Ray Tracing Boundary Value Problems: Simulation and SAFT Reconstruction for Ultrasonic Testing

Please always quote using this URN: urn:nbn:de:0297-zib-58386
  • The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave propagation through the material, in particular travel times between two points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points. In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the eikonal equation. The implementation of such a two point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools. As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value problem allows a straightforward derivation of the ray path from a given transducer position to any pixel in the reconstruction area and reduces the computational cost considerably.

Download full text files

Export metadata

Author:Sebastian Götschel, Christian Höhne, Sanjeevareddy Kolkoori, Steffen Mitzscherling, Jens Prager, Martin WeiserORCiD
Document Type:ZIB-Report
Tag:ODE boundary value problems; nondestructive testing; ray tracing; ultrasonics
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Lxx Ordinary differential equations / 65L10 Boundary value problems
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Exx Material properties given special treatment / 74E05 Inhomogeneity
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Exx Material properties given special treatment / 74E10 Anisotropy
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Jxx Waves / 74J25 Inverse problems
Date of first Publication:2016/03/23
Series (Serial Number):ZIB-Report (16-14)
Published in:Appeared in: Proceedings 19th World Conference on Non-Destructive Testing (WCNDT 2016)