1,721,112 research outputs found
A Differential Formulation based on a Perturbative Approach to Solve the ECT Inverse Problems
No full textWe describe a 3D numerical procedure for the reconstruction of conductivity profiles, a classic nonlinear inverse problem. The related direct field problem is discretized using a finite elements differential formulation in terms of magnetic vector potential and electric scalar potential. Adopting shape functions based on edge-elements, the vector potential is gauged using a tree-cotree decomposition of the finite element mesh. The nonlinear inverse problem is approximated by expanding, up to the second order, the nonlinear operator mapping the conductivity into the magnetic field at the probes location. The solution is obtained by minimizing an error functional related to the distance between measurements and their numerical approximation. The geometrical properties of this error functional are reviewed, showing how the presence of local minima can be controlled. From the numerical point of view, this perturbative approach enlarges the range of validity of the classic linear Born approximation, since the quadratic term takes into account, at least partially, the effects due to the reaction field. Several examples highlight the main features of the method. (C) 1999 Elsevier Science S.A. All rights reserved
Recent developments of a monotonicity imaging method for magnetic induction tomography in the small skin-depth regime
No full textThis paper is focused on the non-iterative (direct) imaging of conductive materials from magnetic induction tomography data. Specifically, the interest is on the imaging of surface-breaking defects in the so-called small skin-depth regime where (i) the skin depth is smaller than the relevant geometrical size of the problem and (ii) the displacement current is still negligible. Under these conditions the problem can be modeled by means of an elliptic PDE. Therefore, the inverse problem can be solved by means of the 'monotonicity imaging method', a fast non-iterative algorithm recently developed by the authors for solving inverse problems arising from elliptic PDEs as in the case of electrical resistance tomography, electrical capacitance tomography and low-frequency magnetic induction tomography (in the large skin-depth regime). Major contributions of this work are (i) an advancement of the inversion method and (ii) amethodology to systematically design the probe. Numerical examples prove the effectiveness of this near real-time imaging method
An efficient numerical model for a magnetic core eddy current probe
No full textIn this paper, we study the problem of modeling the response of an eddy-current probe made by one or more coils mounted on magnetic cores. The numerical model is based on an integral formulation in terms of the induced eddy-current J and the magnetization vector M. In terms of numerical modeling, the presence of the magnetic material has a major impact on the computational cost when, as in usual eddy current test operations, the probe is moved on the surface of the test specimen. Here, we propose an efficient numerical method, based on an integral formulation, to model the response of eddy-current testing probes with a magnetic core. The magnetic material is supposed to be homogeneous and linear. This last assumption is motivated by the circumstance that the fields levels occurring in typical eddy-current testing operations are low. The magnetization vector is, then, the gradient of an harmonic function and it admits a minimal representation made by a set of unknowns associated to a proper subset of edges of the boundary of the magnetic domain. An experimental test shows the accuracy of the method and the foundation of the underlying hypothesis
A Differential Formulation based on a Perturbative Approach to Solve the ECT Inverse Problems
No full textWe describe a 3D numerical procedure for the reconstruction of conductivity profiles, a classic nonlinear inverse problem. The related direct field problem is discretized using a finite elements differential formulation in terms of magnetic vector potential and electric scalar potential. Adopting shape functions based on edge-elements, the vector potential is gauged using a tree-cotree decomposition of the finite element mesh. The nonlinear inverse problem is approximated by expanding, up to the second order, the nonlinear operator mapping the conductivity into the magnetic field at the probes location. The solution is obtained by minimizing an error functional related to the distance between measurements and their numerical approximation. The geometrical properties of this error functional are reviewed, showing how the presence of local minima can be controlled. From the numerical point of view, this perturbative approach enlarges the range of validity of the classic linear Born approximation, since the quadratic term takes into account, at least partially, the effects due to the reaction field. Several examples highlight the main features of the method. (C) 1999 Elsevier Science S.A. All rights reserved
Fast numerical techniques for electromagnetic nondestructive evaluation
No full textThis work is focused on quantitative imaging of defects in conductive materials by means of eddy current testing (ECT). By quantitative imaging we mean imaging methods based on numerical models of the interaction between the probe and the defect(s). The imaging methods attempt to provide an image of the defect at variance of commercial instruments that generally detect the defect and may have limited capabilities of extracting its major sizes by means of calibration curves obtained in predefined conditions. In addition, numerical models of the probe-defect interaction play a relevant role for the computer-aided design of the probe. The paper will present methods for the solution of both the forward and the inverse problems. The methods have been developed ad hoc for ECT and have been optimised for accuracy and speed in view of real-time applications
A FFT integral formulation using edge-elements for Eddy Current Testing
No full textThis paper presents a new approach for reducing the computational cost needed to solve the forward problem, i.e. the prediction of the measurements of a given ECT measurement system. This issue is mandatory in any inversion algorithm which, typically, requires the solution of a large number of direct problems. Integral formulations are attractive for ECT since they require the discretization of the conductive body only. However they also give rise to a full stiffness matrix whose inversion, typically obtained using direct solvers, has a computational cost that grows as O (n(3)) where n is the number of unknowns arising from the discretization. Iterative algorithms achieve a computational cost that is lower than direct solvers when the stiffness matrix is sparse. The approach proposed in this paper makes it possible to represent the stiffness matrix arising from an edge-elements based integral formulation, by means of the Fast Fourier Transform. This representation is achieved for bounded conductive domains meshed by a regular mesh and incurs a computational cost that grows as O(N log h)
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