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Volume 8 Issue 3
Mar.  2021

IEEE/CAA Journal of Automatica Sinica

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Shiming Liu, Yifan Xia, Zhusheng Shi, Hui Yu, Zhiqiang Li and Jianguo Lin, "Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network," IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 565-581, Mar. 2021. doi: 10.1109/JAS.2021.1003871
Citation: Shiming Liu, Yifan Xia, Zhusheng Shi, Hui Yu, Zhiqiang Li and Jianguo Lin, "Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network," IEEE/CAA J. Autom. Sinica, vol. 8, no. 3, pp. 565-581, Mar. 2021. doi: 10.1109/JAS.2021.1003871

Deep Learning in Sheet Metal Bending With a Novel Theory-Guided Deep Neural Network

doi: 10.1109/JAS.2021.1003871
Funds:  This work was supported by Aviation Industry Corporation of China (AVIC) Manufacturing Technology Institute (MTI) and in part by China Scholarship Council (CSC) (201908060236)
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  • Sheet metal forming technologies have been intensively studied for decades to meet the increasing demand for lightweight metal components. To surmount the springback occurring in sheet metal forming processes, numerous studies have been performed to develop compensation methods. However, for most existing methods, the development cycle is still considerably time-consumptive and demands high computational or capital cost. In this paper, a novel theory-guided regularization method for training of deep neural networks (DNNs), implanted in a learning system, is introduced to learn the intrinsic relationship between the workpiece shape after springback and the required process parameter, e.g., loading stroke, in sheet metal bending processes. By directly bridging the workpiece shape to the process parameter, issues concerning springback in the process design would be circumvented. The novel regularization method utilizes the well-recognized theories in material mechanics, Swift’s law, by penalizing divergence from this law throughout the network training process. The regularization is implemented by a multi-task learning network architecture, with the learning of extra tasks regularized during training. The stress-strain curve describing the material properties and the prior knowledge used to guide learning are stored in the database and the knowledge base, respectively. One can obtain the predicted loading stroke for a new workpiece shape by importing the target geometry through the user interface. In this research, the neural models were found to outperform a traditional machine learning model, support vector regression model, in experiments with different amount of training data. Through a series of studies with varying conditions of training data structure and amount, workpiece material and applied bending processes, the theory-guided DNN has been shown to achieve superior generalization and learning consistency than the data-driven DNNs, especially when only scarce and scattered experiment data are available for training which is often the case in practice. The theory-guided DNN could also be applicable to other sheet metal forming processes. It provides an alternative method for compensating springback with significantly shorter development cycle and less capital cost and computational requirement than traditional compensation methods in sheet metal forming industry.


