Machine learning enabling prediction in mechanical performance of Ti6Al4V fabricated by large-scale laser powder bed fusion via a stacking model

doi:10.1007/s11465-024-0796-0

2024, Vol. 19

Issue (4) : 25 https://doi.org/10.1007/s11465-024-0796-0

Machine learning enabling prediction in mechanical performance of Ti6Al4V fabricated by large-scale laser powder bed fusion via a stacking model

Changjun HAN¹, Fubao YAN¹, Daolin YUAN¹, Kai LI¹, Yongqiang YANG¹, Jiong ZHANG², Di WANG¹(

)

¹. School of Mechanical and Automotive Engineering, South China University of Technology, Guangzhou 510641, China
². Department of Mechanical Engineering, College of Engineering, City University of Hong Kong, Hong Kong 999077, China

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Abstract

Determining appropriate process parameters in large-scale laser powder bed fusion (LPBF) additive manufacturing pose formidable challenges that necessitate advanced approaches to minimize trial-and-error during experimentation. This work proposed a data-driven approach based on stacking ensemble learning to predict the mechanical properties of Ti6Al4V alloy fabricated by large-scale LPBF for the first time. This method can adapt to the complexity of large-scale LPBF data distribution and exhibits a more generalized predictive capability compared to base models. Specifically, the stacking model utilized artificial neural network (ANN), gradient boosting regressor, kernel ridge regression, and elastic net as base models, with the Lasso model serving as the meta-model. Bayesian optimization and cross-validation were utilized for model optimization and training based on a limited data set, resulting in higher predictive accuracy compared to traditional artificial neural network model. The statistical analysis of the ANN and stacking models indicates that the stacking model exhibits superior performance on the test set, with a coefficient of determination value of 0.944, mean absolute percentage error of 2.51%, and root mean squared error of 27.64, surpassing that of the ANN model. All statistical metrics demonstrate superiority over those obtained from the ANN model. These results confirm that by integrating the base models, the stacking model exhibits superior predictive stability compared to individual base models alone, thereby providing a reliable assessment approach for predicting the mechanical properties of metal parts fabricated by the LPBF process.

Keywords machine learning laser powder bed fusion ensemble learning stacking algorithm additive manufacturing

Corresponding Author(s): Di WANG

Issue Date: 23 August 2024

Cite this article:

Di WANG,Jiong ZHANG,Yongqiang YANG, et al. Machine learning enabling prediction in mechanical performance of Ti6Al4V fabricated by large-scale laser powder bed fusion via a stacking model[J]. Front. Mech. Eng., 2024, 19(4): 25.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-024-0796-0
https://academic.hep.com.cn/fme/EN/Y2024/V19/I4/25

Fig.1 (a) DiMetal-450 laser powder bed fusion equipment. (b) Fabrication of Ti6Al4V tensile specimen.

Fig.2 Schematic representation of artificial neural network during laser powder bed fusion processing of Ti6Al4V, featuring an input layer, a hidden layer, and an output layer.

Fig.3 Scheme of the stacking model for laser powder bed fusion processing.

Fig.4 Workflow diagram for the development of a stacking-based prediction model for tensile strength in large-scale large powder bed fusion.

Fig.5 Heatmap on correlation analysis of 64 sets of data between process parameters and tensile strength (

σ b

) of Ti6Al4V alloy fabricated by large-scale laser powder bed fusion.

Fig.6 Scatter plots of 64 data sets on the relationship between laser powder bed fusion process parameters and tensile strength: (a) unnormalized and (b) normalized plots showing the relationship between process parameters and tensile strength.

Tab.1 Prediction results of stacking model with different number of base models

Fig.7 Mean absolute error (MAE) for different numbers of neurons in hidden layers of the artificial neural network model for the subsequent development of stacking model: (a) single hidden layer; (b) two hidden layers.

Tab.2 Hyperparameters of each base model

Fig.8 Friedman test and post-hoc Nemenyi test diagram for 7-fold cross-validation of different models on the training set.

Fig.9 Training process of the artificial neural network (ANN) and stacking models: scatter plots for the training and validation sets, representing (a) the ANN model and (b) the stacking model. (c, d) Error plots for the training and validation sets for the two models, respectively.

Fig.10 Prediction results of artificial neural network (ANN) and stacking models on the test set: predicted values for (a) ANN and (b) stacking. Prediction errors for (c) ANN and (d) stacking.

Fig.11 Relationship between prediction errors and target values for artificial neural network (ANN) and stacking models: (a) a polar plot illustrating the relationship between prediction errors and target values, and (b) a radar chart displaying evaluation metrics. IA: index of agreement. MAE: mean absolute error. MAPE: mean absolute percentage error. RMSE: root mean squared error.

Fig.12 Taylor diagram for artificial neural network (ANN) and stacking models regarding correlation coefficients, standard deviations, and root mean squared error.

Tab.3 Comparison of the accuracy between the stacking model and other ML models

Fig.13 Comparison of different machine learning models: (a) a line chart depicting predictions, and (b) bar charts showing R² and mean absolute error (MAE).

Abbreviations
ANN	Artificial neural network
BP	Backpropagation
CR	Critical range
ENet	Elastic Net
GBR	Gradient boosting regressor
IA	Index of agreement
KRR	Kernel ridge regression
LPBF	Laser powder bed fusion
LR	Linear regression
MAE	Mean absolute error
MAPE	Mean absolute percentage error
ML	Machine learning
MSE	Mean squared error
ReLU	Linear rectification function
RMSE	Root mean squared error
STD	Standard deviation
SVR-GS	Support vector regression algorithm optimized by grid search
Variables
a	Constant between 1 and 10
D	Dataset
H	Hatch spacing
k	Number of models
L	Layer thickness
m	Number of output nodes
$m^t$	The first moment
n	Number of input nodes
N	Number of data sets
P	Laser power
R²	Coefficient of determination
T_s(X)	The output of the stacking model
$v^t$	The second moment
V	Scanning speed
W	Connection matrix
X	Input vector
Y	Output
$y ¯$	Mean value of the true values
$y^i$	Predicted value for sample $i$
α	Significance level
β_i(X)	The output of the base model at index $i$
$γ$	The second layer model of the stacking model
$ε$	Small constant
$η$	Total number of samples
θ	Hyperparameter
$θ t$	Parameter vector
Θ	Search space
$σ b$	Tensile strength
$φ (X)$	Prediction output of the meta-model
Ψ	Hyperparameter response function

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