A methodology to adapt optical deformation analysis in material characterization and model validation

光学变形分析已成为材料表征和模型验证的核心部分。在工程领域，除了光学传感器和计算机硬件的不断进步之外，数字图像相关领域的成就也支持了这一发展。然而，当在实践中使用数字图像相关时，仍然存在关键的挑战，特别是对于三维测量任务，例如（独立于用户）选择合适的初始值和算法中的自适应评估参数，评估变量（通常是应变）及其时空推导的有意义的计算，包括环境影响或处理不连续性。在抽象的形式，这些现有的挑战可以解释的事实，光学变形分析是一个数学不适定的问题。一方面，这涉及跟踪材料点随时间的运动的任务，并且在立体或多相机系统的情况下，涉及测量对象的空间重建。通过引入假设和边界条件来解决数学上的问题，在某种程度上也可以理解为通过数据同化和正则化的方法来建模测量任务。在申请的研究项目中，这些方法是在材料表征和测试的背景下进行的，设计和研究。用于解决数学不适定问题的假设和边界条件不仅应适用于手头的测量任务，而且还应考虑记录信息的进一步使用，特别是用于参数识别和模型验证。预期研究项目的目的是，从计算机视觉领域的理论基础出发，一方面在整个系统的虚拟环境中，另一方面在真实的实验中，了解光学检测，评估方法和建模环境之间的耦合连接。

Optical deformation analysis has become a core part of materials characterization and model validation. In the field of engineering, this development is supported by achievements in the field of digital image correlation, in addition to constant progress in optical sensors and computer hardware. When using digital image correlation in practice, however, there are still critical challenges, especially for three-dimensional measurement tasks, such as the (user-independent) selection of suitable initial values and adapted evaluation parameters in the algorithm, the meaningful calculation of the evaluation variables (usually strains) and their spatio-temporal derivations, the inclusion of environmental influences or dealing with discontinuities. In abstract form, these existing challenges can be explained by the fact that optical deformation analysis is a mathematically ill-posed problem. On the one hand, this concerns the task of tracking the motion of material points over time and, in the case of stereo or multi-camera systems, the spatial reconstruction of the measurement object. The mathematically ill problem is countered by the introduction of assumptions and boundary conditions, which in a certain respect can also be understood as modeling of the measurement task, by approaches of data assimilation and regularization. In the research project applied for, these approaches are taken up, designed and researched against the background of material characterization and testing. Assumptions and boundary conditions for solving the mathematically ill-posed problem should not only be adaptable to the measurement task at hand, but also take into account the further use of the recorded information, especially for parameter identification and model validation. The aim of the intended research project is, starting from the theoretical foundation of the field of computer vision, to understand the coupled connections between optical detection, evaluation approach and modeling context, on the one hand in a virtual environment of this overall system and on the other hand in a real experiment.