Optimized Solutions for Defect Characterization in 2-D Inverse Eddy Current Testing Problems Using Subregion Finite Element Method

A computational technique is presented in this paper which improves finite element method (FEM) in solving inverse problems. Subregion method is used to select and isolate the area of interest where design parameters for defect shape are updated. An elastic mesh generator is developed in this paper to generate optimal meshes in the selected area to save connectivity matrix until having the most accurate design parameters. Using subregion FEM in solving inverse problems will help in minimizing processing time and memory usage in addition of reducing solution complexity. A 2-D eddy current testing (ECT) problem of detecting and characterizing the location and shape of a defect by separating the defect from entire domain is used to validate the presented subregion FEM algorithm. The elastic mesh generator is investigated to update the preselected design parameters of the defect in each iteration. This meshing technique adds the specialty of using subregion method in inverse problems where elements and nodes numberings are saved inside and outside the defect region. Both the genetic algorithm and simulated annealing optimization techniques are developed to get the accurate defect parameters. The presented subregion FEM results have been verified computationally using conventional FEM. Excellent results of signals agreement and processing time minimization with a factor of 90% with an accuracy of 98% have been achieved. In addition, the presented subregion FEM algorithm has been verified experimentally using aluminum (T6061-T6) and mild steel plate (0.15%-0.30% carbon and Fe) samples. This experiment is carried using an elongated excitation coil in a fixed position mounted on the top of the sample and tunneling magnetoresistive sensor to measure magnetic field. The measured magnetic fields were used as input to the inverse subregion FEM solver and the machined artificial defects were characterized with excellent accuracy.