Point Cloud Based Waveform Inversion

本项目旨在开发一种基于点云的结构正反演分析新技术。在我们以前的工作中，我们已经开发出一种方法，直接耦合的三维点云从立体图像处理所产生的结构分析的身体正在考虑。这种新方法是基于有限单元法（FCM），高阶嵌入域方法，已成功地应用于许多问题的计算力学。使用FCM作为分析工具，可以定义一个特定的点隶属度测试，它允许规避重建的表面模型，以及耗时和容易出错的空间有限元网格的生成。因此，大大减少了基于图像的结构分析的工作量。然而，由于从点云中只能获得结构表面的数据，因此这种向前分析需要对物体内部进行假设，例如，它均匀地填充有均匀的材料。该项目的第一个目标是将目前的方法推广到波的传播，并为基于点云的边界条件开发定制的公式。然后，将正演分析扩展到解决由点云定义的几何形状上的逆问题。将应用全波形反演（FWI）来识别结构的内部，包括退化材料或空隙等缺陷。作为FWI正演分析的算法核心，我们打算使用谱单元法（SCM），它是有限单元法的扩展，可求解非均匀介质的弹性波方程。SCM将结构动力学问题的有效解决方案与嵌入域方法的几何通用性相结合。通过这种方法，我们希望开发一种方法，具有强大的增强功能的无损检测（NDT），特别是在案件中，没有以前的数字模型的几何形状的测试机构。在该项目的第二阶段，我们计划将我们的理论和算法工作与TUM无损检测主席的超声NDT实验研究相结合，并最终将其应用于示例性调查，例如文化遗产文物。

This project aims at developing a new technology for the forward and inverse analysis of structures based on point clouds. In our previous work, we have developed a methodology to directly couple a 3D point cloud resulting from stereographic image processing to the structural analysis of the body under consideration. This new approach is based on the Finite Cell Method (FCM), a higher order embedded domain method, which has been successfully applied to many problems in Computational Mechanics. Using FCM as analysis tool a specific Point Membership Test can be defined which allows circumventing the reconstruction of a surface model as well as the time consuming and error-prone generation of a spatial finite element mesh. Thus, the effort for an image-based structural analysis is drastically reduced. Yet, as only data on the surface of the structure is available from the point cloud, this forward analysis requires assumptions on the interior of the body, e.g. that it is uniformly filled with homogeneous material. The first goal of the proposed project is to generalize this present approach to wave propagation and to develop tailored formulations for point cloud based boundary conditions. Then the forward analysis shall be extended to solve an inverse problem on the geometry defined by point clouds. Full Waveform Inversion (FWI) will be applied to identify the interior of the structure including flaws like degenerate material or voids. As algorithmic kernel for the forward analysis of the FWI we intend to use the Spectral Cell Method (SCM), an extension of the Finite Cell Method, which solves the elastic wave equation for heterogeneous media. SCM combines the efficient solution of problems in structural dynamics with the geometric versatility of the embedded domain method. With this approach, we expect to develop a methodology with strongly enhanced capabilities for Non Destructive Testing (NDT), in particular for cases, where no previous digital model of the geometry of a tested body is available. In a second phase of this project we plan to combine our theoretical and algorithmic work with experimental research on Ultrasound NDT of the TUM Chair for Non Destructive Testing and finally apply it to an exemplary investigation, e.g. of cultural heritage artifacts.