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

In this project, a new, point cloud-based methodology for the forward and backward simulation of structures is being researched. In the first phase, previous work was taken up that directly couples a 3D point cloud resulting from stereographic image processing with a structural analysis of the body in question. This new approach is based on the finite cell method (FCM), a higher-order embedded domain method. Using the FCM as an analysis tool, a specific point membership test can be defined, which makes it possible to completely bypass the reconstruction of a surface model and the subsequent time-consuming and error-prone generation of a spatial finite element mesh. This drastically reduces the effort required for image-based structural analysis. However, since only data about the surface of the structure is available from the point cloud, this forward analysis requires assumptions regarding the interior of the body, for example that it is uniformly filled with a homogeneous material. The first goal of the proposed project was to generalize this approach to a simulation of acoustic and elastic wave propagation and to develop tailored formulations for point cloud-based boundary conditions. The forward analysis was then extended to solve an inverse problem on the geometry defined by point clouds. It was found that scaling the density in the Full Waveform Inversion (FWI) method is particularly advantageous to identify voids inside the structure. As the algorithmic core for the forward and backward simulation of the FWI, the Spectral Cell Method (SCM), an extension of the Finite Cell Method, was supplemented by an IMEX approach, which integrates the wave equation explicitly on uncut and implicitly on cut cells in time. This combines the efficient solution of structural dynamics problems with the geometric flexibility of embedded domain methods. With this approach, a methodology with significantly improved functionality for non-destructive testing (NDT) has now been developed. In the second phase of this project, we plan to compare this method with established methods such as the Total Focusing Method and with experiments conducted at the Chair of NDT at TUM. These experiments are of increasing difficulty so that the improvement of the method development planned in the second phase can be accurately assessed. This includes modelling the distributed source properties of piezoelectric transducers by means of inversion as well as improving the inversion results through regularization.

• DFG Programme: Research Grants