# A Prediction Model for Additive Manufacturing of Inconel 718 Superalloy
## 5 Conclusions  
The potential of the neural network model for predicting the output data in the LPBF of an IN718 superalloy was studied. The samples were fabricated by different process  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Statistical Parameters** & **Training** & **Testing** \\ \hline Residual sum of squares & 0.41591 & 0.96734 \\ Pearson’s r & 0.98102 & 0.97897 \\ Coefficient of determination (R2) & 0.96241 & 0.95839 \\ Adj. R-squared & 0.95865 & 0.94452 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The statistical report of linear regression in the training and testing phases (hardness top).  
Figure 5: Comparison between the measured and the predicted hardness tops in the training/testing phases.  
Figure 6: The trends of testing samples for height (left) and hardness top (right).  
parameters, designed based on the DOE approach. Analysis of the sample height and surface hardness of the printed IN718 samples led to the following observations:  
* As observed in both SS-LP and HS-SS diagrams, the scanning speed played a significant role in the accuracy of the sample height dimension, with a higher scanning speed (lower energy density) resulting in a lower sample height.
* Hatch spacing had a substantial impact on the surface hardness of the samples, with an inverse relationship being found for these parameters.
* The ANN model, consisting of three inputs (LP, SS, HS) and two hidden layers, was employed to predict the height of the samples. Comparison between the measured and predicted sample heights in both training and testing phases proved the accuracy and capability of the applied algorithms in this study.
* By comparing the measured and predicted hardness results, the ability of the proposed model to predict the output data was confirmed.
* Overall, the results demonstrated a perfect fit between the measured and predicted data extracted by the model used in this study. The R2 index around 96-97%, achieved for both sample height and surface hardness, proved the reliability of the proposed ANN model.  
The motivation of this study was to reveal the potential of the neural network model for predicting the output data in SLM manufacturing of the IN718 superalloy. This approach can be applied as an effective solution for predicting, controlling, and managing the input parameters--laser power, scanning speed, and hatch spacing--and can be a proper alternative to analytical and numerical models. This study employed, in particular, LM and BP algorithms in order to estimate the sample height and surface hardness of the printed IN718 samples. The ANN model was trained based on the experimental data, including both input and output data sets. The predicted parameters were evaluated based on the mean error approach and, in particular, the coefficient of determination. The results demonstrated a perfect fit between the measured and predicted data, which proved the reliability of this ANN model as the R2 index was about 96-97% for both sample height and surface hardness.  
Conceptualization, N.S.M., A.A. and M.M.; methodology, M.M.; software, M.M., A.R.; validation, B.B.R., A.R. and B.F.; formal analysis, B.B.R., A.R. and B.F.; investigation, B.B.R., A.R. and B.F.; resources, N.S.M., A.A. and M.M.; data curation, B.B.R. and A.R.; writing--original draft preparation, A.A. and M.M.; writing--review and editing, B.B.R., A.R. and B.F.; visualization, B.B.R., A.R. and B.F.; supervision, N.S.M., A.A. and M.M.; project administration, M.M.; funding acquisition, N.S.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by University of Texas System STARs award.  
Not applicable.  
This work was supported by a University of Texas System STARs award.  
The authors declare no conflict of interest.