{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T07:03:05Z","timestamp":1769324585255,"version":"3.49.0"},"reference-count":48,"publisher":"Walter de Gruyter GmbH","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,3,26]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Stamping and bending technology uses a sequence of stamping and bending steps to manufacture complex metal parts. The execution order and design of each step are crucial for the quality of a produced part. However, simulating different process orders is hard due to uncertainties in the production process. We propose a data-driven model using neural networks to optimize the execution order to reduce the effects of uncertainties on the deviation in product quality. The process steps are modeled individually by neural networks, which are concatenated to model different process orders. To ensure accurate predictions, we use set-based training to make the neural networks robust against input uncertainties. We demonstrate the usefulness of our model by numerical experiments for the production process of a busbar.<\/jats:p>","DOI":"10.1515\/auto-2024-0132","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T06:32:10Z","timestamp":1740465130000},"page":"198-209","source":"Crossref","is-referenced-by-count":3,"title":["Training robust neural networks for uncertainty prediction in stamping technology"],"prefix":"10.1515","volume":"73","author":[{"given":"Lukas","family":"Koller","sequence":"first","affiliation":[{"name":"Cyber Physical Systems Group , Technical University of Munich , Munich , Germany"}]},{"given":"Christoph","family":"Hartmann","sequence":"additional","affiliation":[{"name":"Chair of Metal Forming and Casting , Technical University of Munich , Munich , Germany"}]},{"given":"Lukas","family":"Martinitz","sequence":"additional","affiliation":[{"name":"Chair of Metal Forming and Casting , Technical University of Munich , Munich , Germany"}]},{"given":"Wolfram","family":"Volk","sequence":"additional","affiliation":[{"name":"Chair of Metal Forming and Casting , Technical University of Munich , Munich , Germany"}]},{"given":"Matthias","family":"Althoff","sequence":"additional","affiliation":[{"name":"Cyber Physical Systems Group , Technical University of Munich , Munich , Germany"}]}],"member":"374","published-online":{"date-parts":[[2025,2,26]]},"reference":[{"key":"2026012407010959557_j_auto-2024-0132_ref_037","doi-asserted-by":"crossref","unstructured":"R. Norz, V. Simon, and W. Volk, \u201cFailure behaviour of various pre-formed steel sheets with respect to the mechanical grain boundary properties,\u201d Int. J. Material Form., vol.\u00a015, no.\u00a04, 2022, Art. no. 54, https:\/\/doi.org\/10.1007\/s12289-022-01700-9.","DOI":"10.1007\/s12289-022-01700-9"},{"key":"2026012407010959557_j_auto-2024-0132_ref_038","doi-asserted-by":"crossref","unstructured":"R. Norz, et al.., \u201cExperiments on forming behaviour of the aluminium alloy AA6016,\u201d IOP Conf. Ser. Mater. Sci. Eng., vol.\u00a01238, p.\u00a0012023, 2022, https:\/\/doi.org\/10.1088\/1757-899x\/1238\/1\/012023.","DOI":"10.1088\/1757-899X\/1238\/1\/012023"},{"key":"2026012407010959557_j_auto-2024-0132_ref_032","doi-asserted-by":"crossref","unstructured":"M. Liewald, et al.., \u201cPerspectives on data-driven models and its potentials in metal forming and blanking technologies,\u201d Prod. Eng., vol.\u00a016, pp.\u00a0607\u2013625, 2022, https:\/\/doi.org\/10.1007\/s11740-022-01115-0.","DOI":"10.1007\/s11740-022-01115-0"},{"key":"2026012407010959557_j_auto-2024-0132_ref_020","doi-asserted-by":"crossref","unstructured":"G. Hinton, et al.., \u201cDeep neural networks for acoustic modeling in speech recognition: the shared views of four research groups,\u201d IEEE Signal Process. Mag., vol.