Optimizing the Powder Metallurgy Parameters to Enhance the Mechanical Properties of Al-4Cu/xAl2O3 Composites Using Machine Learning and Response Surface Approaches
Abstract
:1. Introduction
2. Methodology
2.1. Experimental Design
2.2. Experimental Procedure
2.3. Machine Learning (ML)
2.3.1. Linear Regression
2.3.2. Regression Trees
2.3.3. Random Forest Regression
2.3.4. Gaussian Process Regression
2.3.5. Artificial Neural Networks
2.4. Statistical Analysis and Regression Model
3. Results and Discussion
3.1. Relative Density (RD)
3.1.1. Machine Learning Prediction Models of RD
3.1.2. Regression Models and 3D Plots of RD
3.1.3. Optimization of RD
3.2. Hardness Distribution
3.2.1. Machine Learning Prediction Models of Hardness Distribution
3.2.2. Regression Models and 3D Plots of Hardness Distribution
3.2.3. Optimization of Hardness
3.3. Compression Properties
3.3.1. Machine Learning Prediction Models of Compression Distribution
3.3.2. Regression Models and 3D Plots of Compression Distribution
3.3.3. Optimization Results
4. Conclusions
- The maximum RD obtained experimentally reached a value of 92.55% when the pressure was set at 700 MPa and the H/D was 1.25 for the Al-4Cu discs with no Al2O3;
- The RSM optimization findings confirm the maximum value of 92.791% and led the optimal AMC conditions to be a pressure = 893.89 MPa, H/D = 0.854, and Al2O3% = 0.031%;
- The outcomes of the RSM optimization performed on the hardness gave a maximum value of 121.199 Hv and led the optimal AMC conditions to be a pressure = 875.087 MPa, H/D = 0.87, and Al2O3% = 9.845%;
- The best yield strength obtained experimentally had a value of 312 MPa at 10% Al2O3, 700 MPa, and a 1.25 H/D, whereas the best compression strength obtained experimentally had a value of 384 MPa at 10% Al2O3, 700 MPa, and a 1.25 H/D. Moreover, the maximum fracture strain obtained experimentally had a value of 13 at 700 MPa, a 1.25 H/D, and 0% Al2O3;
- The outcomes of the RSM optimization performed on the yield strength gave a maximum value of 341.372 MPa and led the optimal AMC conditions to be a pressure = 884.2 MPa, H/D = 0.762, and Al2O3% = 8.57%;
- The RSM optimization findings show a maximum value of the compressive strength of 410.93 MPa, which led the optimal AMC conditions to be a pressure = 506.142 MPa, H/D = 0.873, and Al2O3% = 9.71%;
- The outcomes of the RSM optimization performed on the fracture strain gave a maximum of 13.54 and led the optimal AMC conditions to be a pressure = 501.692 MPa, H/D = 0.757, and Al2O3% = 0.017%.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Exp. No. | Hardness Hv | Yield Stress σy | Compressive Strength σuc | Fracture Strain εf | RD (%) |
---|---|---|---|---|---|
1 | 69.5 | 225 | 315 | 11.7 | 90.15 |
2 | 64 | 218 | 287 | 12 | 89.65 |
3 | 68 | 224 | 298 | 11.4 | 90.30 |
4 | 72.5 | 245 | 319 | 11.1 | 91.05 |
5 | 74 | 256 | 314 | 10.5 | 90.44 |