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  • [1]
    K. L. Zheng, D. J. Politis, L. L. Wang, and J. G. Lin, “A review on forming techniques for manufacturing lightweight complex-shaped aluminium panel components,” Int. J. Light. Mater. Manuf., vol. 1, no. 2, pp. 55–80, Jun. 2018.
    L. H. Zhan, J. G. Lin, T. A. Dean, and M. H. Huang, “Experimental studies and constitutive modelling of the hardening of aluminium alloy 7055 under creep age forming conditions,” Int. J. Mech. Sci., vol. 53, no. 8, pp. 595–605, Aug. 2011. doi: 10.1016/j.ijmecsci.2011.05.006
    W. L. Xu, C. H. Ma, C. H. Li, and W. J. Feng, “Sensitive factors in springback simulation for sheet metal forming,” J. Mater. Process. Technol., vol. 151, no. 1–3, pp. 217–222, Sep. 2004. doi: 10.1016/j.jmatprotec.2004.04.044
    K. P. Li, W. P. Carden, and R. H. Wagoner, “Simulation of springback,” Int. J. Mech. Sci., vol. 44, no. 1, pp. 103–122, Jan. 2002. doi: 10.1016/S0020-7403(01)00083-2
    X. A. Yang and F. Ruan, “A die design method for springback compensation based on displacement adjustment,” Int. J. Mech. Sci., vol. 53, no. 5, pp. 399–406, May 2011. doi: 10.1016/j.ijmecsci.2011.03.002
    Z. K. Zhang, J. J. Wu, S. Zhang, M. Z. Wang, R. C. Guo, and S. C. Guo, “A new iterative method for springback control based on theory analysis and displacement adjustment,” Int. J. Mech. Sci., vol. 105, pp. 330–339, Jan. 2016. doi: 10.1016/j.ijmecsci.2015.11.005
    R. Lingbeek, J. Huétink, S. Ohnimus, M. Petzoldt, and J. Weiher, “The development of a finite elements based springback compensation tool for sheet metal products,” J. Mater. Process. Technol., vol. 169, no. 1, pp. 115–125, Oct. 2005. doi: 10.1016/j.jmatprotec.2005.04.027
    J. Lin, T. A. Dean, R. P. Garrett, and A. D. Foster, A Process in Forming High Strength and Complex-Shaped Al-Alloy Sheet Components, WO2008059242A2, 2008.
    H. Wang, J. Zhou, T. S. Zhao, and Y. P. Tao, “Springback compensation of automotive panel based on three-dimensional scanning and reverse engineering,” Int. J. Adv. Manuf. Technol., vol. 85, no. 5-8, pp. 1187–1193, Jul. 2016. doi: 10.1007/s00170-015-8042-x
    Y. Li, Q. Rong, Z. S. Shi, X. G. Sun, L. C. Meng, and J. G. Lin, “An accelerated springback compensation method for creep age forming,” Int. J. Adv. Manuf. Technol., vol. 102, no. 1–4, pp. 121–134, May 2019. doi: 10.1007/s00170-018-3175-3
    J. Cao, E. Brinksmeier, M. W. Fu, R. X. Gao, B. Liang, M. Merklein, M. Schmidt, and J. Yanagimoto, “Manufacturing of advanced smart tooling for metal forming,” CIRP Ann., vol. 68, no. 2, pp. 605–628, Jun. 2019.
    M. Ghahramani, Y. Qiao, M. C. Zhou, A. O’Hagan, and J. Sweeney, “AI-based modeling and data-driven evaluation for smart manufacturing processes,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 4, pp. 1026–1037, Jul. 2020. doi: 10.1109/JAS.2020.1003114
    C. Ieracitano, A. Paviglianiti, M. Campolo, A. Hussain, E. Pasero, and F. C. Morabito, “A novel automatic classification system based on hybrid unsupervised and supervised machine learning for electrospun nanofibers,” IEEE/CAA J. Autom. Sinica, vol. 8, no. 1, pp. 64–76, Jan. 2021.
    C. Jaremenko, N. Ravikumar, E. Affronti, M. Merklein, and A. Maier, “Determination of forming limits in sheet metal forming using deep learning,” Materials, vol. 12, no. 7, pp. 1051, Mar. 2019. doi: 10.3390/ma12071051
    S. M. Liu, Z. S. Shi, J. G. Lin, and Z. Q. Li, “Reinforcement learning in free-form stamping of sheet-metals,” Procedia Manuf., vol. 50, pp. 444–449, Jan. 2020.
    J. W. Xiang, T. Matsumoto, Y. X. Wang, and Z. S. Jiang, “Detect damages in conical shells using curvature mode shape and wavelet finite element method,” Int. J. Mech. Sci., vol. 66, pp. 83–93, Jan. 2013. doi: 10.1016/j.ijmecsci.2012.10.010
    M. A. Dib, N. J. Oliveira, A. E. Marques, M. C. Oliveira, J. V. Fernandes, B. M. Ribeiro, and P. A. Prates, “Single and ensemble classifiers for defect prediction in sheet metal forming under variability,” Neural Comput. Appl., vol. 32, no. 16, pp. 12335–12349, Aug. 2020. doi: 10.1007/s00521-019-04651-6
    X. Y. Liu, Y. J. Du, X. L. Lu, and S. P. Zhao, “Springback prediction and forming accuracy control of micro w-bending using support vector machine,” in Proc. 6th Int. Conf. Frontiers of Industrial Engineering, London, United Kingdom, 2019, pp. 23–l27.
    A. Ben Abdessalem and A. El-Hami, “A probabilistic approach for optimising hydroformed structures using local surrogate models to control failures,” Int. J. Mech. Sci., vol. 96-97, pp. 143–162, Jun. 2015. doi: 10.1016/j.ijmecsci.2015.04.002
