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A Data-Driven Approach for the Fast Prediction of Macrosegregation

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Abstract

Macrosegregation is of great importance to study due to its negative impact on the quality of casting. Although numerical models can predict macrosegregation during alloy solidification, solving the partial differential equations is rather time-consuming. Thus, numerical simulations are almost inoperable for the real-time online monitor-adjustment in industrial production, where the prediction is expected to be completed in an extremely short time. To overcome this challenge, a data-driven approach based on deep learning is proposed to predict the macrosegregation pattern under specific input parameter(s). Based on limited simulation results, this approach focuses on mining certain patterns within massive data, and thus enables fast predictions of macrosegregation, by incorporating a convolutional neural network autoencoder with a fully connected neural network. The best prediction accuracy is achieved after clarifying the effects of the error metric and the convolutional filter size. This method can predict the macrosegregation distribution in less than 0.1 second, and the accuracy is comparable to the conventional numerical simulations. The data-driven approach developed in this work shows instantaneity and adequate accuracy in the prediction of macrosegregation and could be a promising method for the application in the direct visualization and quality control of casting.

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Abbreviations

\({C}_{ls}^{p}\) :

Species exchange due to phase change (\(\mathrm{kg }{{\text{m}}}^{-3} \, {\text{s}}^{-1}\))

\({c}_{0}\) :

Initial concentration of the alloy (-)

\({c}_{l},{c}_{s}\) :

Species concentration (-)

\({c}_{{\text{mix}}}\) :

Mixture concentration (-)

\({c}_{p}^{l},{c}_{p}^{s}\) :

Specific heat (\(\mathrm{J }{{\text{kg}}}^{-1} {\text{K}}^{-1}\))

\({D}_{l}\) :

Diffusion coefficient (\({{\text{m}}}^{2} {{\text{s}}}^{-1}\))

\({\overrightarrow{F}}_{l}\) :

Buoyancy force (\({\text{N}}{{\text{m}}}^{-3}\))

\({f}_{l},{f}_{s}\) :

Volume fraction (-)

\(\overrightarrow{g}\) :

Gravity (\(\mathrm{m }{{\text{s}}}^{-2}\))

\(h\) :

Heat transfer coefficient (\(\mathrm{W }{{\text{m}}}^{-2} {\text{K}}^{-1}\))

\({h}_{l},{h}_{s}\) :

Enthalpy (\(\mathrm{J }{{\text{kg}}}^{-1}\))

\(\Delta {h}_{f}\) :

Latent heat (\(\mathrm{J }{{\text{kg}}}^{-1}\))

\(K\) :

Permeability (\({{\text{m}}}^{2}\))

\(k\) :

Solute partition coefficient (-)

\({k}_{l},{k}_{s}\) :

Thermal conductivity (\(\mathrm{W }{{\text{m}}}^{-1} {\text{K}}^{-1}\))

\({M}_{ls}\) :

Solidification mass transfer rate (\(\mathrm{kg }{{\text{s}}}^{-1} {\text{m}}^{-3}\))

\(m\) :

Liquidus slope of the binary phase diagram (\(\mathrm{K }{\left({\text{wt}}\,{\text{pct}}\right)}^{-1}\))

\(p\) :

Pressure (\({\text{Pa}}\))

\({Q}_{ls}^{d}\) :

Energy exchange by heat transfer (\(\mathrm{J }{{\text{m}}}^{-3} {\text{s}}^{-1}\))

\({Q}_{l}^{p},{Q}_{s}^{p}\) :

Energy source term due to phase change (\(\mathrm{J }{{\text{m}}}^{-3} {\text{s}}^{-1}\))

\(q,\widehat{q}\) :

True value and predict value

\(T,{T}_{l},{T}_{s}\) :

Temperature (\({\text{K}}\))

\({T}_{{\text{EXT}}}\) :

External temperature (\({\text{K}}\))

\(t\) :

Time (\({\text{s}}\))

\({\overrightarrow{U}}_{ls}^{d}\) :

Momentum change due to drag force (\(\mathrm{kg }{{\text{m}}}^{-2} {\text{s}}^{-2}\))

\({\overrightarrow{U}}_{ls}^{p}\) :

Momentum exchange due to phase change (\(\mathrm{kg }{{\text{m}}}^{-2} {\text{s}}^{-2}\))

\(\overrightarrow{u}\) :

Velocity vector of the melt (\(\mathrm{m }{{\text{s}}}^{-1}\))

\({\beta }_{c}\) :