\u00a029, no.\u00a06, pp.\u00a082\u201397, 2012, https:\/\/doi.org\/10.1109\/msp.2012.2205597.","DOI":"10.1109\/MSP.2012.2205597"},{"key":"2026012407010959557_j_auto-2024-0132_ref_045","doi-asserted-by":"crossref","unstructured":"C.-Y. Wang, A. Bochkovskiy, and H.-Y. M. Liao, \u201cYOLOv7: trainable bag-of-freebies sets new state-of-the-art for real-time object detectors,\u201d in Proc. of the IEEE\/CVF Conf. on Computer Vision and Pattern Recognition (CVPR), 2023, pp.\u00a07464\u20137475.","DOI":"10.1109\/CVPR52729.2023.00721"},{"key":"2026012407010959557_j_auto-2024-0132_ref_016","unstructured":"I. Goodfellow, J. Shlens, and C. Szegedy, \u201cExplaining and harnessing adversarial examples,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2015."},{"key":"2026012407010959557_j_auto-2024-0132_ref_026","unstructured":"L. Koller, T. Ladner, and M. Althoff, \u201cSet-based training for neural network verification,\u201d arXiv: 2401.14961 [cs.LG], 2024."},{"key":"2026012407010959557_j_auto-2024-0132_ref_047","unstructured":"M. Wendl, et al.., \u201cTraining verifiably robust agents using set-based reinforcement learning,\u201d arXiv: 2408.09112 [cs.LG], 2024."},{"key":"2026012407010959557_j_auto-2024-0132_ref_008","doi-asserted-by":"crossref","unstructured":"\u0141. Bohdal, et al.., \u201cNumerical investigations of the effect of process parameters on residual stresses, strains and quality of final product in blanking using SPH method,\u201d Mater. Sci. Forum, vol.\u00a0862, pp.\u00a0238\u2013245, 2016, https:\/\/doi.org\/10.4028\/www.scientific.net\/msf.862.238.","DOI":"10.4028\/www.scientific.net\/MSF.862.238"},{"key":"2026012407010959557_j_auto-2024-0132_ref_044","doi-asserted-by":"crossref","unstructured":"T. Sutasn, \u201cFinite-element analysis of V-ring indenter mechanism in fine-blanking process,\u201d Mater. Des., vol.\u00a030, no.\u00a03, pp.\u00a0526\u2013531, 2009, https:\/\/doi.org\/10.1016\/j.matdes.2008.05.072.","DOI":"10.1016\/j.matdes.2008.05.072"},{"key":"2026012407010959557_j_auto-2024-0132_ref_006","doi-asserted-by":"crossref","unstructured":"J. B. Pacheco and A. dos Santos, \u201cA study on the nose radius influence in press brake bending operations by finite element analysis,\u201d Key Eng. Mater., vol.\u00a0554, pp.\u00a01432\u20131442, 2013.","DOI":"10.4028\/www.scientific.net\/KEM.554-557.1432"},{"key":"2026012407010959557_j_auto-2024-0132_ref_046","doi-asserted-by":"crossref","unstructured":"D. Weichert, et al.., \u201cA review of machine learning for the optimization of production processes,\u201d Int. J. Adv. Manuf. Technol., vol.\u00a0104, no.\u00a05, pp.\u00a01889\u20131902, 2019, https:\/\/doi.org\/10.1007\/s00170-019-03988-5.","DOI":"10.1007\/s00170-019-03988-5"},{"key":"2026012407010959557_j_auto-2024-0132_ref_034","doi-asserted-by":"crossref","unstructured":"L. Martinitz and C. Hartmann, \u201cAn artificial neural network approach on crystal plasticity for material modelling in macroscopic simulations,\u201d in IOP Conf. Series Materials Science and Engineering, 2023.","DOI":"10.1088\/1757-899X\/1284\/1\/012052"},{"key":"2026012407010959557_j_auto-2024-0132_ref_005","doi-asserted-by":"crossref","unstructured":"N. P. Belfiore, et al.., \u201cA hybrid approach to the development of a multilayer neural network for wear and fatigue prediction in metal forming,\u201d Tribology Int., vol.\u00a040, no.\u00a010, pp.\u00a01705\u20131717, 2007, https:\/\/doi.org\/10.1016\/j.triboint.2007.01.008.","DOI":"10.1016\/j.triboint.2007.01.008"},{"key":"2026012407010959557_j_auto-2024-0132_ref_018","doi-asserted-by":"crossref","unstructured":"P. Groche, M. Christiany, and Y. Wu, \u201cLoad-dependent wear in sheet metal forming,\u201d Wear, vol.