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MechProNet: Machine Learning Prediction of Mechanical Properties in Metal Additive Manufacturing

Parand Akbari, Masoud Zamani, Amir Mostafaei

arXiv:2209.12605v2cs.LGcond-mat.mtrl-scics.AI

TL;DR

Mechanical-property prediction is important for metal additive manufacturing, yet experimental work is costly and ML offers a flexible alternative. MechProNet benchmarks machine-learning approaches using a broad experimental dataset and tailored features. The tested model families outperform others in the reported benchmark, which the authors describe as generalizable across materials, processes, and machines.

  • Problem

    Predicting mechanical properties matters for MAM part quality and reliability, while experimental estimates are costly and machine learning offers a more flexible approach.

    Source: §1 · p. 2

  • Method

    MechProNet benchmarks machine-learning models on an experimental MAM dataset, exploring featurization, evaluation, optimization, SHAP analysis, and explicit data-driven models.

    Source: §2.3.1 · p. 9, §2.4 · p. 10, §4 · p. 31

  • Results

    Random Forest, Gradient Boosting, and Neural Networks consistently outperformed other tested algorithms, and the authors describe the benchmark model as generalizable across materials, processes, and machines.

    Source: §4 · p. 31

  • Takeaways & Limitations

    The benchmark offers a standardized platform for comparison and evaluation that the authors anticipate will facilitate process optimization and serve the MAM machine-learning community.

    Source: §4 · p. 31

Abstract

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Predicting mechanical properties in metal additive manufacturing (MAM) is essential for ensuring the performance and reliability of printed parts, as well as their suitability for specific applications. However, conducting experiments to estimate mechanical properties in MAM processes can be laborious and expensive, and they are often limited to specific materials and processes. Machine learning (ML) methods offer a more flexible and cost-effective approach to predicting mechanical properties based on processing parameters and material properties. In this study, we introduce a comprehensive framework for benchmarking ML models for predicting mechanical properties. We compiled an extensive experimental dataset from over 90 MAM articles and data sheets from a diverse range of sources, encompassing 140 different MAM data sheets. This dataset includes information on MAM processing conditions, machines, materials, and resulting mechanical properties such as yield strength, ultimate tensile strength, elastic modulus, elongation, hardness, and surface roughness. Our framework incorporates physics-aware featurization specific to MAM, adjustable ML models, and tailored evaluation metrics to construct a comprehensive learning framework for predicting mechanical properties. Additionally, we explore the Explainable AI method, specifically SHAP analysis, to elucidate and interpret the predicted values of ML models for mechanical properties. Furthermore, data-driven explicit models were developed to estimate mechanical properties based on processing parameters and material properties, offering enhanced interpretability compared to conventional ML models.

1. Introduction

Mechanical-property prediction matters for the quality and reliability of metal additive manufacturing, but experiments are costly and often specific to particular materials and processes. MechProNet addresses this scope gap with a broader dataset and machine-learning framework that also includes interpretability methods.

1. Introduction

  • Defects, cooling conditions, and thermal cycles can affect part integrity and microstructure, making prediction of mechanical properties important for application-specific reliability.Relevant targets include yield strength, ultimate tensile strength, elastic modulus, elongation, hardness, and roughness.Source: §1 · p. 2
  • Experiments are labor-intensive, costly, and time-consuming, while measurements and simulations are often specific or difficult to scale across materials and processes.Simulation-based forecasts can also require multiple costly simulations.Source: §1 · p. 2
  • Prior ML studies used datasets, processing parameters, and materials limited in scope, whereas this benchmark consolidates at least 230 experimental data sources into 1,600 points across PBF and DED.The dataset spans processing parameters and alloys, with expansion anticipated.Source: §1 · p. 3
  • MechProNet develops machine-learning methods tailored to additive manufacturing to predict mechanical properties and assess how build-process parameters affect prediction performance.The benchmark workflow includes data acquisition, feature extraction, model training, prediction tasks, and model analysis.Source: §1 · p. 3, Figure 1 · p. 4
  • The framework uses SHAP to elucidate model predictions and introduces data-driven explicit models linking processing parameters and material properties to mechanical characteristics.The explicit models are designed to be more interpretable than conventional machine-learning models.Source: §1 · p. 4

2. Methodology

The methodology is organized as a benchmark workflow spanning data acquisition, feature extraction, model training, prediction tasks, and model analysis.

