@misc{LehrerKapsDaimingeretal., author = {Lehrer, Tobias and Kaps, Arne and Daiminger, Tobias and Lepenies, Ingolf and Duddeck, Fabian and Wagner, Marcus}, title = {Analysis of Global Sensitivities for One-Step and Multi-step Deep-Drawing Simulations}, series = {16th German LS-DYNA Forum : October 11-13, 2022, Bamberg, Germany and online : Book of Abstracts}, journal = {16th German LS-DYNA Forum : October 11-13, 2022, Bamberg, Germany and online : Book of Abstracts}, publisher = {DYNAmore GmbH}, address = {Stuttgart}, isbn = {978-3-9816215-8-7}, pages = {117 -- 118}, abstract = {In practical use cases, simulation engineers are confronted with uncertainties in the simulation parameters. Normally, trust in a model is built from experience, practical assumptions, and parameter studies. This approach, though, is based on the assumption that few parameter combinations are sufficient to represent the whole design space. This lacks an appraisable mathematical basis. To get insights into which parameters most strongly affect the results, a global sensitivity analysis can be conducted [2, 3]. The results are utilized to rank the most influential parameters and to filter less relevant ones. This gives feedback which improved set of input data will lead to more certainty in the simulation results. To enable this in the framework of multi-fidelity analysis and optimization, we compare here global sensitivities and uncertainties of the implicit One-Step approach (low-fidelity) with those of the explicit multi-step deep drawing approach (high-fidelity).}, language = {en} } @article{SchmailzlKaesbauerMartanetal., author = {Schmailzl, Anton and K{\"a}sbauer, Johannes and Martan, Jiř{\´i} and Honnerov{\´a}, Petra and Sch{\"a}fer, Felix and Fichtl, Maximilian and Lehrer, Tobias and Pruš{\´a}kov{\´a}, L. and Tesař, Jiř{\´i} and Sk{\´a}la, J. and Honner, Milan and Hierl, Stefan}, title = {Measurement of Core Temperature through Semi-Transparent Polyamide 6 using Scanner-Integrated Pyrometer in Laser Welding}, series = {International Journal of Heat and Mass Transfer}, volume = {146}, journal = {International Journal of Heat and Mass Transfer}, number = {January}, publisher = {Elsevier}, doi = {10.1016/j.ijheatmasstransfer.2019.118814}, abstract = {Predicting the core temperature during welding is an ambitious aim in many research works. In this work, a 3D-scanner with integrated pyrometer is characterized and used to measure the temperature during quasi-simultaneous laser transmission welding of polyamide 6. However, due to welding in an overlap configuration, the heat radiation emitted from the joining zone of a laser transmission weld has to pass through the upper polymer, which is itself a semi-transparent emitter. Therefore, the spectral filtering of the heat radiation in the upper polymer is taken into account by calibrating the pyrometer for the measurement task. Thermal process simulations are performed to compare the temperature field with the measured temperature signal. The absorption coefficients of the polymers are measured, in order to get precise results from the computation. The temperature signals during welding are in good agreement with the computed mean temperature inside the detection spot, located in the joining area. This is also true for varying laser power, laser beam diameter and the carbon black content in the lower polymer. Both, the computed mean temperature and the temperature signal are representing the core temperature. In order to evaluate the spatial sensitivity of the measurement system, the emitted heat radiation from both polymers is calculated on basis of the computed temperature field. Hereby it is found, that more than 90 percent of the detected heat radiation comes from the joining area, which is a crucial information for contact-free temperature measurement tasks on semi-transparent polymers.}, language = {en} } @inproceedings{WagnerLehrerFrankeetal., author = {Wagner, Marcus and Lehrer, Tobias and Franke, Markus and Al-Abadi, Ali and Gamil, Ahmed}, title = {A Tank Resonance Model for Power Transformers}, series = {ARWtr 2022 proceedings, 2022 7th Advanced Research Workshop on Transformers (ARWtr): October (23)24-26, 2022, Baiona, Spain}, booktitle = {ARWtr 2022 proceedings, 2022 7th Advanced Research Workshop on Transformers (ARWtr): October (23)24-26, 2022, Baiona, Spain}, publisher = {IEEE}, organization = {Institute of Electrical and Electronics Engineers (IEEE)}, doi = {10.23919/ARWtr54586.2022.9959917}, pages = {7 -- 12}, abstract = {During the factory acceptance test, the sound levels are measured. If the measured sound levels exceed pre-specified values, modifications on the transformer's active part and/or tank need to be conducted. Tank resonance, if occurs, at twice main power frequency and its higher harmonics is one of the main reasons of amplifying the generated sound levels. Therefore, it is preferable to know already in the design stage about the occurrence of the tank resonance and propose reliable tank solutions. The current study presents a newly developed model for calculating the mode shapes and its corresponding eigenfrequencies of the tank.