Supervised Machine Learning Models for Mechanical Properties Prediction in Additively Manufactured Composites
Abstract
:1. Introduction
1.1. Contributions
- A ML pipeline that estimates mechanical properties such as the strength and elasticity of AM composite materials reinforced with continuous fibers—carbon (CRTP), Kevlar (KvRTP), and fiberglass (FGRTP).
- A dataset was constructed from the peer-reviewed literature. It includes mechanical properties (elasticity and strength), materials for continuous fibers, and printing parameters. A robust analysis and the greater reliability of the ML models that have been tested enable the reproducibility and exploration of polymer-based AM technologies.
- In order to determine the most efficient ML models for predicting mechanical properties, this paper examines a variety of linear and nonlinear ML models. The performance analysis reveals their strengths and weaknesses when used within the AM context. As new algorithms are developed, they can be tested with the existing dataset. The modeling workflow used comprises k-fold cross-validation and Monte Carlo resampling, exploring different lightweight machine learning methods like Bayesian Ridge Regression (BAY), CatBoost Regression (CAT), Decision Tree Regression (DTR), k-nearest Neighbors (KNN), Lasso Regression (LAS), Random Forest Regression (RFR), Ridge Regression (RDG), and Support Vector Regression (SVR).
- The manuscript shows how decisive printing parameters are, such as deposition angles and fiber content, for the mechanical properties of Continuous Fiber Reinforced Polymer Matrix Compositess (CFRPCs). Therefore, the results can be used to optimize material properties without conducting extensive experimental campaigns. The identification of such parameters should lead to a more efficient design anddevelopment process.
1.2. Paper Organization
2. Technical Background
2.1. Models to Predict AM Composites’ Elasticity
2.1.1. Square Lattice
2.1.2. Honeycomb or Hexagonal Lattice
2.1.3. Triangular Lattice
2.1.4. Solid Region
2.2. Models to Predict AM Composite Strength
2.3. Machine Learning Models
2.3.1. Linear Regression
2.3.2. CAT Boost Regression
2.3.3. K-Nearest Neighbors Regression
- Euclidean
- Manhattan
- Minkowski
3. Materials and Methods
3.1. Dataset
3.2. Machine Learning Pipeline
4. Results
4.1. Exploratory Analysis
4.2. Numerical Results
4.3. Computational Performance
4.4. Detailed Results
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Material | E [GPa] | [MPa] | % |
---|---|---|---|
Nylon | 1.7 | 33.5 | 4.5 |
Onyx | 1.4 | 36 | 33 |
Standard | ASTM D638 [16] | ASTM D638 [16] | ASTM D638 [16] |
Carbon | 60 | 800 | 1.5 |
Fiberglass | 21 | 590 | 3.8 |
Kevlar | 27 | 610 | 2.7 |
Standard | ASTM D3039 [17] | ASTM D3039 [17] | ASTM D3039 [17] |
Reference | Fiber Type | Fill Pattern | Fill Angle (°) | Fiber Angle (°) | Fiber Distrib. | Properties | |
---|---|---|---|---|---|---|---|
Blok [44] | C | T | NA | X | , , , G, | ||
Dutra [18] | C | NA | NA | X | , , , , , , G, | ||
Klift [45] | C | NA | 0 | NA | C | X | , |