2. Methodology

  • The benchmark workflow covers data acquisition, feature extraction, machine-learning model training, prediction tasks, and model analysis.Source: §2 · p. 4

2.1. Data Collection

The study assembled empirical data from manufacturing and materials publications and company material datasheets, extracting information from tables and figures for model inputs.

2.1. Data Collection

  • Empirical data were collected from manufacturing and materials journals and from additive-manufacturing companies’ material datasheets for commercial machines.Source: §2.1 · p. 4
  • Tables and figures were the main data sources; Plot Digitizer was used to extract figure data, and processing parameters and material properties were collected as model input features.Source: §2.1 · p. 5

2.2. Datasets

The benchmark combines varied MAM experiments, machines, materials, and post-processing conditions with processing and material features to predict mechanical-property labels.

2.2. Datasets

  • The literature-sourced dataset contains 1,600 entries with process, machine, material, post-processing, orientation, and processing-parameter inputs, and mechanical-property labels including strength, modulus, elongation, hardness, and roughness.The entries cover experiments across diverse materials, parameters, machines, and post-processing techniques.Source: §2.2 · p. 5
  • The dataset covers PBF and DED processes, with L-PBF standardizing trade names including SLM, DMLM, DMLS, and LMF.The benchmark includes machines from multiple manufacturers for these process types.Source: §2.2 · p. 5, Table 1 · p. 6
  • DED is grouped by heat source and feed method into L-DED, E-DED, arc-DED, and wire-L-DED, with multiple commercial process names represented.The cited examples include LENS and WAAM, and the table summarizes included processes, subprocesses, and manufacturers.Source: §2.2 · pp. 5–6, Table 1 · p. 6
  • The dataset analyzes 68 metals; nearly 600 points are as-built, while others include heat treatment, hot isostatic pressing, or stress relieving.Rz roughness data also cover as-built, bead-blasted, shot-peened, and corundum-blasted surfaces.Source: §2.2 · p. 6
  • The benchmark includes vertical, horizontal, and 45-degree orientations and charts the distributions of MAM subprocesses, post-processing, materials, and machines.The cited figures also show surface-post-processing and processing-parameter distributions.Source: Figure 2 · p. 7, §2.2 · p. 8
  • Processing-parameter distributions cover beam power, scanning speed, layer thickness, and beam diameter; training uses only samples with all required input features.Source: §2.2 · p. 8, Figure 3 · p. 8

2.3. Featurization

The benchmark combines common processing and material inputs with alternative material representations, including elemental features weighted by alloy composition.

2.3. Featurization

  • Baseline featurization combines processing parameters and material properties with categorical MAM descriptors for predicting mechanical properties.Quantitative inputs include beam power, layer thickness, density, specific heat, thermal conductivity, coefficient of thermal expansion, and melting temperature; categorical inputs are one-hot encoded.Source: §2.3 · pp. 8–9

2.3.1. Material featurization

  • Elemental featurization adds elemental characteristics to the baseline feature set, while composition-based features encode each element’s mass percentage.A linear mixture rule weights elemental properties by each element’s fraction in the alloy.Source: §2.3.1 · p. 9, Table 3 · p. 10

2.4. Data splitting and Evaluation Metrics

The benchmark standardizes quantitative features and evaluates models using shuffled five-fold cross-validation, reporting average performance with MAE and R2.

2.4. Data splitting and Evaluation Metrics

  • Quantitative features are standardized to mean zero and unit standard deviation because heterogeneous measurement units can affect model accuracy.The transformation subtracts each feature’s mean and divides by its standard deviation.Source: §2.4 · p. 10
  • The dataset is randomly shuffled and evaluated with five-fold cross-validation, using each fold once as the test set and the other four for training.Reported benchmark results average the five iterations.Source: §2.4 · p. 10
  • Prediction performance is assessed with mean absolute error (MAE) and the coefficient of determination (R2).The test subset is reserved for evaluating prediction accuracy.Source: §2.4 · p. 10

2.5. Models

The benchmark applies a suite of regression models to its MAM dataset, spanning ensemble trees, support-vector and probabilistic regressors, regularized linear models, and neural networks.

