## 4 Application to an Additive Manufacturing Benchmark Test
### Sensitivity Analysis  
For sensitivity analysis, we considered five input parameters: three machine parameters and two material parameters. The study considers the primary parameters of layer thickness, laser speed, hatch spacing, Young's modulus, and Poisson ratio. The input parameters' effects were measured using the normal strains, and by calculating the first-order Sobol indices for each node. Similar to the uncertainty analysis, the normal strains were calculated at z = 9.536 along the bridge direction in each simulation.  
Figure 19 presents the variation in the Sobol indices along the bridge length. A pie chart is provided for each parameter, representing the importance of each parameter as a percentage. From Figure 19, we can conclude that the Young modulus and the Poisson ratio are the most critical parameters for the SLM and that hatch spacing is the least important parameter among the five parameters considered. If we consider the x-directional strains, then the Poisson ratio and the Young modulus are the most important parameters. While both parameters' influence changes along the bridge length, both contribute 30% to 65% in the SLM output. The three machine parameters are less influential than the material parameters, but they contribute significantly to the directional strains. Figure 19b shows the effect of input variables on y-directional strains, indicating that the Poisson ratio is the most dominating factor among the input variables. The Poisson ratio contributes between 86 and 90% in the y-directional strains. The other four parameters are equally essential and make contributions of 2 to 5% to the normal strain in the y-direction. However, the situation is the opposite in the case of z strains, where the most dominating factor is Young's modulus instead of the Poisson ratio. Young's modulus is 65 to 68% more important than the other parameters for z strains, while the Poisson ratio is the second most dominant factor.  
Figure 18: Uncertainty quantification along the three sides of the AMB2018-01 bridge structure. (**a**) represents the results along the length of the bridge, (**b**) indicates the results along the width of the bridge, and (**c**) shows the results along the height of the bridge.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Input Variable** & **Lower Bound** & **Upper Bound** \\ \hline laser speed & 680 mm/s & 920 \\ layer thickness & 0.085 mm & 0.115 \\ hatch spacing & 0.017 mm & 0.023 \\ cY & 0.85 & 1.15 \\ _cv_ & 0.85 & 1.15 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Lower and upper bound for the input variables.  
If we look at all the results we find that the machine parameters are less influential than the material parameters. However, the machine parameters' effects are still significant in the SLM process. Thus, we cannot ignore their importance in the SLM output, and we need to consider these machine parameters to optimize the SLM output. In the next section, we consider all five parameters and perform an optimization analysis to find the best configuration of the input variables to obtain the optimal SLM to build-part.