}, language = {en} } @article{KapsLehrerLepeniesetal., author = {Kaps, Arne and Lehrer, Tobias and Lepenies, Ingolf and Wagner, Marcus and Duddeck, Fabian}, title = {Multi-fidelity optimization of metal sheets concerning manufacturability in deep-drawing processes}, series = {Structural and Multidisciplinary Optimization}, volume = {66}, journal = {Structural and Multidisciplinary Optimization}, publisher = {Springer Nature}, doi = {10.1007/s00158-023-03631-8}, abstract = {Multi-fidelity optimization, which complements an expensive high-fidelity function with cheaper low-fidelity functions, has been successfully applied in many fields of structural optimization. In the present work, an exemplary cross-die deep-drawing optimization problem is investigated to compare different objective functions and to assess the performance of a multi-fidelity efficient global optimization technique. To that end, hierarchical kriging is combined with an infill criterion called variable-fidelity expected improvement. Findings depend significantly on the choice of objective function, highlighting the importance of careful consideration when defining an objective function. We show that one function based on the share of bad elements in a forming limit diagram is not well suited to optimize the example problem. In contrast, two other definitions of objective functions, the average sheet thickness reduction and an averaged limit violation in the forming limit diagram, confirm the potential of a multi-fidelity approach. They significantly reduce computational cost at comparable result quality or even improve result quality compared to a single-fidelity optimization.}, language = {en} } @article{LehrerStockerDuddecketal., author = {Lehrer, Tobias and Stocker, Philipp and Duddeck, Fabian and Wagner, Marcus}, title = {UCSM: Dataset of U-shaped parametric CAD geometries and real-world sheet metal meshes for deep drawing}, series = {Computer-aided design}, volume = {188}, journal = {Computer-aided design}, publisher = {Elsevier}, doi = {10.1016/j.cad.2025.103924}, pages = {17}, abstract = {The development of machine learning (ML) applications in deep drawing is hindered by limited data availability and the absence of open-access benchmarks for validating novel approaches, including domain generalization over distinct geometries. This paper addresses these challenges by introducing a comprehensive U-shaped dataset tailored to this manufacturing process. Our U-Channel sheet metal (UCSM) dataset combines 90 real-world meshes with an infinite number of synthetic geometry samples generated from four parametric Computer-Aided Design (CAD) models, ensuring extensive geometry variety and data quantity. Additionally, a ready-to-use dataset for drawability assessment and segmentation is provided. Leveraging CAD and mesh data sources bridges the gap between sparse data availability and ML requirements. Our analysis demonstrates that the proposed parametric models are geometrically valid, and real-world and synthetic data complement each other effectively, providing robust support for ML model development. While the dataset is confined to U-shaped, thin-walled, deep drawing scenarios, it considerably aids in overcoming data scarcity. Thereby, it facilitates the validation and comparison of new geometry-generalizing ML methodologies in this domain. By providing this benchmark dataset, we enhance the comparability and validation of emerging methods for ML advancements in sheet metal forming.}, language = {en} } @article{LehrerKapsLepeniesetal., author = {Lehrer, Tobias and Kaps, Arne and Lepenies, Ingolf and Raponi, Elena and Wagner, Marcus and Duddeck, Fabian}, title = {Complementing Drawability Assessment of Deep-Drawn Components with Surrogate-Based Global Sensitivity Analysis}, series = {ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering}, journal = {ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering}, publisher = {ASME}, issn = {2332-9025}, doi = {10.1115/1.4065143}, pages = {1 -- 10}, abstract = {In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions. Complementing this process with a global sensitivity analysis can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component. Here, we show in an exemplary application problem, that both a standard kriging model and an ensemble model can provide commendable results at a fraction of the computational cost. Moreover, we compare our surrogate models to existing approaches in the field. Furthermore, we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.