
On the potential of using ensemble learning algorithm to approach the partitioning coefficient (k) value in Scheil–Gulliver equation
Ziyu Li1,2(), He Tan3, Anders E. W. Jarfors2(
), Jacob Steggo2, Lucia Lattanzi2, Per Jansson1
Materials Genome Engineering Advances ›› 2024, Vol. 2 ›› Issue (3) : e46.
On the potential of using ensemble learning algorithm to approach the partitioning coefficient (k) value in Scheil–Gulliver equation
The Scheil–Gulliver equation is essential for assessing solid fractions during alloy solidification in materials science. Despite the prevalent use of the Calculation of Phase Diagrams (CALPHAD) method, its computational intensity and time are limiting the simulation efficiency. Recently, Artificial Intelligence has emerged as a potent tool in materials science, offering robust and reliable predictive modeling capabilities. This study introduces an ensemble-based method that has the potential to enhance the prediction of the partitioning coefficient (k) in the Scheil equation by inputting various alloy compositions. The findings demonstrate that this approach can predict the temperature and solid fraction at the eutectic temperature with an accuracy exceeding 90%, while the accuracy for k prediction surpasses 70%. Additionally, a case study on a commercial alloy revealed that the model’s predictions are within a 5°C deviation from experimental results, and the predicted solid fraction at the eutectic temperature is within a 15% difference of the values obtained from the CALPHAD model.
AI application / partitioning coefficient / scheil–gulliver equation / solidification
1 | Scheil E. Bemerkungen zur schichtkristallbildung. Int J Mater Res. 1942;34(3):70-72. https://www.degruyter.com/document/doi/10.1515/ijmr-1942-340303/html |
2 | GH G. The quantitative effect of rapid cooling upon the constitution of binary alloys. J Inst Met. 1915;9:120-157. |
3 | Andersson JO, Helander T, Höglund L, Shi P, Sundman B. Thermocalc dictra, computational tools for materials science. Calphad. 2002;26(2):273-312. |
4 | Schaffnit P, Stallybrass C, Konrad J, Stein F, Weinberg M. A scheilgulliver model dedicated to the solidification of steel. Calphad Comput Coupling Phase Diagrams Thermochem. 2015;48:184-188. |
5 | Chen Q, Sundman B. Computation of Partial Equilibrium Solidification with Complete Interstitial and Negligible Substitutional Solute Back Diffusion;2002:551-559. |
6 | Farnin CJ, Rickman JM, DuPont JN. Solutions to the scheil equation with a variable partition coefficient. Metallurgical Mater Trans A Phys Metallurgy Mater Sci. 2021;52(12):5443-5448. |
7 | Xu LD, Xu EL, Li L. Industry 4.0: state of the art and future trends. Int J Prod Res. 2018;56(8):2941-2962. https://www.tandfonline.com/doi/abs/10.1080/00207543.2018.1444806 |
8 | Rai JK, Lajimi AM, Xirouchakis P. An intelligent system for predicting hpdc process variables in interactive environment. J Mater Process Technol. 2008;203(1-3):72-79. |
9 | Bramahhazela JH, Kumar TR, Kavitha S, Deepa D, Lalar S, Karunakaran P. Machine learning: supervised algorithms to determine the defect in high-precision foundry operation. J Nanomater. 2022;2022:1-9. |
10 | Le T, Wei Q, Wang J, De-Jian X, Yong-Peng Y. A neural network based defect prediction approach for virtual high pressure die casting you may also like a neural network based defect prediction approach for virtual high pressure die casting. J Phys Conf. 2021. |
11 | Guan B, Wang DH, Shu D, Zhu SQ, Ji XY, Sun BD. Data-driven casting defect prediction model for sand casting based on random forest classification algorithm. China Foundry. 2024;21(2):137-146. |
12 | Wang Z, Hu XG, Lu HX, Zhu Q. Quality control of semi-solid die casting by filling pressure based on machine learning method. Solid State Phenom. 2023;347:191-196. https://www.scientific.net/SSP.347.191 |
13 | Tarasov V, Tan H, Jarfors AE, Seifeddine S. Fuzzy logic-based modelling of yield strength of as-cast a356 alloy. Neural Comput Appl. 2020;32(10):5833-5844. |
