Neural Networks with Input Dimensionality Reduction for ‎Efficient Temperature Distribution Prediction in a Warm ‎Stamping Process

Document Type : Research Paper


Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, Canada‎


Hot stamping involves deforming a heated blank to form components with increased mechanical strength. More recently, warm stamping procedures have been researched. The forming occurs at lower temperatures to improve process efficiency. The process is non-linear and inefficient to solve using finite element simulations and surrogate models. This paper presents the use of dimension-reduced neural networks (DR-NNs) for predicting temperature distribution in FEM warm stamping simulations. Dimensionality reduction methods transformed the input space, consisting of assembly, material, and thermal features, to a set of principal components used as input to the neural networks. The DR-NNs are compared against a standalone neural network and show improvements in terms of lower computational time, error, and prediction uncertainty.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

‎[1] S. Kashid and S. Kumar, Applications of Artificial Neural Network to Sheet Metal Work - A Review, American Journal of Intelligent Systems, ‎‎2(7), 2012, 168-176. ‎
‎[2] A. Shahani, S. Setayeshi, S. Nodamaie, M. Asadi and S. Rezaie, Prediction of influence parameters on the hot rolling process using finite ‎element method and neural network, Journal of Materials Processing Technology, 209(4), 2009, 1920-1935. ‎
‎[3] Y.-F. Zhang, P. Fitch and P. Thorburn, Predicting the Trend of Dissolved Oxygen Based onthe kPCA-RNN Model, Water, 12(2), 2020, 585. ‎
‎[4] J. Tao, G. Sun, L. Guo and X. Wang, Application of a PCA-DBN-based surrogate model to robust aerodynamic design optimization, Chinese Journal of Aeronautics, 33(6), 2020, 1573-1588. ‎
‎[5] D. Kapsoulis, K. Tsiakas, X. A. V. Trompoukis and K. Giannakoglou, A PCA-assisted hybrid algorithm combining EAs and adjoint methods for ‎CFD-based optimization, Applied Soft Computing, 73, 2018, 520-529. ‎
‎[6] M. Kamali, K. Ponnambalam and E. Soulis, Integration of surrogate optimization and PCA for calibration of hydrologic models, A WATCLASS ‎case study, in 2007 IEEE International Conference on Systems, Man and Cybernetics, Montreal, Canada, 2007. ‎
‎[7] P. Ravier, L. Aranda and Y. Chastel, Hot Stamping Experiment And Numerical Simulation Of Pre-coated USIBOR1500 Quenchable Steels, in International Body Engineering Coference & Exposition, Detroit, Michigan, USA, 1998. ‎
‎[8] M. Naderi and W. Bleck, Hot Stamping of Ultra High-Strength Steels, Materials Science, 2008. ‎
‎[9] F. Borsetto, A. Ghiotti and S. Bruschi, Investigation of the high strength steel Al-Si coating during hot stamping operations, Key Engineering Materials, 410, 2009, 289-296. ‎
‎[10] J. Lechler and M. Merklein, Hot stamping of ultra strength steels as a key technology for lightweight construction, Journal of Materials Science and Technology, 3, 2008, 1698-1807. ‎
‎[11] C. Jing, D. Ye, J. Zhao, T. Lin, C. Wu and Q. Lei, Effect of hot stamping and quenching & partitioning process on microstructure and ‎mechanical properties of ultra-high strength steel, Materials Research Express, 8, 2021, 036506. ‎
‎[12] Y. Nakagawa, T. Maeno and K.-I. Mori, Forming and quenching behaviours in hot stamping of thin quenchable sheets, in MATEC Web of Conferences, 2015. ‎
‎[13] Y. Nakagawa, K. Mori, T. Maeno and Y. Nakao, Reduction in holding time at bottom dead centre in hot stamping by water and die ‎quenching, in 17th International Conference on Metal Forming, Toyohashi, Japan, 2018. ‎
‎[14] C. Tong, Q. Rong, V. Yardley, X. Li, J. Luo, G. Zhu and Z. Shi, New Developments and Future Trends in Low-Temperature Hot Stamping ‎Technologies: A Review, Metals, 10(12), 2020, 1652. ‎
‎[15] D. Balint, Dean TA and J. Lin, A method of forming parts from sheet steel, US Patent 2014/0352388, 2014.‎
‎[16] E. Ota, Y. Yogo, T. Iwata, N. Iwata, K. Ishida and K. Takeda, Formability improvement technique for heated sheet metal forming by partial ‎cooling, Key Engineering Materials, 622-623, 2014, 292-283. ‎
‎[17] M. Ganapathy, N. Li, M. Abspoel and D. Bhattacharjee, Experimental investigation of a new low-temperature hot stamping process for boron ‎steels, The International Journal of Advanced Manufacturing Technology, 105, 2019, 669-682. ‎
