A Robust Inversion Method for Quantitative 3D Shape Reconstruction from Coaxial Eddy Current Measurements
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- 作者：Houssem Haddar ; Zixian Jiang ; Mohamed Kamel Riahi
- 关键词：Electromagnetism ; Non ; destructive testing ; Time ; harmonic eddy current ; Inverse problem ; Shape optimization
- 刊名：Journal of Scientific Computing
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：70
- 期：1
- 页码：29-59
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1573-7691
- 卷排序：70
文摘
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.