Point Cloud Based Waveform Inversion

• Applicants: Professor Dr.-Ing. Stefan Kollmannsberger; Professor Dr. Ernst Rank
• Subject Area: Applied Mechanics, Statics and Dynamics ; Structural Engineering, Building Informatics and Construction Operation
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 438252876

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.

• DFG Programme: Research Grants