14 | Ghosh I, Das SK, Chakraborty N. An artificial neural network model to characterize porosity defects during solidification of a356 aluminum alloy. Neural Comput Appl. 2014;25(3-4):653-662. https://linkspringer-com.proxy.library.ju.se/article/10.1007/s00521-013-1532-6 |
15 | Enes Parlak İ, Emel E. Deep learning-based detection of aluminum casting defects and their types. Eng Appl Artif Intell. 2023;118:105636. |
16 | Jiang L, Wang Y, Tang Z, Miao Y, Chen S. Casting defect detection in x-ray images using convolutional neural networks and attention-guided data augmentation. Measurement. 2021;170:108736. |
17 | Ekambaram D, Ponnusamy V. Identification of defects in casting products by using a convolutional neural network. IEIE Trans Smart Process Comput. 2022;11(3):149-155. |
18 | Ferguson M, Ak R, Lee YTT, Law KH. Detection and segmentation of manufacturing defects with convolutional neural networks and transfer learning. Smart Sustain Manuf Syst. 2018;2(1):137-164. |
19 | Puncreobutr C, Lohwongwatana B, Chongstitvattana P. Genetic programming approach to determining thermal properties of lead-free solder alloys. In: Proc. of National Computer Science and Engineering Conference; 2009. |
20 | Li Z, Tan H, Lattanzi L, Jarfors AE, Jansson P. On the possibility of replacing scheil-gulliver modeling with machine learning and neural network models. Solid State Phenom. 2023;347:157-163. |
21 | Conway PL, Klaver TP, Steggo J, Ghassemali E. High entropy alloys towards industrial applications: high-throughput screening and experimental investigation. Mater Sci Eng, A. 2022;830:142297. |
22 | Ghassemali E, Conway PL. High-throughput calphad: a powerful tool towards accelerated metallurgy. Frontiers in Materials. 2022;9:889771. |
23 | Thermo-calc software tcal aluminum-based alloys version 9. Accessed January 12, 2024. https://thermocalc.com/products/databases/aluminum-based-alloys/ |
24 | Dantzig JA, Rappaz M. Solidification. 2nd ed. Emepfel Express;2016:124-126. ISBN:2940222975. https://www.epflpress.org/produit/501/9782940222971/solidification |
25 | Jin X, Han J. K-means clustering. Encyclopedia of Machine Learning. 2011:563-564. https://link.springer.com/referenceworkentry/10.1007/978-0-387-30164-8_425 |
26 | Steinley D, Brusco MJ. Initializing k-means batch clustering: a critical evaluation of several techniques. J Classif. 2007;24(1):99-121. |
27 | Scikit. Elbow method —yellowbrick v1.5 documentation. Accessed February 2, 2023. https://www.scikit-yb.org/en/latest/api/cluster/elbow.html |
28 | Breiman L. Random forests. Mach Learn. 2001;45(1):5-32. https://link.springer.com/article/10.1023/A:1010933404324 |
29 | Prokhorenkova L, Gusev G, Vorobev A, Dorogush AV, Gulin A. Catboost: unbiased boosting with categorical features. Adv Neural Inf Process Syst. 2018:6638-6648. https://arxiv.org/abs/1706.09516v5 |
30 | Ke G, Meng Q, Finley T, et al. Lightgbm: a highly efficient gradient boosting decision tree. https://github.com/Microsoft/LightGBM |
31 | Saber M, Boulmaiz T, Guermoui M, et al. Examining lightgbm and catboost models for wadi flash flood susceptibility prediction. Geocarto Int. 2022;37(25):7462-7487. https://www.tandfonline.com/doi/abs/10.1080/10106049.2021.1974959 |
32 | Ibrahim AA, Ridwan RL, Muhammed MM, Abdulaziz RO, Saheed GA. Comparison of the catboost classifier with other machine learning methods. IJACSA Int J Adv Comput Sci Appl. 2020;11. www.ijacsa. thesai.org |
33 | Catboost V. Xgboost V. Lightgbm—Kaggle. Accessed April 4, 2023. https://www.kaggle.com/code/nholloway/catboost-v-xgboost-vlightgbm |
34 | Kingma DP, Ba JL. Adam: a method for stochastic optimization. In: 3rd International Conference on Learning Representations, ICLR 2015 - Conference Track Proceedings. Vol 12;2014. https://arxiv.org/abs/1412.6980v9 |
35 | Tofallis C. A better measure of relative prediction accuracy for model selection and model estimation. J Oper Res Soc. 2015;66(8):1352-1362. |
/
〈 |
|
〉 |