}, language = {en} } @article{LehrerKapsLepeniesetal., author = {Lehrer, Tobias and Kaps, Arne and Lepenies, Ingolf and Duddeck, Fabian and Wagner, Marcus}, title = {2S-ML: A simulation-based classification and regression approach for drawability assessment in deep drawing}, series = {International Journal of Material Forming}, volume = {16}, journal = {International Journal of Material Forming}, publisher = {Springer}, doi = {10.1007/s12289-023-01770-3}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-64664}, pages = {1 -- 17}, abstract = {New structural sheet metal parts are developed in an iterative, time-consuming manner. To improve the reproducibility and speed up the iterative drawability assessment, we propose a novel low-dimensional multi-fidelity inspired machine learning architecture. The approach utilizes the results of low-fidelity and high-fidelity finite element deep drawing simulation schemes. It hereby relies not only on parameters, but also on additional features to improve the generalization ability and applicability of the drawability assessment compared to classical approaches. Using the machine learning approach on a generated data set for a wide range of different cross-die drawing configurations, a classifier is trained to distinguish between drawable and non-drawable setups. Furthermore, two regression models, one for drawable and one for non-drawable designs are developed that rank designs by drawability. At instantaneous evaluation time, classification scores of high accuracy as well as regression scores of high quality for both regressors are achieved. The presented models can substitute low-fidelity finite element models due to their low evaluation times while at the same time, their predictive quality is close to high-fidelity models. This approach may enable fast and efficient assessments of designs in early development phases at the accuracy of a later design phase in the future.}, language = {en} } @misc{LehrerStockerDuddecketal., author = {Lehrer, Tobias and Stocker, Philipp and Duddeck, Fabian and Wagner, Marcus}, title = {Comparison of Low- vs. High-Dimensional Machine Learning Approaches for Sheet Metal Drawability Assessment}, series = {Third International Conference on Computational Science and AI in Industry (CSAI 2023), Trondheim, Norway, 28-30 August 2023}, journal = {Third International Conference on Computational Science and AI in Industry (CSAI 2023), Trondheim, Norway, 28-30 August 2023}, publisher = {International Centre for Numerical Methods in Engineering}, doi = {10.35096/othr/pub-6477}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:898-opus4-64772}, abstract = {Developing new deep-drawn sheet metal parts is a challenging task due to conflicting demands for low costs, durability, and crash properties. Ensuring manufacturability throughout geometrical changes adds to the complexity, leading engineers to rely on experience-driven iterative design changes that compromise requirements and lack reproducibility. Finite Element (FE) simulation models are employed to ensure manufacturability, albeit at the expense of high computational costs and delays in part development. To improve efficiency, a Machine learning (ML)-centered approach was proposed to ensure manufacturability. However, the limited availability of data raises uncertainty about whether a low- or high-dimensional ML approach is most suitable for drawability assessment. This work compares the accuracy of a low-dimensional, feature-based Linear Support Vector surrogate and an adapted high-dimensional PointNet model under different dataset sizes. The dataset is composed of parametrically generated, U-shaped structural sheet metal parts. We use a one-step simulation scheme and evaluate results with a Forming Limit Diagram (FLD) to label drawability. Results show the point of transition to be at about 500 training samples, from which onwards Deep learning is advantageous. Moreover, the generalizability of these models is tested on a second dataset with topologically similar components. This is to assess the potential for a geometrically more comprehensive evaluation. We discuss several influences on model performances and outline future potentials.