Predicting Relative Density in L-PBF Using Machine Learning

Article
Predicting the Relative Density of Stainless Steel and Aluminum
Alloys Manufactured by L-PBF Using Machine Learning
José Luis Mullo 1, * , Iván La Fé-Perdomo 2 , Jorge Ramos-Grez 3 , Ángel F. Moreira Romero 4 ,
Alejandra Ramírez-Albán 5 , Mélany Yarad-Jácome 5 and Germán Omar Barrionuevo 6,7, *
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3
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5
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7
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Academic Editor: Xiaoming Yu
Received: 15 April 2025
Revised: 13 May 2025
Accepted: 23 May 2025
Published: 3 June 2025
Citation: Mullo, J.L.; La Fé-Perdomo,
I.; Ramos-Grez, J.; Moreira Romero,
Á.F.; Ramírez-Albán, A.; YaradJácome, M.; Barrionuevo, G.O.
Predicting the Relative Density of
Grupo de Ingeniería Automotriz, Movilidad y Transporte (GiAUTO), Carrera de Ingeniería
Automotriz-Campus Sur, Universidad Politécnica Salesiana, Quito 170702, Ecuador
Escuela de Ingeniería Mecánica, Pontificia Universidad Católica de Valparaíso, Valparaíso 2340025, Chile
Department of Mechanical and Metallurgical Engineering, School of Engineering, Pontificia Universidad
Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago 8320165, Chile
Carrera de Ingeniería Industrial, Universidad Laica Eloy Alfaro de Manabí, Manta 130222, Ecuador
Departamento de Seguridad y Defensa, Universidad de las Fuerzas Armadas ESPE,
Sangolquí 171103, Ecuador
Departamento de Ciencias de la Energía y Mecánica, Universidad de las Fuerzas Armadas ESPE,
Sangolquí 171103, Ecuador
Department of Engineering, Universidad Católica del Uruguay, Av. 8 de Octubre 2738,
Montevideo 11600, Uruguay
Correspondence: jmullo@ups.edu.ec (J.L.M.); gobarrionuevo@espe.edu.ec (G.O.B.)
Abstract: Metal additive manufacturing is a disruptive technology that is changing how
various alloys are processed. Although this technology has several advantages over conventional manufacturing, it is still necessary to standardize its properties, which are dependent
on the relative density (RD). In addition, since experimental designs are costly, one solution
is using machine learning algorithms that allow the effects of variations in the processing
parameters on the resulting density of the additively manufactured components to be
anticipated. This work assembled a database based on data from 673 observations and
10 predictors to forecast the relative density of 316L stainless steel and AlSi10Mg components produced by laser powder bed fusion (L-PBF). LazyPredict was employed to select
the algorithm that best models the variability of the inherent data. Ensemble boosting
regressors offer higher accuracy, providing hyperparameter fitting and optimization advantages. The predictions’ precision for aluminum and stainless steel obtained an R2 value
greater than 0.86 and 0.83, respectively. The results of the SHAP values indicated that
laser power and energy density are the parameters that have the greatest impact on the
predictability of the relative density of Al-Si10-Mg and SS 316L materials processed by
L-PBF. This study presents a compendium of data for the additive fabrication of stainless
steel and aluminum alloys, offering researchers a guide to understanding how processing
parameters influence RD.
Stainless Steel and Aluminum Alloys
Manufactured by L-PBF Using
Machine Learning. J. Manuf. Mater.
Keywords: stainless steel; aluminum alloy; laser powder bed fusion; relative density;
machine learning; prediction
Process. 2025, 9, 185. https://
doi.org/10.3390/jmmp9060185
Copyright: © 2025 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://creativecommons.org/
licenses/by/4.0/).
J. Manuf. Mater. Process. 2025, 9, 185
1. Introduction
Additive manufacturing (AM), particularly laser-based powder bed fusion (L-PBF),
represents a transformative technology in modern manufacturing. L-PBF allows for the precise fabrication of complex geometries by selectively melting and fusing layers of powdered
material with a high-power laser [1–3]. This method offers unparalleled design freedom,
enabling the production of lightweight, customized, and highly intricate components that
https://doi.org/10.3390/jmmp9060185
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are challenging or costly to achieve through traditional manufacturing [4,5]. L-PBF is
especially impactful in the aerospace, automotive, and medical industries, where weight
reduction, material efficiency, and customization are critical. Additionally, its ability to
minimize material waste and streamline production processes contributes to sustainability
and cost-efficiency, making it a cornerstone of advanced manufacturing [6].