\u00a0422, pp.\u00a0252\u2013260, 2019, https:\/\/doi.org\/10.1016\/j.wear.2019.01.071.","DOI":"10.1016\/j.wear.2019.01.071"},{"key":"2026012407010959557_j_auto-2024-0132_ref_028","doi-asserted-by":"crossref","unstructured":"C. Kubik, S. M. Knauer, and P. Groche, \u201cSmart sheet metal forming: importance of data acquisition, preprocessing and transformation on the performance of a multiclass support vector machine for predicting wear states during blanking,\u201d J. Intell. Manuf., vol.\u00a033, no.\u00a01, pp.\u00a0259\u2013282, 2022, https:\/\/doi.org\/10.1007\/s10845-021-01789-w.","DOI":"10.1007\/s10845-021-01789-w"},{"key":"2026012407010959557_j_auto-2024-0132_ref_010","doi-asserted-by":"crossref","unstructured":"D. J. Cruz, et al.., \u201cApplication of machine learning to bending processes and material identification,\u201d Metals, vol.\u00a011, no.\u00a09, p.\u00a01418, 2021, https:\/\/doi.org\/10.3390\/met11091418.","DOI":"10.3390\/met11091418"},{"key":"2026012407010959557_j_auto-2024-0132_ref_048","doi-asserted-by":"crossref","unstructured":"V. E. \u00d6. \u015eenol and H. Darendeliler, \u201cSpringback analysis in air bending process through experiment based artificial neural networks,\u201d Procedia Eng., vol. 11, no. 9, pp. 999\u20131004, 2014.","DOI":"10.1016\/j.proeng.2014.10.131"},{"key":"2026012407010959557_j_auto-2024-0132_ref_039","doi-asserted-by":"crossref","unstructured":"H. Peters, et al.., \u201cData-driven modeling of multi-stage punch-bending processes using graphical modeling notation,\u201d in at \u2013 Automatisierungstechnik \u2013 Datengetriebene Prozessmodellierung in der Umformtechnik, 2025, submitted.","DOI":"10.1515\/auto-2024-0112"},{"key":"2026012407010959557_j_auto-2024-0132_ref_040","doi-asserted-by":"crossref","unstructured":"A. Schenek, et al.., \u201cApplication of a neural network for predicting cutting surface quality of punching processes based on tooling parameters,\u201d in IOP Conf. Series: Materials Science and Engineering, 2023.","DOI":"10.1088\/1757-899X\/1284\/1\/012014"},{"key":"2026012407010959557_j_auto-2024-0132_ref_019","doi-asserted-by":"crossref","unstructured":"Y. Han, et al.., \u201cDynamic neural networks: a survey,\u201d IEEE Trans. Pattern Anal. Mach. Intell., vol.\u00a044, no.\u00a011, pp.\u00a07436\u20137456, 2022, https:\/\/doi.org\/10.1109\/tpami.2021.3117837.","DOI":"10.1109\/TPAMI.2021.3117837"},{"key":"2026012407010959557_j_auto-2024-0132_ref_024","unstructured":"L. Kirsch, J. Kunze, and D. Barber, \u201cModular networks: learning to decompose neural computation,\u201d in Advances in Neural Information Processing Systems (NeurIPS), 2018."},{"key":"2026012407010959557_j_auto-2024-0132_ref_004","unstructured":"A. Jacob, et al.., \u201cNeural module networks,\u201d in Proc. of the IEEE\/CVF Conf. on Computer Vision and Pattern Recognition (CVPR), 2016."},{"key":"2026012407010959557_j_auto-2024-0132_ref_027","unstructured":"K. Adam, et al.., \u201cCompositional convolutional neural networks: a deep architecture with innate robustness to partial occlusion,\u201d in Proc. of the IEEE\/CVF Conf. on Computer Vision and Pattern Recognition (CVPR), 2020, pp.\u00a08940\u20138949."},{"key":"2026012407010959557_j_auto-2024-0132_ref_041","unstructured":"N. Shazeer, et al.., \u201cOutrageously large neural networks: the sparsely-gated mixture-of-experts layer,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2017."},{"key":"2026012407010959557_j_auto-2024-0132_ref_011","doi-asserted-by":"crossref","unstructured":"C. Devin, et al.., \u201cLearning modular neural network policies for multi-task and multi-robot transfer,\u201d in Proc. of the Int. Conf. on Robotics and Automation (ICRA), 2017, pp.