Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply these methods, suitable data representations for components under development as well as for related design criteria have to be found. While a component's geometry is typically represented by a polygon surface mesh, it is often not clear how to parametrize critical design properties in order to enable efficient computational analysis. In the present work, we propose a novel methodology to obtain a parameterization of a component's plastic deformation behavior under stress, which is an important design criterion in many application domains, for example, when optimizing the crash behavior in the automotive context. Existing parameterizations limit computational analysis to relatively simple deformations and typically require extensive input by an expert, making the design process time intensive and costly. Hence, we propose a way to derive a compact descriptor of deformation behavior that is based on spectral mesh processing and enables a low-dimensional representation of also complex deformations.We demonstrate the descriptor's ability to represent relevant deformation behavior by applying it in a nearest-neighbor search to identify similar simulation results in a filtering task. The proposed descriptor provides a novel approach to the parametrization of geometric deformation behavior and enables the use of state-of-the-art data analysis techniques such as machine learning to engineering tasks concerned with plastic deformation behavior.

中文翻译：

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形状变形的紧凑谱描述符

工程领域的现代产品设计越来越受到计算分析的驱动，包括基于有限元的模拟、计算优化和现代数据分析技术，如机器学习。为了应用这些方法，必须为正在开发的组件以及相关的设计标准找到合适的数据表示。虽然组件的几何形状通常由多边形表面网格表示，但通常不清楚如何对关键设计属性进行参数化以实现高效的计算分析。在目前的工作中，我们提出了一种新的方法来获得部件在应力下的塑性变形行为的参数化，这是许多应用领域的重要设计标准，例如，在汽车环境中优化碰撞行为时。现有的参数化将计算分析限制为相对简单的变形，并且通常需要专家的大量输入，这使得设计过程既费时又费钱。因此，我们提出了一种推导变形行为的紧凑描述子的方法，该描述子基于频谱网格处理并能够对复杂变形进行低维表示。邻居搜索以识别过滤任务中的相似模拟结果。