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Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin

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Abstract

In the realm of forging processes, the challenge of real-time process control amid inherent variabilities is prominent. To tackle this challenge, this article introduces a Proper Orthogonal Decomposition (POD)-based surrogate model for a one-blow cold upsetting process in copper billets. This model effectively addresses the issue by accurately forecasting energy setpoints, billet geometry changes, and deformation fields following a single forging operation. It utilizes Bézier curves to parametrically capture billet geometries and employs POD for concise deformation field representation. With a substantial database of 36,000 entries from 60 predictive numerical simulations using FORGE® software, the surrogate model is trained using a multilayer perceptron artificial neural network (MLP ANN) featuring 300 neurons across 3 hidden layers using the Keras API within the TensorFlow framework in Python. Model validation against experimental and numerical data underscores its precision in predicting energy setpoints, geometry changes, and deformation fields. This advancement holds the potential for enhancing real-time process control and optimization, facilitating the development of a digital twin for the process.

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References

  1. Ji H, Wu W, Song C, Li J, Pei W, Huang X (2022) Numerical simulation, experiment, and optimization of a multidirectional die forging process for oil cutoff valves. Mater Today Commun 33:104838. https://doi.org/10.1016/j.mtcomm.2022.104838

    Article  Google Scholar 

  2. Luo S, Yao J, Li J, Du H, Liu H, Yu F (2020) Influence of forging velocity on temperature and phases of forged Ti-6Al-4V turbine blade. J Mater Res Technol 9(6):12043–12051. https://doi.org/10.1016/j.jmrt.2020.08.106

    Article  Google Scholar 

  3. Allam Z, Becker E, Baudouin C, Bigot R, Krumpipe P (2014) Forging process control: influence of key parameters variation on product specifications deviations. Procedia Eng 81:2524–2529. https://doi.org/10.1016/j.proeng.2014.10.361

    Article  Google Scholar 

  4. Behrens B-A et al (2020) A combined numerical and experimental investigation on deterministic deviations in hot forging processes. Procedia Manuf 47:295–300. https://doi.org/10.1016/j.promfg.2020.04.231

    Article  Google Scholar 

  5. Chabeauti H, Ritou M, Lavisse B, Germain G, Charbonnier V (2022) Numerical investigation and modeling of residual stress field variability impacting the machining deformations of forged part. Procedia CIRP 108:687–692. https://doi.org/10.1016/j.procir.2022.04.079

    Article  Google Scholar 

  6. Zhang SH, Zhao DW, Gao CR, Wang GD (2012) Analysis of asymmetrical sheet rolling by slab method. Int J Mech Sci 65(1):168–176. https://doi.org/10.1016/j.ijmecsci.2012.09.015

    Article  Google Scholar 

  7. Yin J, Hu R, Shu X (2021) Closed-die forging process of copper alloy valve body: finite element simulation and experiments. J Mater Res Technol 10:1339–1347. https://doi.org/10.1016/j.jmrt.2020.12.087

    Article  Google Scholar 

  8. Alizadeh R, Allen JK, Mistree F (2020) Managing computational complexity using surrogate models: a critical review. Res Eng Des 31(3):275–298. https://doi.org/10.1007/s00163-020-00336-7

    Article  Google Scholar 

  9. Jia L, Alizadeh R, Hao J, Wang G, Allen JK, Mistree F (2020) A rule-based method for automated surrogate model selection. Adv Eng Inform 45:101123. https://doi.org/10.1016/j.aei.2020.101123

    Article  Google Scholar 

  10. Scandola L et al (2021) Development of a numerical compensation framework for geometrical deviations in bulk metal forming exploiting a surrogate model and computed compatible stresses. Int J Mater Form 14(5):901–916. https://doi.org/10.1007/s12289-020-01603-7

    Article  Google Scholar 

  11. Maier D, Hartmann C, Till M, Büdenbender C, Behrens BA, Volk W (2019) Data-driven compensation for bulk formed parts based on material point tracking. Key Eng Mater 794:277–284. https://doi.org/10.4028/www.scientific.net/KEM.794.277

    Article  Google Scholar 

  12. Slimani K, Zaaf M, Balan T (2023) Accurate surrogate models for the flat rolling process. Int J Mater Form 16. https://doi.org/10.1007/s12289-023-01744-5