    M. S. Ashhab, T. Breitsprecher, and S. Wartzack, “Neural network based modeling and optimization of deep drawing – extrusion combined process,” J. Intell. Manuf., vol. 25, no. 1, pp. 77–84, Feb. 2014. doi: 10.1007/s10845-012-0676-z
    R. Narayanasamy and P. Padmanabhan, “Comparison of regression and artificial neural network model for the prediction of springback during air bending process of interstitial free steel sheet,” J. Intell. Manuf., vol. 23, no. 3, pp. 357–364, Jun. 2012. doi: 10.1007/s10845-009-0375-6
    Z. F. Guo and W. C. Tang, “Bending angle prediction model based on BPNN-spline in air bending springback process,” Math. Probl. Eng., vol. 2017, pp. Article ID 7834621, Feb. 2017.
    V. Viswanathan, B. Kinsey, and J. Cao, “Experimental implementation of neural network springback control for sheet metal forming,” J. Eng. Mater. Technol., vol. 125, no. 2, pp. 141–147, Apr. 2003. doi: 10.1115/1.1555652
    N. Mekras, “Using artificial neural networks to model aluminium based sheet forming processes and tools details,” J. Phys.:Conf. Ser., vol. 896, no. 1, pp. 012090, Jul. 2017.
    A. Jenab, I. Sari Sarraf, D. E. Green, T. Rahmaan, and M. J. Worswick, “The use of genetic algorithm and neural network to predict rate-dependent tensile flow behaviour of AA5182-O sheets,” Mater. Des., vol. 94, pp. 262–273, Mar. 2016. doi: 10.1016/j.matdes.2016.01.038
    X. Y. Li, C. C. Roth, and D. Mohr, “Machine-learning based temperature- and rate-dependent plasticity model: Application to analysis of fracture experiments on DP steel,” Int. J. Plast., vol. 118, pp. 320–344, Jul. 2019. doi: 10.1016/j.ijplas.2019.02.012
    C. Hartmann, D. Opritescu, and W. Volk, “An artificial neural network approach for tool path generation in incremental sheet metal free-forming,” J. Intell. Manuf., vol. 30, no. 2, pp. 757–770, Feb. 2019. doi: 10.1007/s10845-016-1279-x
    A. Krizhevsky, I. Sutskever, and G. E. Hinton, “ImageNet classification with deep convolutional neural networks,” Commun. ACM, vol. 60, no. 6, pp. 84–90, Jun. 2017. doi: 10.1145/3065386
    Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature, vol. 521, no. 7553, pp. 436–444, May 2015. doi: 10.1038/nature14539
    Y. F. Xia, H. Yu, and F. Y. Wang, “Accurate and robust eye center localization via fully convolutional networks,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 5, pp. 1127–1138, Sep. 2019. doi: 10.1109/JAS.2019.1911684
    R. Collobert and J. Weston, “A unified architecture for natural language processing: Deep neural networks with multitask learning,” in Proc. 25th Int. Conf. Machine Learning, 2008, pp. 160–167.
    M. L. Seltzer and J. Droppo, “Multi-task learning in deep neural networks for improved phoneme recognition,” in Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing, Vancouver, BC, Canada, 2013, pp. 6965–6969.
    I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning. Cambridge, Massachusetts: The MIT Press, 2016.
    E. Hamouche and E. G. Loukaides, “Classification and selection of sheet forming processes with machine learning,” Int. J. Comput. Integr. Manuf., vol. 31, no. 9, pp. 921–932, Jan. 2018. doi: 10.1080/0951192X.2018.1429668
    C. Sauer, B. Schleich, and S. Wartzack, “Deep learning in sheet-bulk metal forming part design,” in Proc. 15th Int. Design Conf., Dubrovnik, Croatia, 2018, pp. 2999–3010.
    J. Pfrommer, C. Zimmerling, J. Z. Liu, L. Kärger, F. Henning, and J. Beyerer, “Optimisation of manufacturing process parameters using deep neural networks as surrogate models,” Procedia CIRP, vol. 72, pp. 426–431, Mar. 2018. doi: 10.1016/j.procir.2018.03.046
    C. Zimmerling, D. Trippe, B. Fengler, and L. Kärger, “An approach for rapid prediction of textile draping results for variable composite component geometries using deep neural networks,” AIP Conf. Proc., vol. 2113, pp. 020007, Jul. 2019.
    A. M. Tartakovsky, C. O. Marrero, P. Perdikaris, G. D. Tartakovsky, and D. Barajas-Solano, “Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems,” Water Resour. Res., vol. 56, no. 5, pp. e2019WR026731, May 2020.
    R. Y. Zhang, Y. Liu, and H. Sun, “Physics-informed multi-LSTM networks for metamodeling of nonlinear structures,” Comput. Methods Appl. Mech. Eng., vol. 369, pp. 113226, Sep. 2020. doi: 10.1016/j.cma.2020.113226
    M. Raissi, P. Perdikaris, and G. E. Karniadakis, “Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,” J. Comput. Phys., vol. 378, pp. 686–707, Feb. 2019. doi: 10.1016/j.jcp.2018.10.045
    M. A. Nabian and H. Meidani, “Physics-driven regularization of deep neural networks for enhanced engineering design and analysis,” J. Comput. Inf. Sci. Eng., vol. 20, no. 1, pp. 011006, Feb. 2020. doi: 10.1115/1.4044507