\u00a02169\u20132176.","DOI":"10.1109\/ICRA.2017.7989250"},{"key":"2026012407010959557_j_auto-2024-0132_ref_021","doi-asserted-by":"crossref","unstructured":"R. Ivanov, et al.., \u201cCompositional learning and verification of neural network controllers,\u201d ACM Trans. Embed. Comput. Syst., vol.\u00a020, no.\u00a05s, pp.\u00a01\u201326, 2021, https:\/\/doi.org\/10.1145\/3477023.","DOI":"10.1145\/3477023"},{"key":"2026012407010959557_j_auto-2024-0132_ref_017","doi-asserted-by":"crossref","unstructured":"S. Gowal, et al.., \u201cScalable verified training for provably robust image classification,\u201d in Proc. of the IEEE\/CVF Int. Conf. on Computer Vision (ICCV), 2019, pp.\u00a04841\u20134850.","DOI":"10.1109\/ICCV.2019.00494"},{"key":"2026012407010959557_j_auto-2024-0132_ref_033","unstructured":"A. Madry, et al.., \u201cTowards deep learning models resistant to adversarial attacks,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2018."},{"key":"2026012407010959557_j_auto-2024-0132_ref_009","doi-asserted-by":"crossref","unstructured":"C. Brix, et al.., \u201cFirst three years of the international verification of neural networks competition (VNN-COMP),\u201d Int. J. Software Tool. Technol. Tran., vol.\u00a025, no.\u00a03, pp.\u00a0329\u2013339, 2023, https:\/\/doi.org\/10.1007\/s10009-023-00703-4.","DOI":"10.1007\/s10009-023-00703-4"},{"key":"2026012407010959557_j_auto-2024-0132_ref_022","doi-asserted-by":"crossref","unstructured":"G. Katz, et al.., \u201cReluplex: an efficient SMT solver for verifying deep neural networks,\u201d in Int. Conf. on Computer Aided Verification (CAV), 2017, pp.\u00a097\u2013117.","DOI":"10.1007\/978-3-319-63387-9_5"},{"key":"2026012407010959557_j_auto-2024-0132_ref_012","unstructured":"C. Ferrari, et al.., \u201cComplete verification via multi-neuron relaxation guided branch-and-bound,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2022."},{"key":"2026012407010959557_j_auto-2024-0132_ref_025","doi-asserted-by":"crossref","unstructured":"N. Kochdumper, et al.., \u201cOpen- and closed-loop neural network verification using polynomial zonotopes,\u201d in NASA Formal Methods, 2023, pp.\u00a016\u201336.","DOI":"10.1007\/978-3-031-33170-1_2"},{"key":"2026012407010959557_j_auto-2024-0132_ref_042","unstructured":"G. Singh, et al.., \u201cFast and effective robustness certification,\u201d in Advances in Neural Information Processing Systems (NeurIPS), 2018."},{"key":"2026012407010959557_j_auto-2024-0132_ref_029","doi-asserted-by":"crossref","unstructured":"T. Ladner and M. Althoff, \u201cAutomatic abstraction refinement in neural network verification using sensitivity analysis,\u201d in Proc. of the Int. Conf. on Hybrid Systems: Computation and Control (HSCC), 2023, pp.\u00a01\u201313.","DOI":"10.1145\/3575870.3587129"},{"key":"2026012407010959557_j_auto-2024-0132_ref_014","doi-asserted-by":"crossref","unstructured":"G. Antoine, \u201cReachability of uncertain linear systems using zonotopes,\u201d in Proc. of the Int. Conf. on Hybrid Systems: Computation and Control (HSCC), 2005, pp.\u00a0291\u2013305.","DOI":"10.1007\/978-3-540-31954-2_19"},{"key":"2026012407010959557_j_auto-2024-0132_ref_036","unstructured":"M. N. M\u00fcller, et al.., \u201cCertified training: small boxes are all you need,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2023."},{"key":"2026012407010959557_j_auto-2024-0132_ref_013","doi-asserted-by":"crossref","unstructured":"J. Gast and S. Roth, \u201cLightweight probabilistic deep networks,\u201d in Proc. of the IEEE\/CVF Conf. on Computer Vision and Pattern Recognition (CVPR), 2018, pp.