## 3 Experimental Validation
### Ti6 Al4V Validation
#### 3.2.1 Probability ML Validation  
In this Subsection, the Probability ML algorithm has been validated. Figure 13 plots the loss function with respect to the k-fold considered for the validation. As for the AlSi10 Mg alloy, the trend is almost constant, with the loss function being flat and below 0.25, except for the first fold, characterized by a significantly higher value, above 1.75.  
In order to stress the fitting capability of the ML algorithm in the worst condition, the validation and the training dataset for the first k-fold have been considered. Figure 14 shows the Gumbel plot for the k = 1 fold, Figure 14a shows the Gumbel plot for the validation fold, whereas Figure 14b shows the Gumbel plot for a training fold.  
According to Figure 14, the trend predicted with the Probability ML is similar to the experimental one, but the data are significantly above, being less conservative. The percentage difference is in a large range, [4.8, 1289]%, with a median value equal to 94%, as  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Orientation** & **Power** & **Speed** & **Hatch Distance** & **Layer Thickness** & **Average Powder Size** & **Risk Volume** \\ \hline  & [W] & [mm/s] & [ \(\mu\)m] & [ \(\mu\)m] & [\(\mu\)m] & [mm\({}^{3}\)] \\ \hline
[0, 90] & [175, 400] & [150, 1400] & [120, 140] & [30, 60] & [34, 45] & [84, 1204] \\ \hline \end{tabular}
\end{table}
Table 2: Range of process parameters for the datasets on Ti6 Al4V considered for the validation of the developed ML algorithms.  
Figure 14: Gumbel plot for the k = 1 fold considered for the validation; (**a**) validation dataset; (**b**) training data.  
Figure 13: k-fold cross validation of the Probability ML algorithm: loss function with respect to the fold considered for the validation.  
expected. In particular, for defects characterized by small size, the difference tends to be higher and justifies the large percentage difference range. It must be noted that, as for the AlSi10 Mg alloy, the Probability ML has quite poor predictive capability for the validation dataset showing an anomalous trend with respect to the other datasets considered for the training. This criticality in the prediction can be overcome by increasing the number of datasets with defects in the range [150-400] \(\upmu\)m. On the other hand, according to Figure 14b, the estimated ML probabilities are in good agreement with the experimental ones for a training dataset, as for the AlSi10 Mg alloy, with the median percentage difference equal to 2.8%.  
Figure 15a shows the Gumbel plot for the k = 3 validation fold, i.e., a fold characterized by a small loss factor. Figure 15b, shows, on the other hand, the Probability-Probability plot, with the abscissa axis reporting the experimental probability, \(\mathrm{P_{exp}}\), and the ordinate axis the ML probability, \(\mathrm{P_{est}}\).  
According to Figure 15a, the predicted and the experimental data are in good agreement, thus confirming the predicting capability of the proposed method for the range of defect size where many data are available for the training. The largest percentage difference, equal to 60%, has been found for the largest experimental defect, but the median percentage difference is very small, being about 4.7%. As for the AlSi10 Mg alloy, the Probability ML has, on average, very good predictive capabilities, with larger deviations only for specific defect sizes or defect sizes ranges. Since for the other validation k-folds the loss factor has almost the same value, it can be reasonably inferred that the developed ML algorithm also works properly for them. The P-P plot further confirms the validity of this approach, with all the data concentrated close to the bisectors.