3-D Eddy-Current Imaging of Metal Tubes by Gradient-Based, Controlled Evolution of Level Sets

Eddy-current nondestructive testing is widely used to detect defects within a metal structure. It is also useful to characterize their location and shape provided that proper maps of variations of impedance that the defects induce are available. Imaging of void defects in the wall of a hollow, nonmagnetic metal tube, is performed herein by controlled evolution of level sets. Such data are variations of impedance data collected by a circular probe array close to the inner surface of the tube when a coil source operated at one single frequency is set along its axis at some distance from the array, both receiver and coil source being moved simultaneously. The defect zone is represented in implicit fashion as a zero level set, which is amenable to topological changes via a nonlinear iterative method that minimizes a least-square cost functional made of the difference between the measured (computer simulated) and model data. The procedure requires the rigorous calculation of the gradient of the variations of impedance, in the case of a multistatic configuration (different driver and receiver coils), a vector domain integral field formulation being used for that purpose. Numerical examples developed by a dedicated extension of the general-purpose CIVA platform show pros and cons of the approach for inner, outer, and through-wall void defects. Further comparisons present results provided by an independently developed binary-specialized method.