Solutal expansion coefficient (\({\text{wt}}\,{\text{pct}}^{-1}\))

\({\beta }_{T}\) :

Thermal expansion coefficient (\({{\text{K}}}^{-1}\))

\({\lambda }_{1},{\lambda }_{2}\) :

Primary and second dendrite arm spacing of columnar (\({\text{m}}\))

\({\mu }_{l}\) :

Viscosity (\(\mathrm{kg }{{\text{m}}}^{-1} {\text{s}}^{-1}\))

\({\rho }_{l},{\rho }_{s}\) :

Density (\(\mathrm{kg }{{\text{m}}}^{-3}\))

\({\overline{\overline{\tau }}}_{l}\) :

Stress-strain tensors (\(\mathrm{kg }{{\text{m}}}^{-1} {\text{s}}^{-2}\))

\(\varepsilon \) :

Error metric (-)

\(l,s\) :

Indicate liquid and solid phases

\(mae\) :

Indicate absolute error

\(mse\) :

Indicate mean squared error

\(gdl\) :

Indicate a gradient difference loss

\(mse-gdl\) :

Indicate the combination of mean squared error and the gradient difference loss

References

  1. Iron Steel Institute: J. Iron Steel Inst., 1926, vol. 103, pp. 39–151.

    Google Scholar 

  2. E. Marburg: JOM, 1953, vol. 5, pp. 157–72.

    Article  Google Scholar 

  3. A. Olsson, R. West, and H. Fredriksson: Scand. J. Metall., 1986, vol. 15, pp. 104–12.

    CAS  Google Scholar 

  4. R.J. Mcdonald and J.D. Hunt: Trans. Metall. Soc. Aime, 1969, vol. 245, pp. 1993–97.

    CAS  Google Scholar 

  5. R.J. Mcdonald and J.D. Hunt: Metall. Trans., 1970, vol. 1, pp. 1787–88.

    Article  Google Scholar 

  6. T.F. Bower, H.D. Brody, and M.C. Flemings: Trans. Metall. Soc. Aime, 1966, vol. 236, pp. 624–34.

    CAS  Google Scholar 

  7. H.D. Brody and M.C. Flemings: Trans. Metall. Soc. Aime, 1966, vol. 236, pp. 615–24.

    CAS  Google Scholar 

  8. M.C. Flemings and G.E. Nereo: Trans. Metall. Soc. Aime, 1967, vol. 239, pp. 1449–61.

    CAS  Google Scholar 

  9. M.C. Flemings, R. Mehrabian, and G.E. Nereo: Trans. Metall. Soc. Aime, 1968, vol. 242, pp. 41–49.

    CAS  Google Scholar 

  10. A. Ludwig and M. Wu: Mater. Sci. Eng. A, 2005, vol. 413, pp. 109–14.

    Article  Google Scholar 

  11. M.H. Wu and A. Ludwig: Metall. Mater. Trans. A, 2006, vol. 37A, pp. 1613–31.

    Article  CAS  Google Scholar 

  12. H.H. Ge, F.L. Ren, J. Li, X.J. Han, M.X. Xia, and J.G. Li: Metall. Mater. Trans. A, 2017, vol. 48A, pp. 1139–50.

    Article  Google Scholar 

  13. M. Wu, A. Ludwig, and A. Kharicha: Appl. Math. Model., 2017, vol. 41, pp. 102–20.

    Article  Google Scholar 

  14. H.J. Yang, S.P. Vanka, and B.G. Thomas: Isij Int., 2019, vol. 59, pp. 956–72.

    Article  CAS  Google Scholar 

  15. X.W. Xu, J. Li, Z.H. Dong, L. Zeng, Z.M. Xu, and J.G. Li: J. Mater. Res. Technol., 2022, vol. 18, pp. 830–40.

    Article  CAS  Google Scholar 

  16. J. Li, M.H. Wu, A. Ludwig, and A. Kharicha: Int. J. Heat Mass. Trans., 2014, vol. 72, pp. 668–79.

    Article  CAS  Google Scholar 

  17. M. Xie and H. Shen: Front. Mater., 2020, vol. 7, p. 577290.

    Article  Google Scholar 

  18. H.H. Ge, J. Li, Q.T. Guo, F.L. Ren, M.X. Xia, J.H. Yao, and J.G. Li: Metall. Mater. Trans. B, 2021, vol. 52, pp. 2992–3003.