L-PBF is a crucial technology in the growing global AM market and is projected to
reach billions of dollars in value over the next decade [7]. While the initial costs of L-PBF
systems are high due to the expense of advanced lasers, precise optics, specific powders, and
the need for inert gas environments, the technology offers significant advantages, including
reduced material waste, shorter production cycles, and the elimination of costly tooling
in specific use cases, such as low-volume production, prototyping, or highly complex
geometries [8–10]. Nevertheless, one of the main constraints in L-PBF is the limited build
size. In addition, the layer-by-layer nature of the technology can result in long production
times, especially for larger or more complex components, making it less suitable for highvolume manufacturing [11]. Concerning the relative density (RD), factors such as the
laser power, scanning speed, layer thickness, and powder size must be controlled to avoid
defects like porosity, a lack of fusion, or keyhole voids [12,13].
An inconsistent relative density can impact the mechanical properties, leading to
reduced strength, fatigue resistance, or structural integrity. RD is a key metric in multiproperty optimization for LPBF because it directly impacts the mechanical properties,
surface quality, and overall performance of 3D-printed parts. Nevertheless, although
relative density represents a useful parameter to verify the quality of parts manufactured
by additive manufacturing, other parameters such as roughness, dimensional accuracy and
manufacturing speed should be considered [14,15].
Process optimization and quality assurance are crucial but resource-intensive. Using
machine learning (ML) to predict mechanical properties has become increasingly popular
due to its ability to model complex, nonlinear relationships between material features
(e.g., composition, microstructure, processing parameters) and their mechanical behavior.
Several authors have used a variety of ML algorithms to predict the relative density of
materials processed by L-PBF [16–20]. In addition, La Fé-Perdomo et al. [14] evaluated the
relative density, surface roughness, hardness, and stress–strain response of 316L stainless
steel manufactured by LPBF by applying several ML regressors. A similar study was
developed by Toprak and Dogrueret [17] but applied to an AlSi10Mg alloy. Both studies
highlight the importance of using ML as a multi-objective optimization method.
It is worth noting that, due to the complex interaction of the material with the laser and
the variability of the processing parameters, ML predictions have a large variability [16],
so new approaches have been developed to reduce the error. Cao et al. [18] applied a
clustering integrated regression model, increasing the accuracy of predictive ML models.
However, this is a challenging task due to the limited amount of data and the inherent
variability of the process. Incorporating physical principles and domain knowledge into
traditional ML models has been reported to improve reliability and interpretability, as and
combining finite element simulations or analytical models with ML has been performed to
obtain for more accurate predictions [21,22].
Due to the emergence of new machine learning algorithms, selecting the most suitable
algorithm for regression or classification tasks has become data-dependent. On the one
hand, traditional algorithms such as support vector machines or decision trees (weak
learners) are effective in predicting linear and nonlinear behavior; they are easy to interpret,
and their fitting is straightforward [23,24]. Ensemble methods build predictive models by
combining multiple weak learners into strong learners to improve performance, reduce
overfitting, and increase robustness [25,26], outperforming deep learning in structured
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datasets. On the other hand, deep learning (DL) models, while powerful for unstructured
data like images, audio, and text, often underperform or are less efficient than traditional
ML models when dealing with tabular data [27]. Nevertheless, DL can still outperform in
tabular data when the dataset is extremely large or if the dataset is heavily imbalanced and
includes complex patterns.
Pandala [28] developed LazyPredict, a tool able to evaluate multiple machine learning
algorithms without much code to understand which ML models work better without
parameter tuning. This approach automates models’ selection based on common testing
metrics such as the coefficient of determination (R2 ), root mean square error (RMSE), and
the computational time taken for each algorithm. Although this tool is very useful for preselecting algorithms initially, it has some limitations, such as using default hyperparameters,
not including the latest algorithms, and not being suitable for complex problems requiring
deep feature engineering.
Due to the high cost of experimental designs involving high material consumption and
printing machine energy and requiring significant time to produce 3D components, the use
of ML algorithms to predict the relative density represents a breakthrough in improving the
efficiency of LPBF. To this end, this work evaluates two of the most widely used materials in
L-PBF: 316L stainless steel and AlSi10Mg aluminum alloy. Several ML algorithms trained
on literature data and experimental samples are applied to predict their relative density.