  13. Wang Q et al (2022) Application of the gradient boosting decision tree in the online prediction of rolling force in hot rolling. Int J Adv Manuf Technol 125(1–2):387–397. https://doi.org/10.1007/s00170-022-10716-z

    Article  Google Scholar 

  14. Wang Z, Liu Y, Wang T, Gong D, Zhang D (2023) Prediction model of hot strip crown based on industrial data and hybrid the PCA-SDWPSO-ELM approach. Soft Comput 27:1–17. https://doi.org/10.1007/s00500-023-07895-6

    Article  Google Scholar 

  15. Song L, Xu D, Wang X, Yang Q, Ji Y (2022) Application of machine learning to predict and diagnose for hot-rolled strip crown. Int J Adv Manuf Technol 120(1–2):881–890. https://doi.org/10.1007/s00170-022-08825-w

    Article  Google Scholar 

  16. Wang Z, Huang Y, Liu Y, Wang T (2023) Prediction model of strip crown in hot rolling process based on machine learning and industrial data. Metals 13:900. https://doi.org/10.3390/met13050900

    Article  Google Scholar 

  17. Wang L, He S, Zhao Z, Zhang X (2023) Prediction of hot-rolled strip crown based on Boruta and extremely randomized trees algorithms. J Iron Steel Res Int 30. https://doi.org/10.1007/s42243-023-00964-y

  18. Di Schino A, Department of Engineering, University of Perugia, 06125 Perugia, Italy (2021) Open die forging process simulation: a simplified industrial approach based on artificial neural network. AIMSMATES 8(5):685–697. https://doi.org/10.3934/matersci.2021041

    Article  Google Scholar 

  19. Uribe D, Durand C, Baudouin C, Krumpipe P, Bigot R (2024) Towards the real-time piloting of a forging process: development of a surrogate model for a multiple blow operation. In: Proceedings of the 14th International Conference on the Technology of Plasticity - Current Trends in the Technology of Plasticity, Cham, pp 377–388. https://doi.org/10.1007/978-3-031-41341-4_39

  20. Petkar P, Gaitonde V, Karnik S, Kulkarni V, Raju GT, Davim J (2020) Analysis of forming behavior in cold forging of AISI 1010 steel using artificial neural network. Metals - Open Access Metall J 10:1–24. https://doi.org/10.3390/met10111431

    Article  Google Scholar 

  21. Petkar P, Gaitonde V, Kulkarni V, Karnik S, Davim J (2023) A comparative study in forming behavior of different grades of steel in cold forging backward extrusion by integrating Artificial Neural Network (ANN) with Differential Evolution (DE) algorithm. Appl Sci 13:1276. https://doi.org/10.3390/app13031276

    Article  Google Scholar 

  22. de Gooijer B, Havinga J, Geijselaers H, Van den Boogaard T (2021) Evaluation of POD based surrogate models of fields resulting from nonlinear FEM simulations. Adv Model Simul Eng Sci 8. https://doi.org/10.1186/s40323-021-00210-8

  23. Cueto E, Chinesta F, Huerta A (2014) Model order reduction based on proper orthogonal decomposition. In: Chinesta F, Ladevèze P (eds) Separated representations and PGD-based model reduction: fundamentals and applications. Springer, Vienna, pp 1–26. https://doi.org/10.1007/978-3-7091-1794-1_1

    Chapter  Google Scholar 

  24. Chinesta F, Ladeveze P (2014) Separated representations and PGD-based model reduction: fundamentals and applications. https://doi.org/10.1007/978-3-7091-1794-1

  25. Havinga J, Mandal PK, van den Boogaard T (2020) Exploiting data in smart factories: real-time state estimation and model improvement in metal forming mass production. Int J Mater Form 13(5):663–673. https://doi.org/10.1007/s12289-019-01495-2

    Article  Google Scholar 

  26. Hamdaoui M, Le Quilliec G, Breitkopf P, Villon P (2014) POD surrogates for real-time multi-parametric sheet metal forming problems. Int J Mater Form 7(3):337–358. https://doi.org/10.1007/s12289-013-1132-0

    Article  Google Scholar 

  27. Dang VT, Labergere C, Lafon P (2017) POD surrogate models using adaptive sampling space parameters for springback optimization in sheet metal forming. Procedia Eng 207:1588–1593. https://doi.org/10.1016/j.proeng.2017.10.1053