6 | 77.5 | 261 | 330 | 10.9 | 90.67 |
7 | 88.5 | 274 | 362 | 9.1 | 88.25 |
8 | 84 | 261 | 354 | 9.5 | 87.40 |
9 | 91 | 280 | 368.5 | 7.9 | 88.75 |
10 | 99 | 294 | 374 | 7.1 | 89.55 |
11 | 79 | 270 | 328 | 11 | 90.85 |
12 | 77 | 263 | 321 | 10.5 | 90.70 |
13 | 69 | 255 | 311 | 11.3 | 88.05 |
14 | 82 | 279 | 339 | 8.9 | 91.20 |
15 | 86 | 274 | 334.5 | 10.7 | 91.08 |
16 | 66 | 253 | 315 | 11.4 | 89.89 |
17 | 105.5 | 301 | 377 | 6.9 | 85.90 |
18 | 59 | 195 | 255 | 12 | 92.00 |
19 | 69 | 251 | 314 | 11.1 | 88.33 |
20 | 80.5 | 287 | 328.5 | 9.2 | 90.92 |
21 | 84 | 269 | 331 | 10.7 | 91.32 |
22 | 68 | 256 | 318 | 11.5 | 90.05 |
23 | 108 | 312 | 384 | 6.6 | 86.85 |
24 | 57.5 | 199 | 261 | 13 | 92.55 |
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Exp. No. | Al2O3 (wt. %) | H/D | Pressure (MPa) | Remark |
---|---|---|---|---|
1 | 2.5 | 1.5 | 800 | Front-facing corners |
2 | 2.5 | 1.5 | 600 | |
3 | 2.5 | 1.0 | 600 | |
4 | 2.5 | 1.0 | 800 | |
5 | 5.0 | 1.25 | 700 | Repeated center |
6 | 5.0 | 1.25 | 700 | |
7 | 7.5 | 1.5 | 800 | Back-facing corners |
8 | 7.5 | 1.5 | 600 | |
9 | 7.5 | 1.0 | 600 | |
10 | 7.5 | 1.0 | 800 | |
11 | 5.0 | 1.25 | 700 | Repeated center |
12 | 5.0 | 1.25 | 700 | |
13 | 5.0 | 2.0 | 700 | Augmented experiments |
14 | 5.0 | 0.75 | 700 | |
15 | 5.0 | 1.25 | 900 | |
16 | 5.0 | 1.25 | 500 | |
17 | 10.0 | 1.25 | 700 | |
18 | 0.0 | 1.25 | 700 | |
19 | 5.0 | 2.0 | 700 | Repeated augmented experiments |
20 | 5.0 | 0.75 | 700 | |
21 | 5.0 | 1.25 | 900 | |
22 | 5.0 | 1.25 | 500 | |
23 | 10.0 | 1.25 | 700 | |
24 | 0.0 | 1.25 | 700 |
Response | F-Value | Model Significant (p < 0.05) | Adeq Precision (Ratio > 4) | R2 | Adjusted R2 | Predicted R2 |
---|---|---|---|---|---|---|
Relative density (RD%) | 78.25 | <0.0001 | 28.8251 | 0.9031 | 0.8915 | 0.8752 |
Hardness (Hv) | 276.02 | <0.0001 | 56.9531 | 0.9849 | 0.9814 | 0.9755 |
Yield strength (σy) | 184.74 | <0.0001 | 47.7030 | 0.9700 | 0.9647 | 0.9559 |
Compression strength (σc) | 122.52 | <0.0001 | 39.3438 | 0.9554 | 0.9476 | 0.9352 |
Fracture strain (εf) | 190.89 | <0.0001 | 44.7085 | 0.9784 | 0.9732 | 0.9639 |
ML | Training Set | Testing Set | ||
---|---|---|---|---|
RMSE | R2 | RMSE | R2 | |
Linear regression | 0.68 | 0.82 | 0.55 | 0.89 |
Regression trees | 0.28 | 0.97 | 0.74 | 0.79 |
Random forest regression | 0.5 | 0.91 | 0.73 | 0.81 |
Gaussian process regression | 0.27 | 0.97 | 0.58 | 0.87 |
Artificial neural networks | 0.19 | 0.98 | 0.24 | 1 |
Input | RD% | ||||
---|---|---|---|---|---|
Pressure (MPa) | H/D | Al2O3 (wt. %) | Exp. | Predict | Error |
800 | 1.5 | 2.5 | 90.15 | 90.14973858 | 0.000261419 |
600 | 1.5 | 2.5 | 89.65 | 89.65010871 | −1.09 × 10−4 |
600 | 1 | 2.5 | 90.3 | 90.30285476 | −2.85 × 10−3 |
800 | 1 | 2.5 | 91.05 | 91.05233493 | −2.33 × 10−3 |
700 | 1.25 | 5 | 90.44 | 90.65393441 | −0.213934408 |
700 | 1.25 | 5 | 90.67 | 90.65393441 | 0.016065592 |
