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A robust inversion method for quantitative 3D shape reconstruction from coaxial eddy current measurements. (English) Zbl 1440.94004

Summary: 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.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
49N15 Duality theory (optimization)
49N45 Inverse problems in optimal control
49Q10 Optimization of shapes other than minimal surfaces
68U01 General topics in computing methodologies
78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory
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