Numerical modeling and inverse profiling in non-destructive testing

This paper presents mainly two examples of numerical modeling and inverse profiling in non-destructive testing. As the first example, we discuss numerical modeling and optimization of eddy current sensors for the in-line inspection of the hot wire steel. Any type of crack on the upper surface of the steel wire disturbs the eddy current distribution which can be detected by the eddy current sensors. However, the eddy current distribution is only weakly influenced by cracks which are parallel to the wire, so-called longitudinal cracks. To detect such longitudinal cracks a series of new sensors are developed, optimized by numerical modeling and successfully tested. As the second example, we present a time-domain technique to reconstruct the unknown permittivity and electric conductivity profile of a one-dimensional slab of finite length. The inverse scattering problem is solved by an invariant embedding method which requires a finite time trace of reflection data and therefore, is suitable for reconstructing the material parameters in real-time. The implemented method is validated against synthetic and measured time domain reflectometry (TDR) data. Thus, the 1-D profile reconstruction technique fulfils an identified need to determine unknown one-dimensional profiles and hence, plays an important role in electromagnetics, non-destructive testing and geophysics.