# Machine Learning-Based Prediction and Optimisation System for Laser Shock Peening
## 5 Results and Discussion
### Parametric Studies  
Parametric studies were undertaken using actual data and by bridging artificial single variable experiments via predicted data to exemplify the complex relationships existing in the process variables and residual stresses. Parametric studies were used to elucidate the data dependencies and to reveal complex mechanisms that can also aid in the mechanistic understanding of the LSP process. In single-shot laser peening (see Figure 9), the residual stresses are expressed as a function of number of layers for different spot size and power density combinations. In Figure 9i, for the spot size and power density combination (8.5 mm and 1 GW/cm\({}^{2}\)), maximum compressive residual stresses of \(-\)200 MPa were observed at the surface. Importantly, the variation of the residual stresses along the depth was not significant for different number of layers (1-7). On the other hand, in Figure 9 ii, relatively higher magnitude of residual stresses and extent of penetration were found both at the surface and deep into the material for the spot size and power density combination of 5 mm with 3 GW/cm\({}^{2}\). This was possibly due to the generation of stronger shock waves propagated through the material, resulting in higher plastic deformation. It was also found that the magnitude of compressive stresses and the extent of penetration were much higher with increasing number of layers. Further, in Figure 9 iii, for the spot size and power density combination of 3.5 mm with 6 GW/cm\({}^{2}\), we see a decline in the magnitude of compressive stresses close to the surface in both longitudinal and transverse directions. However, in the transverse direction, there was considerable increase in the compressive residual stresses through the depth even with fewer number of layers. This was not consistent in the longitudinal direction, which could be attributed to the reverse plasticity effect as a result of over-peening and the generation of a large elastic strain field, causing a sharp decrease in the magnitude of compressive residual stresses near the surface. Furthermore, this analysis demonstrates the nonlinear nature of the process variables and justifies the use of data-based modelling approaches to extract non-evident relationships in the input and output data. Results from the parametric studies in multiple-shot laser peening with overlap (dataset 2) are shown in Figure 10. Here, the residual stress distribution as a function of depth below the peened surface is presented as a function of spot size for different combinations of offset distance and layers. The offset distance also defines the overlapping density, i.e., the number of laser spots in a given area. It is important to note that with low offset distance, the overlapping density increased and vice versa. In Figure 10 ii,ii (offset distance = 0.4 mm and 0.5 mm), maximum compressive stresses of magnitude over \(-\)400 MPa were observed at the surface and up to a depth of 200 \(\upmu\)m in the longitudinal direction for spot size range 1.8 mm-2.0 mm. In the transverse direction, maximum compressive stresses of about \(-\)300 MPa were observed up to a depth of 250 \(\upmu\)m for spot size less than 1.8 mm. In Figure 10 iii, there was a slight decrease in the compressive zone of residual stresses along the longitudinal direction and no significant changes in the transverse direction. However, in Figure 10 iv, there was a clear decrease in the magnitude of compressive stresses both at the surface and into the depth. This pattern was consistently observed in both the longitudinal and transverse directions. Overall, we see a significant shift in the compressive residual stresses as a function of distance from the peened surface when the offset distance was varied from 0.4 mm to 0.7 mm. In the multiple-shot laser peening data with overlap (dataset 2), there was considerably less scatter in the training data as opposed to the single-shot laser peening data (dataset 1) as evident in Figure 7a,c.