    Article  CAS  Google Scholar 

  19. R. Ramprasad, R. Batra, and G. Pilania: NPJ Comput. Mater., 2017, vol. 3, p. 54.

    Article  Google Scholar 

  20. K.T. Butler, D.W. Davies, H. Cartwright, O. Isayev, and A. Walsh: Nature, 2018, vol. 559, pp. 547–55.

    Article  CAS  PubMed  Google Scholar 

  21. A. Agrawal and A. Choudhary: MRS Commun., 2019, vol. 9, pp. 779–92.

    Article  CAS  Google Scholar 

  22. J. Schmidt, M.R.G. Marques, S. Botti, and M.A.L. Marques: NPJ Comput. Mater., 2019, vol. 5, p. 83.

    Article  Google Scholar 

  23. C. Yang, Y. Kim, S. Ryu, and G.X. Gu: Mater. Des., 2020, vol. 189, p. 108509.

    Article  Google Scholar 

  24. Z.B. Wei, J.X. Yu, Y. Lu, J.J. Han, C.P. Wang, and X.J. Liu: Mater. Des., 2021, vol. 198, p. 109287.

    Article  CAS  Google Scholar 

  25. Q. Xie, M. Suvarna, J.L. Li, X.Z. Zhu, J.J. Cai, and X.N. Wang: Mater. Des., 2021, vol. 197, p. 109201.

    Article  CAS  Google Scholar 

  26. Z.R. Pei and J.Q. Yin: Mater. Des., 2019, vol. 172, p. 107759.

    Article  CAS  Google Scholar 

  27. B. Meredig, A. Agrawal, S. Kirklin, J.E. Saal, J.W. Doak, A. Thompson, K. Zhang, A. Choudhary, and C. Wolverton: Phys. Rev. B, 2014, vol. 89, p. 094104.

    Article  Google Scholar 

  28. Y. Liu, T. Zhao, Ju. Wangwei, and S. Shi: J. Materiom., 2017, vol. 3, pp. 159–77.

    Article  Google Scholar 

  29. J.R. Li, R. Jin, and H.Z. Yu: Mater. Des., 2018, vol. 139, pp. 473–85.

    Article  Google Scholar 

  30. Q. Zhu, A. Samanta, B. Li, R.E. Rudd, and T. Frolov: Nat. Commun., 2018, vol. 9, p. 467.

    Article  PubMed  PubMed Central  Google Scholar 

  31. W.S. Yan, J. Melville, V. Yadav, K. Everett, L. Yang, M.S. Kesler, A.R. Krause, M.R. Tonks, and J.B. Harley: Mater. Des., 2022, vol. 222, p. 111032.

    Article  Google Scholar 

  32. K. Ryan, J. Lengyel, and M. Shatruk: J. Am. Chem. Soc., 2018, vol. 140, pp. 10158–68.

    Article  PubMed  Google Scholar 

  33. S. Feng, H. Zhou, and H. Dong: Mater. Des., 2019, vol. 162, pp. 300–10.

    Article  Google Scholar 

  34. G.W. Song, B.A. Tama, J. Park, J.Y. Hwang, J. Bang, S.J. Park, and S. Lee: Steel Res. Int., 2019, vol. 90, p. 1900321.

    Article  CAS  Google Scholar 

  35. S.Y. Lee, B.A. Tama, C. Choi, J.-Y. Hwang, J. Bang, and S. Lee: IEEE Access, 2020, vol. 8, pp. 21953–65.

    Article  Google Scholar 

  36. J. Li, M. Wu, J. Hao, A. Kharicha, and A. Ludwig: Comput. Mater. Sci., 2012, vol. 55, pp. 419–29.

    Article  CAS  Google Scholar 

  37. J. Li, M. Wu, J. Hao, and A. Ludwig: Comput. Mater. Sci., 2012, vol. 55, pp. 407–18.

    Article  CAS  Google Scholar 

  38. M. Bellet, H. Combeau, Y. Fautrelle, D. Gobin, M. Rady, E. Arquis, O. Budenkova, B. Dussoubs, Y. Duterrail, A. Kumar, C.A. Gandin, B. Goyeau, S. Mosbah, and M. Zaloznik: Int. J. Therm. Sci., 2009, vol. 48, pp. 2013–16.

