Figure 12.Comparison of neural network predictions and finite element simulations of compressive residual stress curves.

Table 1 .
Design of the box-behnken experiment.

Table 3 .
Results of the box-behnken experiment.

Table 5 .
The arc height variance table.

Table 6 .
The SP parameters and response results of the optimal group and control groups.