2. Materials and Methods
2.1. Materials Properties
More than seventy articles reporting the relative density of 316L stainless steel and
AlSi10Mg were evaluated from scientific databases such as Scopus and Web of Science to
assemble a representative dataset. Restrictions were applied to the process parameters
and relative density evaluation methods. The data were not considered if their collection
process was not described in a clear and reproducible manner. A total of 332 datasets were
obtained for the stainless steel and 341 for the aluminum alloy. The dataset is available
at https://github.com/GermanOmar/LPBF (accessed on 14 April 2025). The nominal
chemical composition of each alloy is reported in Table 1.
Table 1. Nominal chemical composition of the metallic powders of stainless steel 316L and aluminum
alloy Al-Si-10Mg.
Material
SS 316L
Al-Si10-Mg
Elements (wt%)
Fe
Bal.
Al
Bal.
Cr
16.5–18
Si
10
Ni
10–13
Mg
0.4
Mo
0.22
Cu
0.25
Mn
0–2
Ni
0.05
Si
0–1
Fe
0.25
P
<0.045
Mn
0.1
S
<0.03
Ti
0.15
The average powder size (PS) for the SS 316L was 30.4 ± 6.7 µm and 35.6 ± 5 µm
for Al-Si10-Mg. The morphology of the powders in both materials is spherical with some
deviation, and in some cases, satellites around the particles are reported [29,30].
2.2. Additive Manufacturing
Regarding the additive manufacturing parameters, the ranges of the laser power (P),
scanning speed (v), layer thickness (l), and hatch spacing (h) are given in Table 2. The
volumetric energy density (VED) was determined by Equation (1):
VED =
P
v×h×l
(1)
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Table 2. Range of processing parameters employed in L-PBF.
Material
P (W)
v (mm/s)
l (µm)
h (µm)
References
SS 316L
Al-Si10-Mg
70–350
100–700
50–3000
100–8000
20–400
20–90
20–150
30–400
[12,14,16,28–45]
[2,46–64]
The average laser spot diameter for stainless steel processing is 76 µm, while that for
aluminum is slightly higher, at about 90 µm. In most cases, the scanning strategy employs
a zig-zag configuration, while the geometry of the parts is mainly prismatic and, to a lesser
extent, cylindrical.
2.3. Exploratory Data Analysis
To analyze the effect of processing parameters on the relative density (RD) of both alloys,
feature importance (FI) and Pearson correlation were employed. Based on mutual information
(MI), FI evaluates the dependency between each feature and the target variable (RD), quantifying how much information a feature contributes to explaining RD. MI is particularly effective
for capturing linear and non-linear relationships, as it measures the shared information between variables. In contrast, Pearson correlation assesses the strength and direction of the
linear relationship between two continuous variables. It is commonly used in feature selection
to determine how strongly a feature correlates with the target variable (RD).
The parameters presented in Figure 1 include all the processing parameters used for
algorithm training. In the LPBF process, the main parameters considered are the laser
power (Power), scanning speed (Speed), layer thickness (Thickness), and hatch space
(Hatch). A parameter widely used to evaluate LPBF processing is the volumetric energy
density (Energy). In addition, raw material parameters such as the particle size (PS) and
laser system parameters such as the diameter of the laser spot (Spot), atmosphere, part
geometry, and scanning strategy were used.
Figure 1. Feature importance response (a,b) and Pearson correlation (c,d) for Al-Si10-Mg (left) and
SS 316L (right).
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Figure 1 shows that despite undergoing the same process, the processing parameters
for aluminum and stainless steel have different impacts on the RD. In both cases, the
average powder size (PS) appears to be the variable with the greatest impact on the target.
The Pearson correlation validates this observation. In addition, it could be established that
laser power also strongly correlates with RD, and that the influence of the atmosphere
could be ruled out.
The difference in the effect of the processing parameters on the RD can be attributed
to aluminum’s high reflectivity and thermal conductivity, making it more challenging to
process than stainless steel, requiring higher energy input and different scan strategies.
