Page 52 - MSAM-2-1

Materials Science in Additive Manufacturing Data imputation strategies of PBF Ti64

Figure 9. Cumulative distribution plots for k-nearest neighbor-imputed (left), multivariate imputation by chained equations-imputed (middle), and graph
imputation neural network-imputed (right) datasets for selected incomplete variables.

the best for six variables, including exposure duration, correct relationship. Most of the sums of imputed density
hatch spacing, laser focus, layer thickness, point distance, and porosity values add up to 100% when rounded to 2
and Young’s modulus. GINN gave the best imputation for decimal places.
seven variables, including laser spot, density, elongation, The performances of the models were validated by
microhardness, macrohardness, ultimate tensile strength, comparing the values obtained from the models with
and yield strength. MICE only outperformed kNN and the actual values calculated from a known relationship.
GINN in two variables, that is, scan speed and porosity. The laser scan speed is known to be related with other
It is interesting to note that kNN performed better in parameters by the equation below.
imputing variables related to process parameters, whereas
GINN performed better in variables related to material V = P (V)
properties. Ehl
For the MICE-imputed dataset, the imputed values were where V is the laser scan speed, P is the laser power, E is
much more varied, and the imputations showed a stronger the volumetric energy density, h is the hatch spacing, and l
relationship between the process parameters and material is the layer thickness. There are 48 datarows in the dataset
properties than the kNN-imputed dataset. While MICE that contains missing data for the laser scan speed while
performed better than kNN in that aspect, there were more other parameters such as laser power, energy density, hatch
instances where microhardness values were lower than spacing and layer thickness are available. These datarows
macrohardness values (137 for MICE versus 73 for kNN). can be used to validate the performance of the imputation
The sum of the imputed density and porosity values also do models by comparing the imputed laser scan speed with the
not add up to 100%, instead ranging from 99.92% to 100.12%. calculated laser scan speed using the known relationship
The GINN algorithm can be said to have performed as shown in Equation V. Figure 11 shows the performance
the best with the closest distribution to the original dataset of the models. It is found that the KNN model tends to
and the most varied imputed values, although with 109 overpredict the laser scan speed, while the GINN model
instances of lower values of microhardness compared to tends to underestimate the laser scan speed. The MICE
macrohardness, translating to 73% of the data showing the model is able to predict the laser scan speed correctly in

Volume 2 Issue 1 (2023) 11 https://doi.org/10.36922/msam.50