Melenka [19] | Kv | NA | 0 | NA | NA | , | |
Dickson [46] | C, Kv, FG | NA | NA | NA | C | NA | , , , |
Justo [47] | C, FG | NA | 0, 90 | NA | NA | , , , , | |
Al-Abadi [48] | C, Kv, FG | NA | 0, 90 | C | NA | , | |
Goh [13] | C, FG | NA | NA | 0, 90, | I | X | J, , |
Fidan [49,50] | C, Kv, FG | NA | NA | NA | NA | NA | , , , |
Todoroki [51] | C | NA | NA | NA | NA | , , | |
Araya [52] | Kv | R, H | NA | I, C | NA | , , , | |
González [53] | C, FG | T | 0 | C | NA | , | |
Pertuz [54] | C, FG, Kv | T | NA | 0 | I | X | , , |
Podda [55] | C | NA | NA | 0, 90 | NA | NA | , |
Agarwal [56] | FG | H | NA | NA | NA | , , | |
Mei [57] | C, FG, Kv | T, H, R | NA | 0 | C | NA | , |
Naranjo [58] | C | T | NA | NA | NA | - | , |
Pyl [59] | C | NA | NA | 0 | I | NA | , |
Saeed [60] | C | S | 0 | I | X | , | |
Tessarin [61] | C, Kv, HSHT | S | 0 | I | X | , | |
Lawrence [62] | C, FG | S | 0 | 0 | I | X | , |
Santos [63] | C, FG | S | 0 | 0 | I | X | , |
Leon [36] | C | S | 0 | I | X | , | |
Heitkamp [64] | C, Kv | S | 0 | 0 | I | X | , |
Bendine [65] | C | S | 0 | 0 | I | X | , |
Ojha [66] | Kv | S | 0 | 0 | I | X | , |
Siddiqui [4] | C | S | 0 | 0 | I | X | , |
Zeeshan Ali [67] | C | R | 0 | 0 | I | X | , |
Xiang [68] | C | R | 0 | ±45 | C | X | , |
Lee [69] | C, FG | S | 0 | ±45 | C | X | , |
Moreno-Nuñez [70] | Kv | R | 0 | ±45 | C | X | , |
Gljuscic [71] | C | S | 0 | 0 | I | X | , |
Model | Mean | Std Dev | Min. | 1st Quartile | Median | 3rd Quartile | Max |
---|---|---|---|---|---|---|---|
BAY | 16.2405 | 3.2572 | 9.4879 | 14.0424 | 15.8779 | 18.3325 | 24.2133 |
RDG | 16.2256 | 3.4534 | 9.0721 | 13.8824 | 16.0427 | 18.6324 | 25.0582 |
LAS | 16.1670 | 3.2741 | 8.9366 | 14.1336 | 15.6067 | 18.0086 | 23.7556 |
DTR | 14.8774 | 4.3100 | 7.6346 | 12.0422 | 14.4884 | 16.7512 | 27.0928 |
SVR | 11.7524 | 5.0485 | 2.9113 | 7.6782 | 12.4260 | 15.4035 | 21.4587 |
RFR | 9.8297 | 3.6813 | 3.6341 | 6.8087 | 8.6466 | 12.3373 | 19.6891 |
KNN | 9.8020 | 4.1159 | 3.7364 | 6.6482 | 9.3383 | 11.9770 | 23.3197 |
CAT | 9.4446 | 3.3558 | 3.0735 | 7.2028 | 8.8084 | 11.7664 | 18.1977 |
Model | Mean | Std Dev | Min. | 1st Quartile | Median | 3rd Quartile | Max |
---|---|---|---|---|---|---|---|
BAY | 159.7859 | 24.6198 | 131.2626 | 143.6800 | 156.5881 | 166.6547 | 258.1069 |
RDG | 159.4300 | 25.2739 | 128.5327 | 143.7674 | 155.4155 | 167.4714 | 258.7639 |
LAS | 159.3340 | 25.2431 | 129.0285 | 143.4035 | 155.3209 | 166.2181 | 258.7624 |
DTR | 152.2683 | 45.3625 | 76.5504 | 115.0226 | 150.2737 | 170.3594 | 289.0174 |
SVR | 142.2886 | 43.2337 | 71.5865 | 115.0798 | 144.5133 | 164.2971 | 258.5963 |
KNN | 121.4163 | 42.1382 | 53.4138 | 91.3910 | 111.6907 | 141.3862 | 251.2954 |
CAT | 114.4038 | 32.6867 | 54.2600 | 91.3665 | 109.3586 | 139.4164 | 197.8857 |
RFR | 113.1730 | 36.8256 | 52.8864 | 84.8905 | 107.1129 | 136.4452 | 209.2337 |
Target | Model | Prediction Time (ms) | Model Size (kB) |
---|---|---|---|
E | BAY | 0.2464 ± 0.0655 | 1.8690 ± 0.0000 |
E | RDG | 0.2571 ± 0.1237 | 1.0540 ± 0.0000 |
E | LAS | 0.3108 ± 0.2160 | 1.1542 ± 0.0004 |