2.4. Machine Learning
The general process for relative density prediction using machine learning is outlined
in Figure 2. Initially, the relevant literature was searched for the relative density in L-PBF,
then the database was assembled, and the descriptors were scaled and normalized. The feature importance and Pearson correlation were analyzed for data exploration. Subsequently,
the ‘Lazy Predict’ tool evaluated the algorithm best suited to each dataset. Once the most
favorable algorithms for relative density prediction were established, the hyperparameters
were adjusted by applying random search optimization, and the accuracy of each algorithm
was individually evaluated by using metrics such as the mean absolute error (MAE), mean
squared error (MSE), and the coefficient of determination R2 , followed by 5-fold crossvalidation. Since the LazyPredict tool only considers Scikit-learn [65] algorithms, two more
powerful algorithms, Xtreme gradient boosting regressor (XGBR) [66] and deep learning,
were also evaluated to compare their effectiveness in RD prediction. The description of
the hyperparameters used for each algorithm is detailed in the repository. Finally, the
model was evaluated with experimental data to verify its applicability in predicting RD for
stainless steel and aluminum alloys.
Figure 2. Schematic process for the ML prediction of the relative density in L-PBF processing.
SHapley Additive exPlanations (SHAP) values were employed to explain the predictions of machine learning models. They are based on concepts from cooperative game
theory and provide a way to understand how much each feature contributes to a specific
prediction [67]. By aggregating SHAP values across forecasts, it is possible to comprehend
the feature importance for the entire dataset, explaining predictions to stakeholders for
better decision-making.
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3. Results and Discussion
This section first analyzes the results of the aluminum alloy’s relative density predictions and then analyzes the response of the stainless steel. Start with the algorithms
recommended by LazyPredict that have the highest R2 . Then, they are compared with the
results of more robust algorithms such as Extreme Gradient Boosting Regressor (XGBR)
and deep learning. Deep neural networks are assembled in PyTorch v.2.7 [68]. Finally, the
impact of assembling a database with aluminum and stainless steel data is discussed.
3.1. Aluminum Alloy Al-Si10-Mg Relative Density Prediction
Figure 3 presents all the algorithms evaluated and their response to the coefficient of
determination (R2 ). ExtraTressRegressor (ETR) and KNeighborsRegressor (KNR) offer an
R2 higher than 0.8. The five algorithms with the highest accuracy are shown in Table 3.
Figure 3. ML model evaluation for the relative density prediction of Al-Si10-Mg in L-PBF processing.
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Table 3. Accuracy evaluation of the relative density prediction of Al-Si10-Mg.
Model
Adjusted R2
R2
RMSE
Time Taken [s]
ExtraTreesRegressor
KNeighborsRegressor
ExtraTreeRegressor
BaggingRegressor
RandomForestRegressor
0.83
0.82
0.74
0.72
0.72
0.85
0.84
0.78
0.76
0.76
1.29
1.33
1.58
1.65
1.65
0.12
0.01
0.01
0.03
0.21
Figure 4 shows the prediction of the relative density by applying ETR, KNR, and XGBR.
The algorithms that best model the training dataset are ETR and XGBR, with an R2 of 0.95.
However, ETR achieves higher accuracy for the testing dataset (R2 = 0.86). Therefore, this
would be the algorithm chosen to predict the relative density of the Al-Si10-Mg alloy.
Figure 4. Scatter plot for predicting the relative density of Al-Si10-Mg in L-PBF processing. Performance evaluation of (a) Extra Tress Regressor (ETR), (b) K-Neighbors Regressor (KNR), and
(c) Extreme Gradient Boosting Regressor (XGBR).
In order to benchmark traditional algorithms, deep learning was used to verify their
predictive ability on structured data. Figure 5 shows the response for both training and
testing. For the training stage, it reaches a high fidelity with an R2 of 0.93; however, for
the evaluation dataset, the response does not reach an acceptable accuracy, obtaining
an R2 of only 0.52. Consequently, it is possible to establish that traditional algorithms,
particularly ensemble learning models, can better predict the relative density of the Al-Si10Mg manufactured by L-PBF.
Figure 5. Deep learning performance: (a) Loss function evaluation during training and testing;
(b) Scatter plot for predicting the relative density of Al-Si10-Mg.
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Models like ETR, KNR, and XGBR are designed to handle structured data efficiently
and naturally take advantage of feature engineering. In contrast, deep learning models
work better with raw data and require significant pre-processing to handle categorical
features or missing values effectively [69].
Figure 6 shows the distribution of Shapley values to understand the features’ importance. Figure 6a shows that processing parameters such as the laser power, scanning speed,
and energy (VED) have the highest impact on predicting the relative density. In addition,
Figure 6b indicates the mean absolute Shapley values denoting the feature importance of
each processing parameter. These results are in agreement with research related to the
processing and optimization of Al-Si10-Mg processed by L-PBF [52,55,56].
Figure 6. (a) Distribution of Shapley values, (b) feature importance to better understand the predictability of the relative density of Al-Si10-Mg.