800 | 1.5 | 7.5 | 88.25 | 88.24640343 | 3.60 × 10−3 |
600 | 1.5 | 7.5 | 87.4 | 87.40036937 | −0.000369373 |
600 | 1 | 7.5 | 88.75 | 88.75127021 | −1.27 × 10−3 |
800 | 1 | 7.5 | 89.55 | 89.54729311 | 2.71 × 10−3 |
700 | 1.25 | 5 | 90.85 | 90.65393441 | 1.96 × 10−1 |
700 | 1.25 | 5 | 90.7 | 90.65393441 | 4.61 × 10−2 |
700 | 2 | 5 | 88.05 | 88.18914371 | −1.39 × 10−1 |
700 | 0.75 | 5 | 91.2 | 90.9179379 | 2.82 × 10−1 |
900 | 1.25 | 5 | 91.08 | 91.19658434 | −0.116584341 |
500 | 1.25 | 5 | 89.89 | 89.85855976 | 0.031440242 |
700 | 1.25 | 10 | 85.9 | 86.37184757 | −4.72 × 10−1 |
700 | 1.25 | 0 | 92 | 92.27624419 | −0.276244187 |
700 | 2 | 5 | 88.33 | 88.18914371 | 1.41 × 10−1 |
700 | 0.75 | 5 | 90.92 | 90.9179379 | 2.06 × 10−3 |
900 | 1.25 | 5 | 91.32 | 91.19658434 | 1.23 × 10−1 |
500 | 1.25 | 5 | 90.05 | 89.85855976 | 1.91 × 10−1 |
700 | 1.25 | 10 | 86.85 | 86.37184757 | 4.78 × 10−1 |
700 | 1.25 | 0 | 92.55 | 92.27624419 | 0.273755813 |
ML | Training Set | Testing Set | ||
---|---|---|---|---|
RMSE | R2 | RMSE | R2 | |
Linear regression | 2.81 | 0.95 | 2.21 | 0.93 |
Regression trees | 1.12 | 0.99 | 2 | 0.94 |
Random forest regression | 2.04 | 0.97 | 2.99 | 0.87 |
Gaussian process regression | 1.13 | 0.99 | 2.15 | 0.95 |
Artificial neural networks | 0.818 | 0.996 | 2.19 | 1 |
Input | Hardness (HV) | ||||
---|---|---|---|---|---|
Pressure (MPa) | H/D | Al2O3 (wt. %) | Exp. | Predict | Error |
800 | 1.5 | 2.5 | 69.5 | 69.5 | 5.97 × 10−13 |
600 | 1.5 | 2.5 | 64 | 64 | −1.07 × 10−12 |
600 | 1 | 2.5 | 68 | 68 | 3.45 × 10−12 |
800 | 1 | 2.5 | 72.5 | 72.5 | −2.67 × 10−12 |
700 | 1.25 | 5 | 74 | 76.166667 | −2.166667 |
700 | 1.25 | 5 | 77.5 | 76.166667 | 1.3333333 |
800 | 1.5 | 7.5 | 88.5 | 88.5 | 7.82 × 10−13 |
600 | 1.5 | 7.5 | 84 | 82.725113 | 1.2748867 |
600 | 1 | 7.5 | 91 | 91 | 1.42 × 10−13 |
800 | 1 | 7.5 | 99 | 99 | −4.55 × 10−13 |
700 | 1.25 | 5 | 79 | 76.166667 | 2.8333333 |
700 | 1.25 | 5 | 77 | 76.166667 | 0.8333333 |
700 | 2 | 5 | 69 | 69 | 7.11 × 10−14 |
700 | 0.75 | 5 | 82 | 81.25 | 0.75 |
900 | 1.25 | 5 | 86 | 86 | 7.39 × 10−13 |
500 | 1.25 | 5 | 66 | 67 | −1 |
700 | 1.25 | 10 | 105.5 | 106.75 | −1.25 |
700 | 1.25 | 0 | 59 | 59 | 9.95 × 10−14 |
700 | 2 | 5 | 69 | 69 | 7.11 × 10−14 |
700 | 0.75 | 5 | 80.5 | 81.25 | −0.75 |
900 | 1.25 | 5 | 84 | 86 | −2 |
500 | 1.25 | 5 | 68 | 67 | 1 |
700 | 1.25 | 10 | 108 | 106.75 | 1.25 |
700 | 1.25 | 0 | 57.5 | 59 | −1.5 |
Response | ML | Training Set | Testing Set | ||
---|---|---|---|---|---|
RMSE | R2 | RMSE | R2 | ||
σy (MPa) | Linear regression | 8.27 | 0.918 | 5.14 | 0.91 |
Regression trees | 3.87 | 0.98 | 6.8 | 0.83 | |
Random forest regression | 5.69 | 0.96 | 9.01 | 0.71 | |
Gaussian process regression | 5.63 | 0.96 | 14.44 | 0.80 | |
Artificial neural networks | 3.17 | 0.98 | 5.19 | 0.99 | |
σuc (MPa) | Linear regression | 7.51 | 0.95 | 3.04 | 0.99 |
Regression trees | 4.21 | 0.98 | 7.72 | 0.96 | |