    Article  Google Scholar 

  28. Dang V-T, Labergère C, Lafon P (2019) Adaptive metamodel-assisted shape optimization for springback in metal forming processes. Int J Mater Form 12(4):535–552. https://doi.org/10.1007/s12289-018-1433-4

    Article  Google Scholar 

  29. Raseli S, Faisal N, Mahat N (2022) Construction of Cubic Bezier Curve. J Comput Res Innov 7:111–120. https://doi.org/10.24191/jcrinn.v7i2.291

    Article  Google Scholar 

  30. Baydas S, Karakas B (2019) Defining a curve as a Bezier curve. J Taibah Univ Sci 13:522–528. https://doi.org/10.1080/16583655.2019.1601913

    Article  Google Scholar 

  31. Amaishi T, Tsutamori H, Nishiwaki T, Kimoto T (2020) Description of anisotropic properties of sheet metal based on spline curves and hole expansion test simulation of high-strength steel. Int J Solids Struct 202. https://doi.org/10.1016/j.ijsolstr.2020.07.010

  32. Ahn YJ, soo Kim Y, Shin Y (2004) Approximation of circular arcs and offset curves by Bézier curves of high degree. J Comput Appl Math 167(2):405–416. https://doi.org/10.1016/j.cam.2003.10.008

    Article  MathSciNet  Google Scholar 

  33. Oruç H, Phillips GM (2003) q-Bernstein polynomials and Bézier curves. J Comput Appl Math 151(1):1–12. https://doi.org/10.1016/S0377-0427(02)00733-1

    Article  MathSciNet  Google Scholar 

  34. Fitter HN, Pandey AB, Patel DD, Mistry JM (2014) A review on approaches for handling Bezier Curves in CAD for manufacturing. Procedia Eng 97:1155–1166. https://doi.org/10.1016/j.proeng.2014.12.394

    Article  Google Scholar 

  35. Farin G (2014) Curves and surfaces for computer-aided geometric design: a practical guide. Elsevier

    Google Scholar 

  36. Liu Y, Yin G (2020) The Delaunay triangulation learner and its ensembles. Comput Stat Data Anal 152:107030. https://doi.org/10.1016/j.csda.2020.107030

    Article  MathSciNet  Google Scholar 

  37. Lee S, Quagliato L, Park D, Kwon I, Sun J, Kim N (2021) A new approach to preform design in metal forging processes based on the convolution neural network. Appl Sci 11(17):7948. https://doi.org/10.3390/app11177948

    Article  Google Scholar 

  38. Mull J-F, Durand C, Baudouin C, Bigot R (2020) A new tailored solution to predict blow efficiency and energy consumption of hammer-forging machines. Int J Adv Manuf Technol 111(7–8):1941–1954. https://doi.org/10.1007/s00170-020-06237-2

    Article  Google Scholar 

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Acknowledgements

We would like to sincerely thank the Technical Center for Mechanical Industry (CETIM) for their financial support in this research project. Specifically, we would like to thank Pierre KRUMPIPE, Stéphane MAGRON, and Valérie SULIS for their project follow-up and advice. We would also like to thank Francisco CHINESTA, a university professor and researcher at the Laboratory for Processes and Engineering in Mechanics and Materials (PIMM), for his contribution to this project through his expertise in dimensional reduction and surrogate models. Finally, we would like to thank Sébastien BURGUN and Alexandre FENDLER for their technical support during the various tests conducted.

Funding

This study was funded by the Technical Center for Mechanical Industry (CETIM) and the Carnot Institut ARTS (Research Actions for Technology and Society).

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Authors and Affiliations

  1. HESAM Université, Arts et Métiers Institute of Technology, Université de Lorraine, LCFC, F-57070, Metz, France

    David Uribe, Cyrille Baudouin, Camille Durand & Régis Bigot

Authors
  1. David Uribe
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  2. Cyrille Baudouin
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Contributions

DU: Investigation, Data curation, Software, Writing-original draft, Writing-review & editing; CB: Methodology, Formal Analysis, Writing- review & editing; CD: Conceptualization, Validation, Writing-review & editing; RB: Resources, Supervision, Writing–review & editing, Funding acquisition.

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Correspondence to David Uribe.

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Uribe, D., Baudouin, C., Durand, C. et al. Predictive control for a single-blow cold upsetting using surrogate modeling for a digital twin. Int J Mater Form 17, 7 (2024). https://doi.org/10.1007/s12289-023-01803-x

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