‎[18] M. Ganapathy, N. Li, J. Lin and D. Bhattacharjee, Investigation of a new hot stamping process with improved formability and productivity, Precedia Engineering, 207, 2017, 771-776. ‎
‎[19] T. Cai, C. Lei, W. Yang, H. Fu and Z. Xing, Local-Induction-Heating Bending Process of B1500HS Thin-Walled Rectangular Steel Tubes: A ‎Simulation and Experimental Investigation, Metals, 11(1), 2021, 132. ‎
‎[20] Z. Xing, J. Bao and Y. Yang, Numerical simulation of hot stamping of quenchable boron steel, Materials Science and Engineering A, 499(‎1-2), 2009, 28-31. ‎
‎[21] H. Hajbarati and A. Zajkani, A novel finite element simulation of hot stamping process of DP780 steel based on the Chaboche ‎thermomechanically hardening model, The International Journal of Advanced Manufacturing Technology, 111(9-10), 2020, 1-14. ‎
‎[22] H. Liu, Z. Xing, J. Bao and B. Song, Investigation of the Hot-Stamping Process for Advanced High-Strength Steel Sheet by Numerical ‎Simulation, Journal of Materials Engineering and Performance, 19(3), 2010, 325-334. ‎
‎[23] H. B. J. Liu, X. Zhongwen, D. Zhang, B. Song and C. Lei, Modeling and FE Simulation of Quenchable High Strength Steels Sheet Metal Hot ‎Forming Process, Journal of Materials Engineering and Performance, 20(6), 2011, 894-902. ‎
‎[24] K. Dehghani and A. Nekahi, Artificial neural network to predict the effect of thermomechanical treatments on bake hardenability of low ‎carbon steels, Materials & Design, 31(4), 2010, 2224-2229. ‎
‎[25] P. Chokshi, Development of an artificial neural network (ANN) based phase distribution prediction model for 22MnB5 boron steel during tailored hot stamping, PhD Thesis, University of Warwick, Warwick, 2017.‎
‎[26] H. Maan, The influence of blankholder gap on deep drawing process using finite element method, International Journal of Mechanical Engineering and Technology, 9(13), 2018, 1510-1518. ‎
‎[27] F. Cardarelli, Materials Handbook, 2nd ed., London, Springer-Verlag, 2008. ‎
‎[28] ‎22MnB5, Ovako, 17 May 2021. [Online]. Available: [Accessed 2022].‎
‎[29] H. Hou, L. Huiping and L. He, Effect of technological parameters on microstructure and accuracy of B1500HS steel parts in the hot blanking, The International Journal of Advanced Manufacturing Technology, 95(1-2), 2018, 3275–3287. ‎
‎[30] B. Tang, F. Wu, Q. Wang, C. Li, J. Liu and G. H., Numerical and experimental study on ductile fracture of quenchable boron steels with ‎different microstructures, International Journal of Lightweight Materials and Manufacture, 3, 2020, 55-65. ‎
‎[31] M. Merklein, Investigation of the thermo-mechanical properties of hot stamping steels, Journal of Materials Processing Technology, 177(‎‎1-3), 2006, 452-455. ‎
‎[32] M. Merklein, J. Lechler and T. Stoehr, Investigations on the thermal behavior of ultra high strength boron manganese steels within hot ‎stamping, International Journal of Material Forming, 2(1), 2009, 259-262. ‎
‎[33] J. Lechler, M. Merlein and M. Geiger, Determination of thermal and mechanical material properties of ultra-high strength steels for hot ‎stamping, Steel Research International, 79(2), 2008, 98-104. ‎
‎[34] A. Naganathan, Hot Stamping of Manganese Boron Steel, Ohio, PhD Thesis, The Ohio State University, USA, 2010. ‎
‎[35] I. Jolliffe and J. Cadima, Principal component analysis: a review and recent developments, Philosophical Transactions A, 374, 2016, 20150202. ‎
‎[36] J. Lee, C. Yoo, S. Choi, P. Vanrolleghem and I. Lee, Nonlinear process monitoring using kernel principal component analysis, Chemical Engineering Science, 59, 2004, 223-234. ‎
‎[37] K. Kim, K. Jung and H. Kim, Face recognition using kernel principal component analysis, IEEE Signal Processing Letters, 9(2), 2002, 40-42. ‎
‎[38] S. Maitra and J. Yan, Principle Component Analysis and Partial Least Squares: Two Dimension Reduction Techniques for Regression, 2008. ‎
‎[39] H. S and B. Triggs, Feature Sets and Dimensionality Reduction for Visual Object Detection, in British Machine Vision Conference, Aberystwyth, ‎‎2010. ‎
‎[40] S. Wold, M. Sjostrom and L. Eriksson, PLS-Regression: a basic tool of chemometrics, Chemometrics and Intelligent Laboratory Systems, 2001. ‎
‎[41] T.C.R. Hsiao and H.K. Chiang, Partial least-squares algorithm for weights initialization of backpropagation network, Neurocomputing, 50, 2003, 237-247.