Random forest regression | 5.97 | 0.97 | 12.11 | 0.91 | |
Gaussian process regression | 3.52 | 0.98 | 4.36 | 0.98 | |
Artificial neural networks | 3.58 | 0.98 | 4.55 | 0.98 | |
εf (%) | Linear regression | 0.59 | 0.87 | 0.68 | 0.91 |
Regression trees | 0.24 | 0.97 | 0.51 | 0.86 | |
Random forest regression | 0.26 | 0.97 | 0.21 | 0.97 | |
Gaussian process regression | 0.198 | 0.98 | 0.264 | 0.97 | |
Artificial neural networks | 0.2 | 0.98 | 0.2 | 1 |
Input | Compressive Strength | Yield Strength | Fracture Strain | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Pressure (MPa) | H/D | Al2O3 (wt. %) | Exp. | Predict | Error | Exp. | Predict | Error | Exp. | Predict | Error |
800 | 1.5 | 2.5 | 225 | 225.000061 | −6.17 × 10−5 | 315 | 315.14025 | −1.40 × 10−1 | 11.7 | 11.68187 | 1.81 × 10−2 |
600 | 1.5 | 2.5 | 218 | 218.000009 | −9.59 × 10−6 | 287 | 286.98075 | 1.92 × 10−2 | 12 | 11.93985 | 6.01 × 10−2 |
600 | 1 | 2.5 | 224 | 224.000018 | −1.82 × 10−5 | 298 | 294.62377 | 3.38 × 100 | 11.4 | 11.40852 | −8.52 × 10−3 |
800 | 1 | 2.5 | 245 | 244.999986 | 1.34 × 10−5 | 319 | 318.84562 | 1.54 × 10−1 | 11.1 | 11.09339 | 6.61 × 10−3 |
700 | 1.25 | 5 | 256 | 262.499990 | −6.499990521 | 314 | 323.39536 | −9.395361 | 10.5 | 10.67984 | −0.17984 |
700 | 1.25 | 5 | 261 | 262.499990 | −1.499990521 | 330 | 323.39536 | 6.6046387 | 10.9 | 10.67984 | 0.2201605 |
800 | 1.5 | 7.5 | 274 | 273.999999 | 9.57 × 10−7 | 362 | 362.70417 | −7.04 × 10−1 | 9.1 | 8.918651 | 1.81 × 10−1 |
600 | 1.5 | 7.5 | 261 | 261.000004 | −4.03203 × 10−6 | 354 | 354.13551 | −0.135514 | 9.5 | 9.444270 | 0.0557299 |
600 | 1 | 7.5 | 280 | 279.999997 | 2.54 × 10−6 | 368.5 | 367.07923 | 1.42 × 100 | 7.9 | 7.887332 | 1.27 × 10−2 |
800 | 1 | 7.5 | 294 | 294.000008 | −8.63 × 10−6 | 374 | 374.60069 | −6.01 × 10−1 | 7.1 | 7.047457 | 5.25 × 10−2 |
700 | 1.25 | 5 | 270 | 262.499990 | 7.50 × 100 | 328 | 323.39536 | 4.60 × 100 | 11 | 10.67984 | 3.20 × 10−1 |
700 | 1.25 | 5 | 263 | 262.499990 | 5.00 × 10−1 | 321 | 323.39536 | −2.40 × 100 | 10.5 | 10.67984 | −1.80 × 10−1 |
700 | 2 | 5 | 255 | 253.000037 | 2.00 × 100 | 311 | 311.69067 | −6.91 × 10−1 | 11.3 | 11.10294 | 1.97 × 10−1 |
700 | 0.75 | 5 | 279 | 282.999974 | −3.99997446 | 339 | 334.10906 | 4.8909386 | 8.9 | 9.073309 | −0.173309 |
900 | 1.25 | 5 | 274 | 268.999986 | 5.000013937 | 334.5 | 332.86319 | 1.6368112 | 10.7 | 10.74755 | −0.047559 |
500 | 1.25 | 5 | 253 | 255.999991 | −3.00 × 100 | 315 | 315.79756 | −7.98 × 10−1 | 11.4 | 11.45020 | −5.02 × 10−2 |
700 | 1.25 | 10 | 301 | 306.499993 | −5.49999346 | 377 | 380.21001 | −3.210014 | 6.9 | 6.722916 | 1.77 × 10−1 |
700 | 1.25 | 0 | 195 | 192.296478 | 2.70 × 100 | 255 | 260.97904 | −5.98 × 100 | 12 | 12.47473 | −4.75 × 10−1 |
700 | 2 | 5 | 251 | 253.000037 | −2.00 × 100 | 314 | 311.69067 | 2.31 × 100 | 11.1 | 11.10294 | −2.94 × 10−3 |
700 | 0.75 | 5 | 287 | 282.999974 | 4.00 × 100 | 328.5 | 334.10906 | −5.61 × 100 | 9.2 | 9.073309 | 1.27 × 10−1 |