}, language = {en} } @inproceedings{StockerLehrerDuddecketal., author = {Stocker, Philipp and Lehrer, Tobias and Duddeck, Fabian and Wagner, Marcus}, title = {Face-wise prediction of sheet-metal drawability using graph neural networks}, series = {Journal of Physics: Conference Series}, volume = {3104}, booktitle = {Journal of Physics: Conference Series}, number = {1}, publisher = {IOP Publishing}, issn = {1742-6588}, doi = {10.1088/1742-6596/3104/1/012053}, pages = {11}, abstract = {The early design phase of deep-drawn structural components involves time-consuming iterative development. Traditional drawability assessments rely on finite element simulations, which are computationally expensive and slow the design process. Alternative machine learning (ML) approaches show promise in accelerating this process but face challenges with existing methods. Existing low-dimensional ML models only provide global predictions without identifying specific geometric regions prone to failure. High-dimensional models provide local predictions but require significant amounts of training data. We propose a data-driven approach leveraging graph neural networks (GNNs) for face-wise drawability prediction of sheet metal components in their computer-aided design (CAD) representation. Our method aims to bridge the gap between the computational efficiency of ML and the spatial resolution of simulation by providing face-wise insight into potential failure regions. This study utilises a dataset of parametric U-channel geometries with variability in both geometry and topology. Ground-truth labels are generated using inverse analysis simulations. Geometric entities are represented through the use of UV parameterisations, whereby 3D surfaces are mapped into 2D space to facilitate geometric encoding. Concurrently, the topological relationships are captured using a face adjacency graph. To address data scarcity, we evaluate how different amounts of training data affect model performance and perform ablation studies to analyse the impact of different CAD representation features. Our results show that the proposed approach achieves high accuracy even with limited training data. In addition, the ablation studies provide insights into the most critical CAD features, guiding future research. These results highlight the potential of our GNN to predict face-wise drawability in the early design phase.}, language = {en} } @unpublished{LehrerStockerDuddecketal., author = {Lehrer, Tobias and Stocker, Philipp and Duddeck, Fabian and Wagner, Marcus}, title = {UCSM: Dataset of U-Shaped Parametric CAD Geometries and Real-World Sheet Metal Meshes for Deep Drawing}, publisher = {SSRN}, doi = {10.2139/ssrn.5268323}, pages = {19}, abstract = {The development of machine learning (ML) applications in deep drawing is hindered by limited data availability and the absence of open-access benchmarks for validating novel approaches, including domain generalization over distinct geometries. This paper addresses these challenges by introducing a comprehensive U-shaped dataset tailored to this manufacturing process. Our U-Channel sheet metal (UCSM) dataset combines 90 real-world meshes with an infinite number of synthetic geometry samples generated from four parametric Computer-Aided Design (CAD) models, ensuring extensive geometry variety and data quantity. Additionally, a ready-to-use dataset for drawability assessment and segmentation is provided. Leveraging CAD and mesh data sources bridges the gap between sparse data availability and ML requirements. Our analysis demonstrates that the proposed parametric models are geometrically valid, and real-world and synthetic data complement each other effectively, providing robust support for ML model development. While the dataset is confined to U-shaped, thin-walled, deep drawing scenarios, it considerably aids in overcoming data scarcity. Thereby, it facilitates the validation and comparison of new geometry-generalizing ML methodologies in this domain. By providing this benchmark dataset, we enhance the comparability and validation of emerging methods for ML advancements in sheet metal forming.}, language = {en} } @misc{StockerLehrer, author = {Stocker, Philipp and Lehrer, Tobias}, title = {Machine Learning Dataset of U-Channel Sheet Metal Geometry Representations with Supervision Information for Drawability Assessment and Part Segmentation [Data set]}, doi = {10.5281/zenodo.15327950}, abstract = {The dataset contains 2533 geometries from four different parametric CAD models sampled from the U-Channel python package. The representations include the original CAD geometries (.step), graph binaries (.bin), meshes (.off), and point clouds (.xyz). Additionally, we provide labels for supervised learning use cases of local and global drawability assessment and part segmentation (.json) for all representations. Custom label computation for drawability assessment is enabled by the provided strains.zip file, which contains minor and major true strains for the given meshes. For more details, refer to the associated publication.}, language = {en} }