Inverse Problem in Nondestructive Testing Using Arrayed Eddy Current Sensors (original) (raw)
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Optimized Inverse Problem of Eddy Current Testing for Flaws Angle Determination
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The flaw propagation angle is a vital factor in the behavioral study of fractures, especially in the case of structures under dynamic or fatigue loading. In this paper, Eddy's current testing has been used with the finite element modeling method to determine the flaw angle for a two-dimensional axisymmetric problem in a gas tube. Moreover, the influence of the flaw angle on the sensor impedance during the scanning process is carried out. On the other hand, the inverse problem is optimized using one of the most recent and effective metaheuristic optimization algorithms called Grey Wolf Optimizer (GWO). It allows for defining an optimized relationship between the flaw angle and the sensor impedance. Simulations are carried out to validate the proposed approach and show its efficiency in accurately determining the flaw angle.
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IEEE Transactions on Magnetics, 2000
The ideal crack model is generalized to an arrayed eddy current sensor with the assumption that its coils are connected in series and fed by a current source. We associate the superposition theorem to the reciprocity theorem to reduce the 3-D electromagnetic problem to a 2-D axisymmetrical one, combined with the evaluation of an integral equation. We derive the formula that permits the evaluation of the impedance variation of each coil, taking account of the interaction between the coils.
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Two-level approach for solving the inverse problem of defects identification in Eddy Current Testing - type NDTThis work deals with the inverse problem associated to 3D crack identification inside a conductive material using eddy current measurements. In order to accelerate the time-consuming direct optimization, the reconstruction is provided by the minimization of a last-square functional of the data-model misfit using space mapping (SM) methodology. This technique enables to shift the optimization burden from a time consuming and accurate model to the less precise but faster coarse surrogate model. In this work, the finite element method (FEM) is used as a fine model while the model based on the volume integral method (VIM) serves as a coarse model. The application of the proposed method to the shape reconstruction allows to shorten the evaluation time that is required to provide the proper parameter estimation of surface defects.
A non‐destructive testing application solved with A‐χ geometric eddy‐current formulation
COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, 2010
Purpose-The purpose of this paper is to introduce a perturbation method for the Ax geometric formulation to solve eddy-current problems and apply it to the feasibility design of a non-destructive evaluation device suitable to detect long-longitudinal volumetric flaws in hot steel bars. Design/methodology/approach-The effect of the flaw is accurately and efficiently computed by solving an eddy-current problem over an hexahedral grid which gives directly the perturbation due to the flaw with respect to the unperturbed configuration. Findings-The perturbation method, reducing the cancelation error, produces accurate results also for small variations between the solutions obtained in the perturbed and unperturbed configurations. This is especially required when the tool is used as a forward solver for an inverse problem. The method yields also to a considerable speedup: the mesh used in the perturbed problem can in fact be reduced at a small fraction of the initial mesh, considering only a limited region surrounding the flaw in which the mesh can be refined. Moreover, the full three-dimensional unperturbed problem does not need to be solved, since the source term for computing the perturbation is evaluated by solving a two-dimensional flawless configuration having revolution symmetry. Originality/value-A perturbation method for the Ax geometric formulation to solve eddy-current problems has been introduced. The advantages of the perturbation method for non-destructive testing applications have been described.
The application of finite element method analysis to eddy current nondestructive evaluation
IEEE Transactions on Magnetics, 1979
The Finite Element Method for the computation of eddy current fields is presented. The method is described for geometries with a one component eddy current field. The use of the method for the calculation of the impedance of eddy current sensors in the vicinity of defects is shown. An example is given of the method applied to a C-magnet type sensor positioned over a crack in a plane conducting material.
A non-destructive testing application solved with A-? geometric eddy-current formulation
COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2010
Purpose -The purpose of this paper is to introduce a perturbation method for the A-x geometric formulation to solve eddy-current problems and apply it to the feasibility design of a non-destructive evaluation device suitable to detect long-longitudinal volumetric flaws in hot steel bars. Design/methodology/approach -The effect of the flaw is accurately and efficiently computed by solving an eddy-current problem over an hexahedral grid which gives directly the perturbation due to the flaw with respect to the unperturbed configuration. Findings -The perturbation method, reducing the cancelation error, produces accurate results also for small variations between the solutions obtained in the perturbed and unperturbed configurations. This is especially required when the tool is used as a forward solver for an inverse problem. The method yields also to a considerable speedup: the mesh used in the perturbed problem can in fact be reduced at a small fraction of the initial mesh, considering only a limited region surrounding the flaw in which the mesh can be refined. Moreover, the full three-dimensional unperturbed problem does not need to be solved, since the source term for computing the perturbation is evaluated by solving a two-dimensional flawless configuration having revolution symmetry. Originality/value -A perturbation method for the A-x geometric formulation to solve eddy-current problems has been introduced. The advantages of the perturbation method for non-destructive testing applications have been described.
Periodica Polytechnica Civil Engineering
A new method for computing fracture mechanics parameters applicable for measuring tests relying on Eddy currents is proposed. This method is based on inversing Eddy current with simultaneous use of Artificial Neural Networks (ANN) for the localization and the shape classification of defects. It allows the reconstruction of cracks and damage in the plate profile of an inspected specimen to assess its material properties. The procedure consists on inverting all the Eddy current probe impedance measurements which are recorded according to the position of the probe, the excitation frequency or both. In the non-destructive evaluation by Eddy currents or in the case of an inverse problem which is difficult to solve, results from a lot of variety of concepts such as physics and complex mathematics are needed. The corresponding solution has a significant impact on the characterization of cracks in materials. On the other side, a simulation by a numerical approach based on the finite element...
Transactions of the Institute of Systems, Control and Information Engineers, 2010
This paper is concerned with an optimization method to recover crack profiles from measurement signals obtained by eddy current testing. This inversion technique uses Greedy search algorithm to find the optimum of least-square error between measurement signals and simulation data. In creating simulation data, a database called ECT database is used. This database is constructed as a set of parameters-to-output mapping data, by using hybrid FEM-BEM simulator derived from Maxwell's equations. Numerical experimental results show the effectiveness and feasibility of this method.
Non-destructive eddy current testing technic is more and more exploited because it is quick and none contacting into the inspected materials. In order to increase the signal sensing of non-destructive eddy current testing sensors, we are going to propose an optimal design of coil sensor. This optimization needs to construct a tilted cross section coil according to the tested piece geometry. In our simulations, the finite-element method has been exploited for geometrical and physical modelling. For the extraction of our results, a finite-element method code was built in COMSOL with MATLAB. In this paper we compare the tilted cross section coil with a rectangular cross section coil. To obtain the influence of the coil shape on the sensitivity of eddy current sensor, we use the relationship between the impedance changes and the sensor displacement in the two cases of comparison.