900 | 1.25 | 5 | 269 | 268.999986 | 1.39 × 10−5 | 331 | 332.86319 | −1.86 × 100 | 10.7 | 10.74755 | −0.047559 |
500 | 1.25 | 5 | 256 | 255.999991 | 8.36 × 10−6 | 318 | 315.79756 | 2.20 × 100 | 11.5 | 11.45020 | 0.0497917 |
700 | 1.25 | 10 | 312 | 306.499993 | 5.50000654 | 384 | 380.21001 | 3.7899859 | 6.6 | 6.722916 | −1.23 × 10−1 |
700 | 1.25 | 0 | 199 | 192.296478 | 6.703521764 | 261 | 260.97904 | 0.020957 | 13 | 12.47473 | 0.5252705 |
Response | DOE | RSM | GA | DOE-GA | |
---|---|---|---|---|---|
RD% | Value | 92.872 | 92.791 | 92.872 | 92.872 |
Cond. | P = 900 MPa, H/D = 0.75, Al2O3 = 0% | P = 893.89 MPa, H/D = 0.854, Al2O3 = 0.031% | P = 900 MPa, H/D = 0.75, Al2O3 = 0% | P = 900 MPa, H/D = 0.75, Al2O3 = 0% | |
Hv | Value | 126.27 | 121.199 | 126.15 | 126.15 |
Cond. | P = 900 MPa, H/D= 0.75, Al2O3 = 10% | P = 875.087 MPa, H/D = 0.870, Al2O3 = 9.845% | P = 900 MPa, H/D = 0.75, Al2O3 = 10% | P = 900 MPa, H/D = 0.75, Al2O3 = 10% | |
σy (MPa) | Value | 312 | 341.372 | 350.399 | 350.398 |
Cond. | P = 700 MPa, H/D = 1.25, Al2O3 = 10% | P = 884.243 MPa, H/D = 0.762, Al2O3 = 8.57% | P = 900 MPa, H/D = 0.75, Al2O3 = 10% | P = 900 MPa, H/D = 0.75, Al2O3 = 10% | |
σuc (MPa) | Value | 384 | 410.93 | 421.906 | 421.906 |
Cond. | P = 700 MPa, H/D = 1.25, Al2O3 = 10% | P = 506.142 MPa, H/D = 0.873, Al2O3 = 9.71% | P = 500 MPa, H/D = 0.75, Al2O3 = 10% | P = 500 MPa, H/D = 0.75, Al2O3 = 10% | |
εf | Value | 13 | 13.54 | 13.0851 | 13.464 |
Cond. | P = 700 MPa, H/D = 1.25, Al2O3 = 0% | P = 501.692 MPa, H/D = 0.757, Al2O3 = 0.017% | P = 501.12 MPa, H/D = 0.758, Al2O3 = 0% | P = 510 MPa, H/D = 0.75, Al2O3 = 0% |
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Share and Cite
Elkatatny, S.; Alsharekh, M.F.; Alateyah, A.I.; El-Sanabary, S.; Nassef, A.; Kamel, M.; Alawad, M.O.; BaQais, A.; El-Garaihy, W.H.; Kouta, H. Optimizing the Powder Metallurgy Parameters to Enhance the Mechanical Properties of Al-4Cu/xAl2O3 Composites Using Machine Learning and Response Surface Approaches. Appl. Sci. 2023, 13, 7483. https://doi.org/10.3390/app13137483
Elkatatny S, Alsharekh MF, Alateyah AI, El-Sanabary S, Nassef A, Kamel M, Alawad MO, BaQais A, El-Garaihy WH, Kouta H. Optimizing the Powder Metallurgy Parameters to Enhance the Mechanical Properties of Al-4Cu/xAl2O3 Composites Using Machine Learning and Response Surface Approaches. Applied Sciences. 2023; 13(13):7483. https://doi.org/10.3390/app13137483
Chicago/Turabian StyleElkatatny, Sally, Mohammed F. Alsharekh, Abdulrahman I. Alateyah, Samar El-Sanabary, Ahmed Nassef, Mokhtar Kamel, Majed O. Alawad, Amal BaQais, Waleed H. El-Garaihy, and Hanan Kouta. 2023. "Optimizing the Powder Metallurgy Parameters to Enhance the Mechanical Properties of Al-4Cu/xAl2O3 Composites Using Machine Learning and Response Surface Approaches" Applied Sciences 13, no. 13: 7483. https://doi.org/10.3390/app13137483