Three-dimensional (3D) eddy current non-destructive evaluation of steam generator tubes is cast in a wavefield integral framework and considered from an inverse problem point of view. Three inversion algorithms based on a gradient-type iterative search are studied: the modified gradient method, an inversion via the source-type integral equation, and one based on the localized nonlinear approximation. To overcome the inherent ill-posed nature of the inversion problem, a binary constraint is enforced on the contrast to be retrieved. Special attention is devoted to the evolution of the iterative processes, which is controlled by means of a tunable 'cooling' parameter. The difficulty of such 3D reconstructions is discussed with emphasis on attenuation problems that are typical in eddy current analysis.

The non-intrusive polynomial chaos (NIPC) expansion method is used to quantify the uncertainty of a stochastic system. It potentially reduces the number of numerical simulations in modelling process, thus improving efficiency, whilst ensuring accuracy. However, the number of polynomial bases grows substantially with the increase of random parameters, which may render the technique ineffective due to the excessive computational resources. To address such problems, methods based on the sparse strategy such as the least angle regression (LARS) method with hyperbolic index sets can be used. This paper presents the first work to improve the accuracy of the original LARS method for uncertainty quantification (UQ). We propose an adaptive LARS method in order to quantify the uncertainty of the results from the numerical simulations with higher accuracy than the original LARS method. The proposed method outperforms the original LARS method in terms of accuracy and stability. The L2 regularisation scheme further reduces the number of input samples while maintaining the accuracy of the LARS method.Index Terms-Non-intrusive polynomial chaos (NIPC) expansion, least angle regression (LARS), uncertainty quantification (UQ), finite difference time domain (FDTD), Debye media

Effective eddy current nondestructive evaluation of metal tubes requires accurate modeling of the fields observed in known configurations in order to understand

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International audienceWe present here recent results on detection of surface and subsurface artificial features in Al-Ti planar structures, to show current performance of our eddy-current nondestructive evaluation system based on HTc SQUIDs. The anomalous magnetic fields generated by flaws with known electromagnetic characteristics have been modeled by three-dimensional codes based on finite element method and volume integral formulation and developed for the investigated problem. Both numerical solutions have correctly predicted the shape of the complicated magnetic field response which is mainly the result of the shape of the defect, the geometry of the inducing coil and the characteristics of the SQUID gradiometer

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