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外，数字图像相关领域的成就也支持了这一发展。然而，在实际应用数字图像相关时，仍然存在重大挑战，特别是对于三维测量任务，例如（独立于用户）在算法中选择合适的初始值和自适应的评估参数，评估变量（通常是应变）及其时空衍生的有意义的计算，包括环境影响或处理不连续。在抽象形式中，这些存在的挑战可以用光学变形分析是一个数学上的病态问题这一事实来解释。一方面，这涉及到跟踪材料点随时间的运动的任务，以及在立体或多相机系统的情况下，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，这在某种程度上也可以理解为通过数据同化和正则化方法对测量任务进行建模。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设计和研究的。解决数学上不适定问题的假设和边界条件不仅要适应手头的测量任务，而且要考虑到记录信息的进一步利用，特别是参数识别和模型验证。本拟研究项目的目的是，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、评估方法和建模上下文之间的耦合联系。

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.