Multi-objective optimization of stamping process based on physics-guided extra trees for large thin-walled parts

1. Altmann, A., Toloşi, L., Sander, O., Lengauer, T.: Permutation importance: a corrected feature importance measure. Bioinformatics 26, 1340–1347 (2010). https://doi.org/10.1093/bioinformatics/btq13410.1093/bioinformatics/btq134 ↗

2. Amoura, N., Benaissa, B., Al Ali, M., Khatir, S.: Deep neural network and YUKI algorithm for inner damage characterization based on elastic boundary displacement. In: Capozucca, R., Khatir, S., Milani, G. (eds.) Proceedings of the International Conference of Steel and Composite for Engineering Structures, pp. 220–233. Springer International Publishing, Cham (2023)10.1007/978-3-031-24041-6_18 ↗

3. Attar, H.R., Zhu, L., Li, N.: Deep learning enabled tool compensation for addressing shape distortion in sheet metal stamping. In: Mocellin, K., Bouchard, P.-O., Bigot, R., Balan, T. (eds.) Proceedings of the 14th International Conference on the Technology of Plasticity-Current Trends in the Technology of Plasticity, pp. 48–58. Springer Nature Switzerland, Cham (2024)10.1007/978-3-031-42093-1_5 ↗

4. Atul, T.S., Babu, M.C.L.: A review on effect of thinning, wrinkling and spring-back on deep drawing process. Proc Inst. Mech. Eng. Part B-J. Eng. Manuf. 233, 1011–1036 (2019). https://doi.org/10.1177/095440541775250910.1177/0954405417752509 ↗

5. Behzadian, M., Khanmohammadi Otaghsara, S., Yazdani, M., Ignatius, J.: A state-of the-art survey of TOPSIS applications. Expert Syst. Appl. 39, 13051–13069 (2012). https://doi.org/10.1016/j.eswa.2012.05.05610.1016/j.eswa.2012.05.056 ↗

6. Benaissa, B., Kobayashi, M., Al Ali, M., Khatir, S., Shimoda, M.: A novel exploration strategy for the YUKI algorithm for topology optimization with metaheuristic structural binary distribution. Eng. Optim. 57, 1198–1218 (2025). https://doi.org/10.1080/0305215X.2024.234910410.1080/0305215X.2024.2349104 ↗

7. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6, 182–197 (2002). https://doi.org/10.1109/4235.99601710.1109/4235.996017 ↗

8. Feng, Y., Hong, Z., Gao, Y., Lu, R., Wang, Y., Tan, J.: Optimization of variable blank holder force in deep drawing based on support vector regression model and trust region. Int. J. Adv. Manuf. Technol. 105, 4265–4278 (2019). https://doi.org/10.1007/s00170-019-04477-510.1007/s00170-019-04477-5 ↗

9. Geurts, P., Ernst, D., Wehenkel, L.: Extremely randomized trees. Mach. Learn. 63, 3–42 (2006). https://doi.org/10.1007/s10994-006-6226-110.1007/s10994-006-6226-1 ↗

10. Gnecco, N., Terefe, E.M., Engelke, S.: Extremal random forests. J. Am. Stat. Assoc. 119, 3059–3072 (2024). https://doi.org/10.1080/01621459.2023.230052210.1080/01621459.2023.2300522 ↗

11. Guo, F., Jeong, H., Park, D., Kim, G., Sung, B., Kim, N.: Numerical optimization of variable blank holder force trajectories in stamping process for multi-defect reduction. Materials 17, 2578 (2024). https://doi.org/10.3390/ma1711257810.3390/ma17112578 ↗

12. Guo, H., Chen, B., Lyu, M., Bao, X., Cui, H., Zhou, Y., Yang, L.: Probabilistic and global sensitivity analysis for 3D concrete printing: a point-evolution and Fréchet-derivative framework. Structures 88, 111834 (2026). https://doi.org/10.1016/j.istruc.2026.11183410.1016/j.istruc.2026.111834 ↗

13. He, X., Ma, J., Welo, T.: Real-time and data-efficient springback prediction in tube bending using force measurement and physics-informed machine learning. J. Manuf. Process. 156, 645–660 (2025). https://doi.org/10.1016/j.jmapro.2025.10.10410.1016/j.jmapro.2025.10.104 ↗