    H. P. Yao, Y. Gao, and Y. M. Liu, “FEA-Net: A physics-guided data-driven model for efficient mechanical response prediction,” Comput. Methods Appl. Mech. Eng., vol. 363, pp. 112892, May 2020. doi: 10.1016/j.cma.2020.112892
    Q. Rong, Y. Li, Z. S. Shi, L. C. Meng, X. H. Sun, X. G. Sun, and J. G. Lin, “Experimental investigations of stress-relaxation ageing behaviour of AA6082,” Mater. Sci. Eng. A, vol. 750, pp. 108–116, Mar. 2019. doi: 10.1016/j.msea.2019.02.043
    H. L. Sun, X. K. Song, R. Ma, and J. Zhao, “Theoretical analysis of JCO forming and springback for sheet metal four-point bending in manufacture of LSAW pipe,” China Mech. Eng., vol. 25, no. 2, pp. 257–262, Mar. 2014.
    Z. Marciniak, J. L. Duncan, and S. J. Hu, Mechanics of Sheet Metal Forming. 2nd ed. Oxford: Elsevier, 2002.
    J. Johnson, A. Karpathy, and F. F. Li, “DenseCap: Fully convolutional localization networks for dense captioning,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition, Las Vegas, NV, USA, 2016, pp. 4565–4574.
    C. M. Bishop, Pattern Recognition and Machine Learning. New York: Springer, 2006.
    D. P. Kingma and J. L. Ba, “Adam: A method for stochastic optimization,” in Proc. 3rd Int. Conf. Learning Representations, San Diego, USA, 2015, pp. 1–15. [Online]. Available: https://arxiv.org/abs/1412.6980. Accessed: Jan. 15, 2021.
    G. Hinton, N. Srivastava, and K. Swersky, “Neural networks for machine learning: lecture 6a: Overview of mini-batch gradient descent.” [Online]. Available: https: //www.cs.toronto.edu/~tijmen/csc321/slides/lecture_slides_lec6.pdf. Accessed: Feb. 1, 2020.
    R. Caruana, “Multitask connectionist learning,” in Proc. 1993 Connectionist Models Summer School, Hillsdale, NJ, USA, 1993, pp. 372–379.
    R. Ranjan, V. M. Patel, and R. Chellappa, “HyperFace: A deep multi-task learning framework for face detection, landmark localization, pose estimation, and gender recognition,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 41, no. 1, pp. 121–135, Jan. 2019. doi: 10.1109/TPAMI.2017.2781233
    Z. X. Wang, X. F. Zhu, E. Adeli, Y. Y. Zhu, F. P. Nie, B. Munsell, and G. R. Wu, “Multi-modal classification of neurodegenerative disease by progressive graph-based transductive learning,” Med. Image Anal., vol. 39, pp. 218–230, Jul. 2017. doi: 10.1016/j.media.2017.05.003
    T. Altan and E. Tekkaya, Sheet Metal Forming: Processes and Applications. Metals Park, OH: ASM Int., 2012.
    X. Luo, M. C. Zhou, Y. N. Xia, Q. S. Zhu, A. C. Ammari, and A. Alabdulwahab, “Generating highly accurate predictions for missing QoS data via aggregating nonnegative latent factor models,” IEEE Trans. Neural Netw. Learn. Syst., vol. 27, no. 3, pp. 524–537, Mar. 2016. doi: 10.1109/TNNLS.2015.2412037
    D. Wu, X. Luo, M. S. Shang, Y. He, G. Y. Wang, and X. D. Wu, “A data-characteristic-aware latent factor model for web services QoS prediction,” IEEE Trans. Knowl. Data Eng., DOI: 10.1109/TKDE.2020.3014302, 2020.
    X. Luo, Y. Yuan, S. L. Chen, N. Y. Zeng, and Z. D. Wang, “Position-transitional particle swarm optimization-incorporated latent factor analysis,” IEEE Trans. Knowl. Data Eng., DOI: 10.1109/TKDE.2020.3033324, 2020.
    X. Luo, H. Wu, H. Q. Yuan, and M. C. Zhou, “Temporal pattern-aware QoS prediction via biased non-negative latent factorization of tensors,” IEEE Trans. Cybern., vol. 50, no. 5, pp. 1798–1809, May 2020. doi: 10.1109/TCYB.2019.2903736
    B. Shen, Z. D. Wang, and H. Qiao, “Event-triggered state estimation for discrete-time multidelayed neural networks with stochastic parameters and incomplete measurements,” IEEE Trans. Neural Netw. Learn. Syst., vol. 28, no. 5, pp. 1152–1163, May 2017. doi: 10.1109/TNNLS.2016.2516030
    Y. F. Liu, B. Shen, and H. S. Shu, “Finite-time resilient H state estimation for discrete-time delayed neural networks under dynamic event-triggered mechanism,” Neural Netw., vol. 121, pp. 356–365, Jan. 2020. doi: 10.1016/j.neunet.2019.09.006


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    • Proposed a novel Theory-Guided Deep Neural Network (TG-DNN) for sheet metal forming
    • Directly bridging the workpiece shape to the process parameters like loading stroke
    • Using a well-recognized theory for training by penalizing divergence from the law
    • Outperforming data-driven DNNs especially with scarce and scattered experiment data
    • Providing an alternative method for springback compensation with less time and cost


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