\u00a03369\u20133378.","DOI":"10.1109\/CVPR.2018.00355"},{"key":"2026012407010959557_j_auto-2024-0132_ref_003","doi-asserted-by":"crossref","unstructured":"M. Althoff, O. Stursberg, and M. Buss, \u201cSafety assessment for stochastic linear systems using enclosing hulls of probability density functions,\u201d in Europ. Control Conf. (ECC), 2009, pp.\u00a0625\u2013630.","DOI":"10.23919\/ECC.2009.7074473"},{"key":"2026012407010959557_j_auto-2024-0132_ref_007","unstructured":"C. M. Bishop, Pattern Recognition and machine Learning, New York, NY, Springer, 2006."},{"key":"2026012407010959557_j_auto-2024-0132_ref_002","unstructured":"M. Althoff, \u201cReachability analysis and its application to the safety assessment of autonomous cars,\u201d Ph.D. thesis. Technische Universit\u00e4t M\u00fcnchen, 2010."},{"key":"2026012407010959557_j_auto-2024-0132_ref_030","unstructured":"T. Ladner and M. Althoff, \u201cFully automatic neural network reduction for formal verification,\u201d arXiv: 2305.01932[cs.LG], 2024, Available at: https:\/\/arxiv.org\/abs\/2305.01932."},{"key":"2026012407010959557_j_auto-2024-0132_ref_031","unstructured":"T. Ladner, M. Eichelbeck, and M. Althoff, \u201cFormal verification of graph convolutional networks with uncertain node features and uncertain graph structure,\u201d arXiv: 2404.15065 [cs.LG], 2024, Available at: https:\/\/arxiv.org\/abs\/2404.15065."},{"key":"2026012407010959557_j_auto-2024-0132_ref_043","doi-asserted-by":"crossref","unstructured":"T. Zafer, \u201cAn experimental study on the examination of springback of sheet metals with several thicknesses and properties in bending dies,\u201d J. Mater. Process. Technol., vol.\u00a0145, no.\u00a01, pp.\u00a0109\u2013117, 2004, https:\/\/doi.org\/10.1016\/j.jmatprotec.2003.07.005.","DOI":"10.1016\/j.jmatprotec.2003.07.005"},{"key":"2026012407010959557_j_auto-2024-0132_ref_001","unstructured":"A. Matthias, \u201cAn introduction to CORA 2015,\u201d in Proc. of the Workshop on Applied Verification for Continuous and Hybrid Systems (ARCH), 2015, pp.\u00a0120\u2013151."},{"key":"2026012407010959557_j_auto-2024-0132_ref_035","unstructured":"M. Mirman, T. Gehr, and M. Vechev, \u201cDifferentiable abstract interpretation for provably robust neural networks,\u201d in Proc. of the Int. Conf. on Machine Learning (ICML), 2018, pp.\u00a03578\u20133586."},{"key":"2026012407010959557_j_auto-2024-0132_ref_015","unstructured":"X. Glorot and Y. Bengio, \u201cUnderstanding the difficulty of training deep feedforward neural networks,\u201d in Proc. of the Int. Conf. on Artificial Intelligence and Statistics (AISTATS), 2010, pp.\u00a0249\u2013256."},{"key":"2026012407010959557_j_auto-2024-0132_ref_023","unstructured":"D. P. Kingma and J. Ba, \u201cAdam: a method for stochastic optimization,\u201d in Proc. of the Int. Conf. on Learning Representations (ICLR), 2015."}],"container-title":["at - Automatisierungstechnik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/auto-2024-0132\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/auto-2024-0132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,24]],"date-time":"2026-01-24T07:01:23Z","timestamp":1769238083000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyterbrill.com\/document\/doi\/10.1515\/auto-2024-0132\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,26]]},"references-count":48,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,2,26]]},"published-print":{"date-parts":[[2025,3,26]]}},"alternative-id":["10.1515\/auto-2024-0132"],"URL":"https:\/\/doi.org\/10.1515\/auto-2024-0132","relation":{},"ISSN":["0178-2312","2196-677X"],"issn-type":[{"value":"0178-2312","type":"print"},{"value":"2196-677X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,26]]}}}