14. Heinzelmann, P., Baum, S., Riedmüller, K.R., Liewald, M., Weyrich, M.: A comprehensive benchmark dataset for sheet metal forming: advancing machine learning and surrogate modelling in pro-cess simulations. MATEC Web Conf. 408, 01090 (2025). https://doi.org/10.1051/matecconf/20254080109010.1051/matecconf/202540801090 ↗

15. Hosford, W.F., Caddell, R.M.: Metal Forming: Mechanics and Metallurgy. Cambridge University Press (2011)10.1017/CBO9780511976940 ↗

16. Hou, Y., Myung, D., Park, J.K., Min, J., Lee, H.-R., El-Aty, A.A., Lee, M.-G.: A review of characterization and modelling approaches for sheet metal forming of lightweight metallic materials. Materials (2023). https://doi.org/10.3390/ma1602083610.3390/ma16020836 ↗

17. Jerath, S.: Structural Stability Theory and Practice: Buckling of Columns, Beams, Plates, and Shells. John Wiley & Sons (2020)

18. Jiang, S., Wang, Y., Cheng, Z., Chen, B.: Adaptive forecasting of stochastic crack growth using empirical mode decomposition: gaussian process regression for structural health monitoring. Struct. Infrastruct. Eng. 0, 1–14 (2026). https://doi.org/10.1080/15732479.2026.261796510.1080/15732479.2026.2617965 ↗

19. Karniadakis, G.E., Kevrekidis, I.G., Lu, L., Perdikaris, P., Wang, S., Yang, L.: Physics-informed machine learning. Nat. Rev. Phys. 3, 422–440 (2021). https://doi.org/10.1038/s42254-021-00314-510.1038/s42254-021-00314-5 ↗

20. Kim, M.-G., Ryu, J.-C., Lee, C.-J., Jang, J.-S., Ko, D.-C.: Process design of vinyl-coated metal sheet stamping for prevention of delamination and wrinkling by DNN-based multi-objective optimization. Materials 18, 5589 (2025). https://doi.org/10.3390/ma1824558910.3390/ma18245589 ↗

21. Lechner, P., Scandola, L., Maier, D., Hartmann, C., Rizaiev, Y., Lieb, M.: A physically-informed machine learning model for freeform bending. J. Intell. Manuf. 36, 4351–4363 (2025). https://doi.org/10.1007/s10845-024-02452-w10.1007/s10845-024-02452-w ↗

22. Ma, J., Tang, X., Hou, Y., Li, H., Lin, J., Fu, M.W.: Defects in metal-forming: formation mechanism, prediction and avoidance. Int. J. Mach. Tools Manuf 207, 104268 (2025). https://doi.org/10.1016/j.ijmachtools.2025.10426810.1016/j.ijmachtools.2025.104268 ↗

23. Marciniak, Z., Duncan, J.L., Hu, J.: Mechanics of Sheet Metal Forming. Butterworth-Heinemann (2002)

24. Meng, X., Li, Z., Zhang, D., Karniadakis, G.E.: PPINN: parareal physics-informed neural network for time-dependent PDEs. Comput. Meth. Appl. Mech. Eng. (2020). https://doi.org/10.1016/j.cma.2020.11325010.1016/j.cma.2020.113250 ↗

25. Munzone, F., Hazrati, J., Hakvoort, W., Boogaard, T. van den: Comparative study of artificial neural network and physics-informed neural network application in sheet metal forming. In: Material Forming, ESAFORM 2024: The 27th International ESAFORM Confernce on Material Forming held in Toulouse, France, April 24–26, 2024. pp. 2278–2288. Association of American Publishers (2024)10.21741/9781644903131-251 ↗

26. Pereira, R., Peixinho, N., Costa, S.L.: A Review on Sheet Metal Forming Evaluation of Advanced High Strength Steels (AHSS, https://doi.org/10.20944/preprints202402.1205.v1. (2024)10.20944/preprints202402.1205.v1 ↗

27. Prates, P.A., Marques, A.E., Oliveira, M.C., Fernandes, J.V.: Comparing Metamodeling Techniques For Variability Analysis In Sheet Metal Forming Processes. In: Galdos, L., Arrazola, P., DeArgandona, E.S., Otegi, N., Mendiguren, J., Madariaga, A., and DeBuruaga, M.S. (eds.) In: Proceedings of the 22nd international esaform conference on material forming (ESAFORM 2019). Amer Inst Physics, Vitoria, SPAIN (2019)10.1063/1.5112658 ↗