3.2. Stainless Steel 316L Relative Density Prediction
Table 4 reports the results of the LazyPredict assessment. The algorithms that better
model the relative density are BaggingRegressor (BR), GradientBoostingRegressor (GBR),
and RandomForestRegressor (RFR). All of them show an R2 greater than 0.8. Figure 7
presents all the algorithms evaluated by the LazyPredict and their R2 .
Table 4. Accuracy evaluation of the relative density prediction of SS 316L.
Model
Adjusted R2
R2
RMSE
Time Taken [s]
BaggingRegressor
GradientBoostingRegressor
RandomForestRegressor
ExtraTreesRegressor
LGBMRegressor
0.84
0.80
0.80
0.78
0.74
0.86
0.83
0.83
0.81
0.78
1.39
1.53
1.55
1.63
1.75
0.03
0.17
0.28
0.11
0.11
Figure 8 shows the prediction of the relative density by applying the algorithms
recommended by the LazyPredict tool. Additionally, XGBR was employed to evaluate the
accuracy. The GBR and XGBR show a higher accuracy in modeling the training dataset, with
an R2 of 0.98. However, BR achieves a higher accuracy for the testing dataset (R2 = 0.83).
Thus, this algorithm is chosen to predict the relative density of the 316L SS.
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Figure 7. ML model evaluation for the relative density prediction of 316L SS in L-PBF manufacturing.
Figure 8. Cont.
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Figure 8. Scatter plot for predicting the relative density of 316L SS in L-PBF processing. Performance
evaluation of (a) Bagging Regressor (BR), (b) Gradient Boosting Regressor (GBR), (c) Random Forest
Regressor (RFR), and (d) Extreme Gradient Boosting Regressor (XGBR).
Deep neural networks (DNNs) were used to compare their predictive capability with
traditional algorithms (Figure 9). Although several techniques were employed to improve
accuracy, DNN achieved high accuracy when modeling the training dataset (R2 = 0.93), but
its accuracy for the validation dataset was relatively low (R2 = 0.62). Therefore, we do not
recommend using DNN for structured data.
Figure 9. Deep learning performance: (a) Loss function evaluation during training and testing;
(b) Scatter plot for predicting the relative density of 316L SS.
The results obtained have a similar response to the dataset used to predict the relative
density of the aluminum alloy. Therefore, using DNN for RD prediction in materials
manufactured by L-PBF is not recommended.
Figure 10 shows the distribution of Shapley values to understand the features’ importance. Figure 10a shows that processing parameters such as the scanning strategy,
energy density, and laser power have the highest impact on predicting the relative density.
In addition, Figure 10b indicates the mean absolute Shapley values denoting the feature
importance of each processing parameter where the scanning strategy appears as the most
influential factor, followed by the energy density and laser power. These results validate
the conclusions reached through experimental studies and reflect the validity of machine
learning models [14,17,37,70]. It is worth noting that the measurement method significantly
affects the relative density value; LPBF is usually measured by applying the Archimedes
method. However, some articles present results by image correlation or CT-scanning, and
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some authors reported the percentage of porosity. Therefore, the measurement method
could also influence the variability in the relative density predictions.
Figure 10. Distribution of Shapley values (a) to understand the feature importance (b) when predicting
the relative density of 316L SS.
3.3. Global Relative Density Prediction
The datasets were merged to form a more robust database, and their impact on the
predictability of the relative density was evaluated, considering material type as another
descriptor. The overall performance is depicted in Figure 11.
Figure 11a,b shows the analysis of the impact of processing parameters, including the
material type, on the predictability of the relative density. The new database validates the
effect of particle size on the relative density. This observation is entirely valid, as several
authors have argued that the quality of powders directly impacts their buoyancy and that
the porosity they may have is transmitted into the additively manufactured material [45].
On the other hand, the type of material does not substantially affect the relative density
because the processing conditions are assigned according to the type of material. For
example, for manufacturing stainless steel, an average laser power of 165 W and a scanning
speed of 800 mm/s is commonly used [36,41,43], while for the manufacture of aluminum,
a higher power of about 290 W and a speed of 1200 mm/s are required [46–48].
With respect to the new predictability, modeling was improved in the training set
(R2 = 0.98). However, the testing accuracy was reduced to R2 of 0.7 (Figure 11c,d). The
best-performing algorithms were ETR and XGBR, with an R2 of 0.72 and 0.7, respectively.
