Zixian Jiang

Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models

Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and are therefore important to be identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layers small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. Standard iterative inversion algorithm is then applied to the asymptotic models in order to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and benefit of the inversion procedure are provided.

Artificial boundary conditions for axisymmetric eddy current probe problems

We study different strategies for the truncation of computational domains in the simulation of eddy current probes of elongated axisymmetric tubes. For axial fictitious boundaries, an exact Dirichlet-to-Neumann map is proposed and mathematically analyzed via a non-selfadjoint spectral problem: under general assumptions we show convergence of the solution to an eddy current problem involving a truncated Dirichlet-to-Neumann map to the solution on the entire, unbounded axisymmetric domain as the truncation parameter tends to infinity. Under stronger assumptions on the physical parameters of the eddy current problem, convergence rates are shown. We further validate our theoretical results through numerical experiments for a realistic physical setting inspired by eddy current probes of nuclear reactor core tubes.

A Robust Inversion Method for Quantitative 3D Shape Reconstruction from Coaxial Eddy Current Measurements

This work is motivated by the monitoring of conductive clogging deposits in steam generator at the level of support plates. One would like to use multistatic measurements from coaxial coils in order to obtain estimates on the clogging volume. We propose a 3D shape optimization technique based on simplified shape parametrization of the deposit. This parametrization is adapted to the measurement nature and resolution. The direct problem is modeled by the eddy current approximation of time-harmonic Maxwell’s equations in the low frequency regime. A potential formulation is adopted in order to easily handle the complex topology of the industrial problem setting. We first characterize the shape derivatives of the deposit impedance signal using an adjoint field technique. For the inversion procedure, the direct and adjoint problems have to be solved for each vertical probe position which is excessively time- and memory-consuming. To overcome this difficulty, we propose and discuss a steepest descent method based on a invariant mesh. Numerical experiments are presented to illustrate the convergence and the efficiency of the method.

Identification of magnetic deposits in 2-D axisymmetric eddy current models via shape optimization

The non-destructive control of steam generators is an essential task for the safe and failure-free operation of nuclear power plants. Due to magnetite particles in the cooling water of the plants, a frequent source for failures are magnetic deposits in the cooling loop of steam generators. From eddy current signals measured inside a U-tube in the steam generator, we propose and analyze a regularized shap optimization algorithm to identify magnetic deposits outside the U-tube with either known or unknown physical properties. Motivated by the cylindrical geometry of the U-tubes we assume an axisymmetric problem setting, reducing Maxwell’s equations to a 2-D elliptic eddy current problem. The feasibility of the proposed algorithms is illustrated via numerical examples demonstrating in particular the stability of the method under noise.