28. Quagliato, L., Perin, M., Modanloo, V., Lee, T.: Expert-informed neural network (EINN) for the forming depth prediction from a small-scale sheet metal forming database: 28th International ESAFORM Conference on Material Forming, ESAFORM 2025. 28th International ESAFORM Conference on Material Forming, ESAFORM 2025. 1490–1499 (2025). https://doi.org/10.21741/9781644903599-16110.21741/9781644903599-161 ↗

29. Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019). https://doi.org/10.1016/j.jcp.2018.10.04510.1016/j.jcp.2018.10.045 ↗

30. Santos, R., Vandepitte, D., Moens, D.: Prediction of composite pressure vessels’ burst strength through machine learning. Compos. Struct. (2025). https://doi.org/10.1016/j.compstruct.2024.11861710.1016/j.compstruct.2024.118617 ↗

31. Trieu, Q.-H., Luyen, T.T., Nguyen, D.-T.: Optimization and modelling of fracture height in SECC cylindrical cup deep drawing processes. J. Mach. Eng. 24, 74–86 (2024). https://doi.org/10.36897/jme/18547610.36897/jme/185476 ↗

32. Wadas, T., Tisza, M.: Lightweight manufacturing of automotive parts. IOP Conf. Ser. Mater. Sci. Eng. 903, 012036 (2020). https://doi.org/10.1088/1757-899X/903/1/01203610.1088/1757-899X/903/1/012036 ↗

33. Wang, H., Ye, F., Chen, L., Li, E.: Sheet metal forming optimization by using surrogate modeling techniques. Chin. J. Mech. Eng. 30, 22–36 (2017). https://doi.org/10.3901/CJME.2016.1020.12310.3901/CJME.2016.1020.123 ↗

34. Wang, K., Wang, L., Zheng, K., He, Z., Politis, D.J., Liu, G., Yuan, S.: High-efficiency forming processes for complex thin-walled titanium alloys components: state-of-the-art and perspectives. Int. J. Extrem. Manuf. 2, 032001 (2020). https://doi.org/10.1088/2631-7990/ab949b10.1088/2631-7990/ab949b ↗

35. Wang, Z., Xiang, Y., Zhang, S., Liu, X., Ma, J., Tan, J., Wang, L.: Physics-informed springback prediction of 3D aircraft tubes with six-axis free-bending manufacturing. Aerosp. Sci. Technol. 147, 109022 (2024). https://doi.org/10.1016/j.ast.2024.10902210.1016/j.ast.2024.109022 ↗

36. Weber, M.O., Ehrmann, A.: Necessary modification of the Euler–Eytelwein formula for knitting machines. J. Text. Inst. 103, 687–690 (2012). https://doi.org/10.1080/00405000.2011.59866510.1080/00405000.2011.598665 ↗

37. Xie, Y., Du, L., Zhao, J., Liu, C., Li, W.: Multi-objective optimization of process parameters in stamping based on an improved RBM-BPNN network and MOPSO algorithm. Struct. Multidiscip. Optim. 64, 4209–4235 (2021). https://doi.org/10.1007/s00158-021-03056-110.1007/s00158-021-03056-1 ↗

38. Xie, Y., Li, W., Liu, C., Du, M., Feng, K.: Optimization of stamping process parameters based on improved GA-BP neural network model. Int. J. Precis. Eng. Manuf. 24, 1129–1145 (2023). https://doi.org/10.1007/s12541-023-00811-w10.1007/s12541-023-00811-w ↗

39. Xu, Y., Qin, J., Liu, X., Liu, J.: Process parameter optimization and springback compensation in stamping of high-strength steel complex beams. Eng. Comput. 42, 3991–4016 (2025). https://doi.org/10.1108/EC-02-2025-017710.1108/EC-02-2025-0177 ↗

40. Yoon, J.W., Yang, D.Y., Chung, K., Barlat, F.: A general elasto-plastic finite element formulation based on incremental deformation theory for planar anisotropy and its application to sheet metal forming. Int. J. Plast. 15, 35–67 (1999). https://doi.org/10.1016/S0749-6419(98)00059-X10.1016/S0749-6419(98)00059-X ↗

41. Zhang, H., Wei, W., Long, S., Zhou, M., Li, C.: Optimization of stamping process parameters for sustainable manufacturing: numerical simulation based on AutoForm. Sustainability 17, 341 (2025). https://doi.org/10.3390/su1701034110.3390/su17010341 ↗