DNN results were not included since the accuracy achieved is below that obtained by
traditional models (ETR and XGBR). Figure 11e,f shows the evaluation of the SHAP values,
where laser power and energy density appear as the parameters that have the greatest
impact on the predictability of the relative density of Al-Si10-Mg and SS 316L materials
processed by L-PBF. It is worth noting that energy density has been proposed as a key
parameter for evaluating the printability of materials processed by L-PBF [43,44]. In that
sense, the present research validates its importance as an estimator of relative density in
additive metal manufacturing processes.
For predictions with a smaller margin of error, additional descriptors could be included, such as the type of energy source, irradiance, dimensions of the molten pool and
geometry of the component; physical models could also be included [71]. However, the
present investigation focused on processing parameters that are directly controllable by
the operator. It is worth noting that ML models often predict empirical correlations, but
do not always incorporate fundamental physical principles, which can lead to inaccurate
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predictions under conditions outside the training domain. To overcome these limitations,
hybrid approaches combining ML with physical models (physics-informed ML) have been
proposed as transferable learning techniques.
Figure 11. Evaluation of the global dataset. (a,b) Exploratory data analysis: Feature importance and
Pearson correlation; (c,d) Accuracy evaluation in training and testing datasets utilizing ETR and
XGBR models; (e,f) Effect of Shapley values on relative density prediction.
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It is worth noting that a high and consistent relative density is essential for parts in
aerospace, biomedical, and automotive applications, where regulatory standards demand
minimal internal defects. However, only optimizing the RD can lead to trade-offs (e.g.,
excessive energy input may cause residual stresses or keyholing). Thus, it serves as a
baseline criterion that must be balanced with other targets like surface roughness, scanning
speed, and dimensional accuracy.
4. Conclusions
This research evaluated the predictability of the relative density of 316L stainless steel
and Al-Si10-Mg aluminum alloy, two of the materials most commonly used in additive
manufacturing, particularly in L-PBF. The conclusions obtained from this research are
summarized below:
The LazyPredict library is a useful tool for selecting the machine learning algorithm
that best models the dataset used and thus improves the prediction capacity by optimizing
hyperparameters. In this research, the recommended algorithms were Extra Trees Regressor
(ETR) for aluminum and Bagging Regressor (BR) for stainless steel.
•
•
•
The dataset generated for aluminum alloy and stainless steel presents a wide range of
processing parameters, combining different brands and models of L-PBF machines.
The ML models generated captured the inherent variability of each machine, achieving
fairly accurate R2 values. For Al-Si10-Mg, an R2 of 0.95 was obtained for the training
dataset and an R2 of 0.86 for the testing dataset. For the 316L SS, accurate results were
also obtained, with an R2 of 0.95 for training and 0.83 for testing.
Combining the datasets resulted in a more robust database; however, the variability of
the processing parameters increased as the energy density required to process each
material was different. The predictions obtained a better accuracy for the training
dataset (R2 = 0.98), but it was reduced to 0.72 for the test dataset.
The results of the SHAP values indicated that laser power and energy density are the
parameters that have the greatest impact on the predictability of the relative density of
Al-Si10-Mg and SS 316L materials processed by L-PBF. Energy density is proposed as
a key estimator for evaluating the relative density of materials processed by L-PBF.
Author Contributions: Conceptualization, J.L.M., I.L.F.-P. and G.O.B.; data curation, I.L.F.-P. and
J.R.-G.; formal analysis, Á.F.M.R., A.R.-A. and J.R.-G.; funding acquisition, J.L.M. and J.R.-G.; investigation: I.L.F.-P. and G.O.B.; methodology: J.L.M., G.O.B. and M.Y.-J.; supervision: J.R.-G. and
Á.F.M.R.; validation: A.R.-A. and M.Y.-J.; writing-original draft, J.L.M., A.R.-A. and G.O.B., writing a
review and final editing, J.L.M., M.Y.-J. and G.O.B. All authors have read and agreed to the published
version of the manuscript.
Funding: This research was funded by SENESCYT grant number ARSEQ-BEC-000329-2017, ANID
FONDECYT grant number 1201068 project, and The APC was funded by Universidad Politécnica Salesiana.
Data Availability Statement: The dataset is available at: https://github.com/GermanOmar/LPBF
(accessed on 14 April 2025).
Acknowledgments: We want to thank the researchers who made their experimental data available
through their publications.
Conflicts of Interest: The authors declare no conflicts of interest.
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