# Machine Learning-Based Prediction and Optimisation System for Laser Shock Peening
## 6 Conclusions  
The main findings in this study can be summarized in the following points:  
1. A data-based approach based on artificial neural-network was developed within a Bayesian framework for analysing residual stress data in laser shock peening. The ANN prediction model is capable of estimating the residual stress profile as a function of depth below the peened surface and using different process variables as inputs. 2. The accuracy of the prediction model was evaluated using different performance indicators, such as root mean square error (_RMSE_), absolute fraction of variance (R\({}^{2}\)) and mean absolute percentage error (_MAPE_). The ANN model was able to achieve the respective error values in the test data: Dataset 1--single-shot laser peening with square spots (_RMSE_ = 0.0992, R\({}^{2}\) = 0.9719 and _MAPE_ = 23.8603) and Dataset 2--multiple-shot laser peening with circular spots (_RMSE_ = 0.0912, R\({}^{2}\) = 0.9894 and _MAPE_ = 13.1025). 3. The contributions of different process parameters on the resulting residual stress distribution were evaluated using [PERSON]'s algorithm and parametric studies. 4. The ANN approach was validated using several case studies employing a 'leave-one-out' cross validation method. Very good agreement was observed between the predicted and measured results, suggesting that the model was able to identify the non-evident relationships between the process variables and residual stress distribution. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Relative Depth (x/t)** & **Longitudinal Residual Stress/MPa** & **Transverse Residual Stress/MPa** \\ \hline
1 & 0.6 & \(-35\) & \(-35\) \\
2 & 0.9 & \(-80\) & \(-110\) \\
3 & 0.3 & \(-280\) & \(-280\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Case study–1 using GA: Desired longitudinal and transverse residual stresses at different depths for obtaining optimised inputs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**No.** & **Power** & **Longitudinal Residual Stress (MPa)** & **Transverse Residual Stress (MPa)** & **Mean RMSE Error** \\ \hline
1 & 1.33 & 1 & 8.24 & \(-43.47\) & \(-31.84\) \\
2 & 1.15 & 1 & 7.94 & \(-83.28\) & \(-121.49\) & 7.61 \\
3 & 3.26 & 3 & 4.28 & \(-289.84\) & \(-274.82\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Optimised input parameters using the GA to obtain the desired parameters in Table 7 with three degrees of freedom (only relative depth fixed as an input parameter). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Relative Depth (x/t)** & **Longitudinal Residual Stress (MPa)** & **Transverse Residual Stress (MPa)** & **Mean RMSE Error** \\ \hline
1 & 1.53 & 2 & 8.50 & \(-44.39\) & \(-27.28\) \\
2 & 1.30 & 3 & 8.28 & \(-89.57\) & \(-124.38\) \\
3 & 2.38 & 5 & 7.93 & \(-270.93\) & \(-310.41\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Optimised input parameters using the GA to obtain the desired parameters in Table 9 with two degrees of freedom (relative depth and number of layers fixed as input parameters). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No.** & **Relative Depth (x/t)** & **Longitudinal Residual Stress (MPa)** & **Transverse Residual Stress (MPa)** & **Fixed Number of Layers** \\ \hline
1 & 0.6 & \(-35\) & \(-35\) & 2 \\
2 & 0.9 & \(-80\) & \(-110\) & 3 \\
3 & 0.3 & \(-280\) & \(-280\) & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Case study–2 using GA: Desired longitudinal and transverse residual stresses at different depths for obtaining optimised inputs with fixed number of layers. The ANN-GA integrated system was used to optimise the process parameters for different case studies by specifying the desired residual stress magnitude at a given depth. The GA reported a mean _RMSE_ of 7.61 and 14.64 in case studies with three and two degrees of freedom, respectively.