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.

Abstract In the early stages of engineering design, multitudes of feasible designs can be generated using structural optimization methods by varying the design requirements or user preferences for different performance objectives. Data mining such potentially large datasets is a challenging task. An unsupervised data-centric approach for exploring designs is to find clusters of similar designs and recommend only the cluster representatives for review. Design similarity can be defined not only on a purely functional level but also based on geometric properties, such as size, shape, and topology. While metrics such as chamfer distance measure the geometrical differences intuitively, it is more useful for design exploration to use metrics based on geometric features, which are extracted from high-dimensional 3D geometric data using dimensionality reduction techniques. If the Euclidean distance in the geometric features is meaningful, the features can be combined with performance attributes resulting in an aggregate feature vector that can potentially be useful in design exploration based on both geometry and performance. We propose a novel approach to evaluate such derived metrics by measuring their similarity with the metrics commonly used in 3D object classification. Furthermore, we measure clustering accuracy, which is a state-of-the-art unsupervised approach to evaluate metrics. For this purpose, we use a labeled, synthetic dataset with topologically complex designs. From our results, we conclude that Pointcloud Autoencoder is promising in encoding geometric features and developing a comprehensive design exploration method.

Topology optimization optimizes material layout in a design space for a given objective, such as crash energy absorption, and a set of boundary conditions. In industrial applications, multi-objective topology optimization requires expensive simulations to evaluate the objectives and generate multiple Pareto-optimal solutions. So, it is more economical to identify preferred regions on the Pareto front and generate only the desired solutions. Clustering methods, a widely used subclass of machine learning methods, provide an unsupervised approach to summarize the dataset, which eases the identification of the preferred set of designs. However, generating solutions similar to the preferred designs based on different metrics is a challenging task. In this paper, we present an interactive method to generate designs similar to a preferred set using one of the state-of-the-art weighted-sum approaches called scaled energy weighting - hybrid cellular automata (SEW-HCA). To avoid unnecessary computations, metamodels are used to predict the desired weight vectors needed by SEW-HCA. We evaluate an application of our method for cooperative topology optimization using a cantilever multi-load-case problem and a crashworthiness optimization problem. Using the proposed method, we could successfully generate designs that are similar to preferred solutions based on geometry and performance. We believe that this is a crucial component that will improve the usefulness of multi-objective topology optimization in real-world applications.

This work presents a hybrid optimization approach that couples Efficient Global Optimization (EGO) and Co-variance Matrix Adaptation Evolution Strategy (CMA-ES) in the Topology Optimization (TO) of mechanical structures. Both of these methods are regarded as good optimization strategies for continuous global optimization of expensive and multimodal problems, e.g. associated with vehicle crashworthiness. CMA-ES is flexible and robust to changing circumstances. Moreover, by taking advantage of a low-dimensional parametrization introduced by the Evolutionary Level Set Method (EA-LSM) for structural Topology Optimization, such Evolution Strategy allows for dealing with costly problems even more efficiently. However, it is characterized by high computational costs, which can be mitigated by using the EGO algorithm at the early stages of the optimization process. By means of surrogate models, EGO allows for the construction of cheap-to-evaluate approximations of the objective functions, leading to an initial fast convergence towards the optimum in opposition to a poor exploitive behavior. The approach presented here - the Hybrid Kriging-assisted Level Set Method (HKG-LSM) - first uses the Kriging-based method for Level Set Topology Optimization (KG-LSM) to converge fast at the beginning of the optimization process and explore the design space to find promising regions. Afterwards, the algorithm switches to the EA-LSM using CMA-ES, whose parameters are initialized based on the previous model. A static benchmark test case is used to assess the proposed methodology in terms of convergence speed. The obtained results show that the HKG-LSM represents a valuable option for speeding up the optimization process in real-world applications with limited computational resources. As such, the proposed methodology exhibits a much more general potential, e.g. when dealing with high-fidelity crash simulations.

The main goal in structural Topology Optimization is to find an optimal distribution of material within a defined design domain, under specified boundary conditions. This task is frequently solved with gradient-based methods, but for some problems, e.g. in the domain of crash Topology Optimization, analytical sensitivity information is not available. The recent Evolutionary Level Set Method (EA-LSM) uses Evolutionary Strategies and a representation based on geometric Level Set Functions to solve such problems. However, computational costs associated with Evolutionary Algorithms are relatively high and grow significantly with rising dimensionality of the optimization problem. In this paper, we propose an improved version of EA-LSM, exploiting an adaptive representation, where the number of structural components increases during the optimization. We employ a learning-based approach, where a pre-trained neural network model predicts favorable topological changes, based on the structural state of the design. The proposed algorithm converges quickly at the beginning, determining good designs in low-dimensional search spaces, and the representation is gradually extended by increasing structural complexity. The approach is evaluated on a standard minimum compliance design problem and its superiority with respect to a random adaptive method is demonstrated.

Although Topology Optimization is widely used in many industrial applications, it is still in the initial phase of development for highly nonlinear, multimodal and noisy problems, where the analytical sensitivity information is either not available or difficult to obtain. For these problems, including the highly relevant crashworthiness optimization, alternative approaches, relying not solely on the gradient, are necessary. One option are Evolutionary Algorithms, which are well-suited for this type of problems, but with the drawback of considerable computational costs. In this paper we propose a hybrid evolutionary optimization method using a geometric Level-Set Method for an implicit representation of mechanical structures. Hybrid optimization approach integrates gradient information in stochastic search to improve convergence behavior and global search properties. Gradient information can be obtained from structural state as well as approximated via equivalent state or any known heuristics. In order to evaluate the proposed methods, a minimum compliance problem for a standard cantilever beam benchmark case is considered. These results show that the hybridization is very beneficial in terms of convergence speed and performance of the optimized designs.