    Article  CAS  Google Scholar 

  39. C. Beckermann, J.P. Gu, and W.J. Boettinger: Metall. Mater. Trans. A, 2000, vol. 31A, pp. 2545–57.

    Article  CAS  Google Scholar 

  40. Y.F. Cao, Y. Chen, D.Z. Li, H.W. Liu, and P.X. Fu: Metall. Mater. Trans. A, 2016, vol. 47A, pp. 2927–39.

    Article  Google Scholar 

  41. Q. Li, J. Shen, L. Qin, and Y. Xiong: Mater Charact, 2017, vol. 130, pp. 139–48.

    Article  CAS  Google Scholar 

  42. Q. Li, J. Shen, Y. Xiong, L. Qin, and X. Yue: Mater. Lett., 2018, vol. 228, pp. 281–84.

    Article  CAS  Google Scholar 

  43. C. Dong, C.C. Loy, K. He, and X. Tang: IEEE Trans. Pattern Anal. Mach. Intell., 2016, vol. 38, pp. 295–307.

    Article  PubMed  Google Scholar 

  44. H.C. Shin, H.R. Roth, M. Gao, L. Lu, Z. Xu, I. Nogues, J. Yao, D. Mollura, and R.M. Summers: IEEE Trans. Med. Imaging, 2016, vol. 35, pp. 1285–98.

    Article  PubMed  Google Scholar 

  45. V. Badrinarayanan, A. Kendall, and R. Cipolla: IEEE Trans. Pattern Anal. Mach. Intell., 2017, vol. 39, pp. 2481–95.

    Article  PubMed  Google Scholar 

  46. A. Esteva, B. Kuprel, R.A. Novoa, J. Ko, S.M. Swetter, H.M. Blau, and S. Thrun: Nature, 2017, vol. 542, pp. 115–18.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  47. A. Krizhevsky, I. Sutskever, and G. Hinton: Commun. ACM, 2017, vol. 60, pp. 84–90.

    Article  Google Scholar 

  48. C. Farabet, C. Couprie, L. Najman, and Y. Lecun: IEEE Trans. Pattern Anal. Mach. Intell., 2013, vol. 35, pp. 1915–29.

    Article  PubMed  Google Scholar 

  49. G. Hinton, Li. Deng, Yu. Dong, G. Dahl, A.-R. Mohamed, N. Jaitly, A. Senior, V. Vanhoucke, P. Nguyen, T. Sainath, and B. Kingsbury: IEEE Signal Process. Mag., 2012, vol. 29, pp. 82–97.

    Article  Google Scholar 

  50. A.B. Nassif, I. Shahin, I. Attili, M. Azzeh, and K. Shaalan: IEEE Access, 2019, vol. 7, pp. 19143–65.

    Article  Google Scholar 

  51. M.T. Anvarjon and S. Kwon: Sensors, 2020, vol. 20, p. 5212.

    Article  PubMed  PubMed Central  Google Scholar 

  52. B.J. Abbaschian, D. Sierra-Sosa, and A. Elmaghraby: Sensors-Basel, 2021, vol. 21, p. 1249.

    Article  PubMed  PubMed Central  Google Scholar 

  53. K. Hasegawa, K. Fukami, T. Murata, and K. Fukagata: Theoret. Comput. Fluid Dyn., 2020, vol. 34, pp. 367–83.

    Article  Google Scholar 

  54. D. Chicco, M.J. Warrens, and G. Jurman: Peer J. Comput. Sci., 2021, vol. 7, p. 623.

    Article  Google Scholar 

  55. S. Lee and D. You: J. Fluid Mech., 2019, vol. 879, pp. 217–54.

    Article  Google Scholar 

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Acknowledgments

This work was sponsored by National Natural Science Foundation of China (No. 52074182 and No. 91860121), Natural Science Foundation of Shanghai (No. 22ZR1430700) and the Guided Local Science and Technology Development Projects from the Central Government (No. 2021FRD05006).

Competing Interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Advanced High-temperature Materials and Precision Forming, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China

    Xiaowei Xu, Neng Ren, Ziqing Lu, Jun Li, Mingxu Xia & Jianguo Li

  2. Department of Materials, The University of Manchester, Manchester, M13 9PL, United Kingdom

    Wajira Mirihanage

  3. School of Computer Science and Engineering, Macau University of Science and Technology, Taipa, Macau, 999078, P.R. China

    Eric Tsang

  4. Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, 999077, P.R. China

    Alex Po Leung

  5. School of Engineering, University of Leicester, Leicester, LE1 7RH, United Kingdom

    Hongbiao Dong

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  1. Xiaowei Xu
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Xu, X., Ren, N., Lu, Z. et al. A Data-Driven Approach for the Fast Prediction of Macrosegregation. Metall Mater Trans A (2024). https://doi.org/10.1007/s11661-024-07381-0

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