2.5.1. Random Forest ’RF’

  • Random Forest (RF) trains decision trees in parallel on bootstrapped data subsets and aggregates their predictions for regression.Random feature subsets at each split support handling high-dimensional data.Source: §2.5.1 · pp. 10–11

2.5.2. Gradient Boosting Trees ’GB’

  • Gradient Boosting (GB) builds shallow decision trees sequentially, with each tree correcting errors made by its predecessor.The sequence combines weak learners into a stronger predictive model.Source: §2.5.2 · p. 11

2.5.3. Support Vector Regressor (’SVR’)

  • Support Vector Regression (SVR) fits a hyperplane in feature space, optimizing its position and margin to minimize prediction errors.Support vectors delineate the boundary within the margin.Source: §2.5.3 · p. 12

2.5.4. Gaussian Process Regressor (’GPR’)

  • Gaussian Process Regression (GPR) predicts a probability distribution over possible outputs, supporting uncertainty quantification.The model’s probabilistic outputs can indicate confidence associated with predictions.Source: §2.5.4 · p. 12

2.5.5. Lasso Linear Regression ’Lasso’

  • Lasso uses L1 regularization to set some coefficients to zero, reducing model complexity and selecting features.This is intended to mitigate overfitting.Source: §2.5.5 · pp. 12–13

2.5.6. Ridge Linear Regression ’Ridge’

  • Ridge uses L2 regularization to shrink all feature coefficients, particularly addressing overfitting with multicollinear features.Unlike Lasso, it does not entirely eliminate features.Source: §2.5.6 · p. 13

2.5.7. Neural Network ’NN’

  • Neural Networks learn patterns through iterative weight updates by backpropagation, while XGBoost is used for feature-importance and SHAP analyses.The section describes neural networks as having input, hidden, and output layers; SHAP analysis is used to interpret XGBoost predictions.Source: §2.5.7 · pp. 13–14

2.6. Hyperparameter optimization

The study tunes model hyperparameters with Bayesian optimization using Hyperopt’s TPE algorithm, while exploring model-specific settings for tree ensembles, SVM, and neural networks.

2.6. Hyperparameter optimization

  • Grid search evaluates every predefined hyperparameter combination, whereas random search samples configurations without using information from past evaluations.The passage notes that both can spend time evaluating suboptimal configurations.Source: §2.6 · p. 14
  • Bayesian optimization uses past evaluations to refine a probabilistic surrogate model that guides subsequent hyperparameter choices.The study implements it with Hyperopt’s Tree-structured Parzen Estimator to optimize validation R2.Source: §2.6 · p. 14
  • For Random Forest and Gradient Boosting, the number of trees is optimized against a trade-off between predictive performance and computational cost.More trees can improve performance but require additional memory and computation during training and inference.Source: §2.6 · p. 14
  • SVM tuning explores linear, polynomial, RBF, and sigmoid kernels, along with the regularization parameter C.C governs the balance between training error and model complexity.Source: §2.6 · pp. 14–15
  • Neural-network tuning examines the number of neurons per layer and alpha, which applies L2 regularization to model weights.The number of neurons balances model complexity against overfitting.Source: §2.6 · p. 15

3. Results and discussion

The section benchmarks machine-learning predictions of mechanical properties and examines property correlations, influential features, training-set size, SHAP explanations, and interpretable data-driven models. It also compares identified equations with the best-performing ML models using R2 and describes the trust-region optimization used to identify the equations.

3.1. ML models results

  • Across seven prediction tasks, the best-performing model varied by property, with Random Forest leading several tasks and Gradient Boosting or a neural network leading others.Yield strength: Random Forest achieved 95.77% accuracy and an MAE of 53.97 MPa; ultimate tensile strength: the fourth model achieved an R2 accuracy of 96.94% and an MAE of 47.95 MPa. Elastic modulus: Random Forest achieved an accuracy of 94.27% and an MAE of 6.63 MPa; elongation at break: Random Forest achieved an R2 accuracy of 88.66% and an MAE of 2.89. Vickers hardness: the third Random Forest model achieved the highest R2 accuracy of 99.62%, while Gradient Boosting achieved the lowest MAE of 15.58 HV; Rockwell hardness: Gradient Boosting achieved an accuracy of 96.05% and an MAE of 2.20 HRC; Rz roughness: the neural network achieved a baseline accuracy of 90.07% and an MAE of 4.69 µm.Source: §3.1 · pp. 16, 18, Figure 4 · p. 17, Figure 5 · p. 18