E | DTR | 0.2475 ± 0.0485 | 2.6079 ± 0.0808 |
E | SVR | 0.3114 ± 0.0791 | 9.8657 ± 0.3070 |
E | RFR | 2.5034 ± 0.8491 | 323.2075 ± 107.4422 |
E | KNN | 13.2900 ± 0.3737 | 12.1362 ± 0.0033 |
E | CAT | 1.0333 ± 0.3281 | 213.9868 ± 114.2556 |
BAY | 0.2542 ± 0.0797 | 1.8690 ± 0.0000 | |
RDG | 0.2395 ± 0.0714 | 1.0540 ± 0.0000 | |
LAS | 0.2494 ± 0.0535 | 1.1542 ± 0.0004 | |
DTR | 0.2458 ± 0.0525 | 2.5439 ± 0.1393 | |
SVR | 0.3184 ± 0.0753 | 10.5268 ± 0.0322 | |
KNN | 13.3308 ± 0.3256 | 12.1356 ± 0.0024 | |
CAT | 0.9430 ± 0.2397 | 198.7430 ± 102.1022 | |
RFR | 2.8011 ± 0.9439 | 349.6818 ± 88.7123 |
Fiber Type | Metric | SVR | DTR | RFR | CAT | KNN | RDG | LAS | BAY |
---|---|---|---|---|---|---|---|---|---|
r | 0.5835 | 0.6059 | 0.8062 | 0.8075 | 0.7972 | 0.3697 | 0.3473 | 0.3585 | |
CRTP | 0.3404 | 0.3672 | 0.6500 | 0.6521 | 0.6355 | 0.1367 | 0.1206 | 0.1285 | |
Student’s t-test | - | - | Ok | Ok | - | - | - | - | |
r | −0.0075 | 0.0218 | 0.1100 | 0.1091 | −0.0849 | 0.0250 | −0.0119 | −0.0370 | |
FGRTP | 0.0001 | 0.3672 | 0.6500 | 0.6521 | 0.6355 | 0.1367 | 0.1206 | 0.1285 | |
Student’s t-test | - | - | Ok | Ok | - | - | - | - | |
r | 0.5240 | 0.4342 | 0.5789 | 0.6695 | 0.7870 | 0.2731 | 0.2546 | 0.2715 | |
KvRTP | 0.2746 | 0.1885 | 0.3351 | 0.4482 | 0.6193 | 0.0746 | 0.0648 | 0.0737 | |
Student’s t-test | - | - | - | - | Ok | - | - | - |
Fiber Type | Metric | SVR | DTR | RFR | CAT | KNN | RDG | LAS | BAY |
---|---|---|---|---|---|---|---|---|---|
r | 0.6819 | −0.0686 | −0.1237 | −0.0471 | -0.1073 | −0.0528 | −0.0528 | −0.0408 | |
CRTP | 0.4649 | 0.0047 | 0.0153 | 0.0022 | 0.0115 | 0.0028 | 0.0028 | 0.0017 | |
Student’s t-test | - | Ok | Ok | Ok | - | - | - | - | |
r | 0.0846 | −0.0206 | 0.0897 | 0.0886 | −0.0013 | −0.0325 | -0.0212 | -0.0450 | |
FGRTP | 0.0072 | 0.0004 | 0.0080 | 0.0078 | 0.0000 | 0.0011 | 0.0004 | 0.0020 | |
Student’s t-test | - | - | - | - | - | - | - | - | |
r | 0.8297 | 0.7266 | 0.8532 | 0.8146 | 0.7031 | 0.8235 | 0.8235 | 0.8215 | |
KvRTP | 0.6884 | 0.5279 | 0.7279 | 0.6635 | 0.4944 | 0.6782 | 0.6782 | 0.6749 | |
Student’s t-test | - | - | - | - | - | - | - | - |
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Prada Parra, D.; Ferreira, G.R.B.; Díaz, J.G.; Gheorghe de Castro Ribeiro, M.; Braga, A.M.B. Supervised Machine Learning Models for Mechanical Properties Prediction in Additively Manufactured Composites. Appl. Sci. 2024, 14, 7009. https://doi.org/10.3390/app14167009
Prada Parra D, Ferreira GRB, Díaz JG, Gheorghe de Castro Ribeiro M, Braga AMB. Supervised Machine Learning Models for Mechanical Properties Prediction in Additively Manufactured Composites. Applied Sciences. 2024; 14(16):7009. https://doi.org/10.3390/app14167009
Chicago/Turabian StylePrada Parra, Dario, Guilherme Rezende Bessa Ferreira, Jorge G. Díaz, Mateus Gheorghe de Castro Ribeiro, and Arthur Martins Barbosa Braga. 2024. "Supervised Machine Learning Models for Mechanical Properties Prediction in Additively Manufactured Composites" Applied Sciences 14, no. 16: 7009. https://doi.org/10.3390/app14167009