3D direct and inverse solvers for eddy current testing of deposits in steam generator

TL;DR

This paper develops and validates 3D direct and inverse solvers for eddy current testing of deposits in steam generator tubes, incorporating shape sensitivity analysis and a cylindrical coordinate-based inversion algorithm to improve deposit shape reconstruction.

Contribution

It introduces a shape inversion method using finite element analysis and shape sensitivity in cylindrical coordinates for better deposit shape estimation in steam generator tubes.

Findings

Validated direct problem considering support plates and conductive parts.

Developed explicit gradient formula for shape optimization.

Numerical results demonstrate robustness and accuracy of the method.

Abstract

We consider the inverse problem of estimating the shape profile of an unknown deposit from a set of eddy current impedance measurements. The measurements are acquired with an axial probe, which is modeled by a set of coils that generate a magnetic field inside the tube. For the direct problem, we validate the method that takes into account the tube support plates, highly conductive part, by a surface impedance condition. For the inverse problem, finite element and shape sensitivity analysis related to the eddy current problem are provided in order to determine the explicit formula of the gradient of a least square misfit functional. A geometrical-parametric shape inversion algorithm based on cylindrical coordinates is designed to improve the robustness and the quality of the reconstruction. Several numerical results are given in the experimental part. Numerical experiments on synthetic deposits, nearby or far away from the tube, with different shapes are considered in the axisymmetric configuration.