3.2. Correlation matrix of mechanical properties

  • In the Inconel 718 benchmark, yield strength, ultimate tensile strength, elastic modulus, and hardness correlated positively with one another and negatively with elongation, consistent with the strength-ductility trade-off.Source: §3.2 · p. 21, Figure 7 · p. 21

3.3. Drop-column feature importance

  • Drop-column analysis identified post-processing condition as the most influential feature; beam power and layer thickness were also important across tasks, while orientation chiefly affected elongation.Process, machine type, specimen orientation, and material thermal properties followed among the important features.Source: §3.3 · pp. 21, 23, Figure 8 · p. 22

3.4. XGBoost

  • Because tree-based models performed most accurately, the study used XGBoost gain-based feature importance for yield strength and ultimate tensile strength and selected XGBoost for subsequent SHAP analysis.Gain measures a feature’s importance in generating predictions; Figure 9 summarizes results for the two strength tasks.Source: §3.4 · p. 23, Figure 9 · p. 23

3.5. Explainable AI

  • SHAP analyses linked higher CTE and thermal conductivity to lower predicted yield strength, while heat treatment and Maraging Steel M300 were associated with higher predictions than the average [133].Decision plots for 10 observations showed positive SHAP contributions from CTE, k, and density, and negative contributions from Material and post-processing HT; dependence plots indicated that CTE values above 15·10−6/K corresponded to lower predicted yield strength, while heat treatment had a positive SHAP value.Source: §3.5 · pp. 24, 27, Figure 10 · p. 25, Figure 12 · p. 28

3.6. Impact of Dataset Size on Accuracy

  • With baseline featurization, test MAE decreased as training-set size increased for yield strength and ultimate tensile strength.The comparison used random samples of 20%, 40%, 60%, 80%, and 100% of the training partition and 5-fold cross-validation.Source: §3.6 · p. 27, Figure 13 · p. 28

3.7. Model Identification

  • The model-identification approach aims to produce interpretable mathematical relationships for L-PBF yield strength, ultimate tensile strength, and elastic modulus, with separate models for as-built and heat-treated conditions.It uses nonlinear regression constrained by dimensional consistency, addressing multiple parameters under prior assumptions where existing symbolic-regression and sparse-regression approaches were described as impractical or challenging.Source: §3.7 · pp. 27, 29, 30
  • SciPy constrained optimization using trust-region methods identified equations, but solutions are not guaranteed to reach a global minimum.The paper provides a sample solution for each task in Table 9.Source: §3.7 · p. 30, Table 9 · p. 30
  • Table 9 lists identified equations for modeling mechanical properties with their R2, and Table 10 compares R2 accuracy of identified equations and ML models for yield strength, ultimate tensile strength, and elastic modulus.Source: Table 9 · p. 30, Table 10 · p. 31
  • ML models typically offer superior predictive performance despite interpretability challenges; Table 10 compares R2 for identified equations and best ML models across three mechanical properties.The comparison covers yield strength, ultimate tensile strength, and elastic modulus; the supplied passages do not report the table’s individual scores.Source: §3.7 · p. 30, Table 10 · p. 31

4. Conclusion

MechProNet benchmarks machine-learning prediction of mechanical properties using an extensive dataset spanning MAM processes, materials, and machines. The study reports strong performance from several model families and adds interpretation through SHAP and data-driven explicit models.

4. Conclusion

  • The study assembled an extensive experimental dataset covering diverse MAM processes, materials, and machines to examine their effects on mechanical properties.Several featurization techniques, evaluation metrics, and hyperparameter optimization methods were explored.Source: §4 · p. 31
  • Random Forest, Gradient Boosting, and Neural Networks consistently outperformed other tested algorithms in the benchmark.The resulting benchmark model is reported to generalize across different materials, processes, and machines.Source: §4 · p. 31
  • SHAP analysis was used to interpret yield-strength predictions, while data-driven model identification developed explicit property models from processing and material features.The explicit models were intended to be more interpretable than the employed machine-learning models; the benchmark is anticipated to support process optimization and serve the MAM machine-learning community.Source: §4 · p. 31
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