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  • American Institute of Physics (AIP)  (3)
  • Springer  (3)
  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 73 (1993), S. 501-512 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The inverse eddy current problem can be described as the task of reconstructing an unknown distribution of electrical conductivity from eddy-current probe impedance measurements recorded as a function of probe position, excitation frequency, or both. In eddy current nondestructive evaluation, this is widely recognized as a central theoretical problem whose solution is likely to have a significant impact on the characterization of flaws in conducting materials. Because the inverse problem is nonlinear, we propose using an iterative least-squares algorithm for recovering the conductivity. In this algorithm, the conductivity distribution sought minimizes the mean-square difference between the predicted and measured impedance values. The gradient of the impedance plays a fundamental role since it tells us how to update the conductivity in such a way as to guarantee a reduction in the mean-square difference. The impedance gradient is obtained in analytic form using function-space methods. The resulting expression is independent of the type of discretization ultimately chosen to approximate the flaw, and thus has greater generality than an approach in which discretization is performed first. The gradient is derived from the solution to two forward problems: an ordinary and an "adjoint'' problem. In contrast, a finite difference computation of the gradient requires the solution of multiple forward problems, one for each unknown parameter used in modeling the flaw. Two general types of inverse problems are considered: the reconstruction of a conductivity distribution, and the reconstruction of the shape of an inclusion or crack whose conductivity is known or assumed to be zero. A layered conductor with unknown layer conductivities is treated as an example of the first type of inversion problem. An ellipsoidal crack is presented as an example of the second type of inversion problem.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 75 (1994), S. 8138-8144 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Eddy-current inversion is the process whereby the geometry of a flaw in a metal is derived from electromagnetic probe measurements. An inversion scheme is described for finding the shape and size of cracks from eddy-current probe impedance measurements. The approach is based on an optimization scheme that seeks to minimize a global error function quantifying the difference between predicted and observed probe impedances. The error minimum is sought using a standard descent algorithm that requires a knowledge of the gradient of the error with respect to a variation of the flaw geometry. Computation of the gradient is based on a provisional flaw estimate, then the flaw estimate is updated in a "direction'' that reduces the error. The process continues iteratively until a convergence criterion has been satisfied. Then the final flaw estimate should match the shape of the real defect. An equation for the gradient has been derived using an integral formulation of the ideal crack problem. Numerical estimates of the error gradient and the probe impedances have been calculated using approximations based on the moment method. Tests of the inversion scheme using single frequency probe impedance measurements have been carried out by calculating the shapes of narrow slots in aluminum alloy plates. Good agreement is found between the optimum profiles and the measured slot shapes.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Journal of Applied Physics 76 (1994), S. 2007-2015 
    ISSN: 1089-7550
    Source: AIP Digital Archive
    Topics: Physics
    Notes: When a fan beam of monoenergetic γ rays is emitted from a point source into a plane and the scattered photons are recorded by a point detector, the locus of points over which singly Compton-scattered photons suffer the same energy loss is a circle passing through the source and detector points. Thus, the number of scattered photons recorded at a particular detector and energy can be expressed as a weighted line integral of the electron density over a circular path uniquely determined by the energy and the detector location. This defines a novel tomographic reconstruction problem in which, by recording the number of scattered photons as a function of energy and detector position, an image of electron density can be reconstructed from measurements of its line integrals over many overlapping circular paths. It is shown here that this image reconstruction problem has an analytical solution which bears some resemblance to the filtered-backprojection algorithm used in conventional (transmission) computed tomography (CT). A tomographic imaging scheme based on this idea would have several potential advantages over conventional CT systems in the field of industrial nondestructive evaluation, e.g., the ability to image from one side of the object, and the absence of moving parts.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Research in nondestructive evaluation 4 (1992), S. 205-219 
    ISSN: 1432-2110
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract By making multifrequency eddy current measurements on a layered conductor, it is possible to acquire information on the depth dependence of the conductivity. We consider an inversion problem in which coil impedance data are used to determine either the layer thicknesses or layer conductivities. The algorithm is based on a well known forward model which gives the impedance of an air cored coil above a stratified conductor from a closed form expression. In the forward calculation, estimates of the unknown material parameters are used to get tentative predictions of the measurements. Differences between these predictions and measured impedances are expressed in terms of a global error that is minimized iteratively with the aid of a descent algorithm by varying the parameters of the structure. Examples of minimization searches for layer parameters are given.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Research in nondestructive evaluation 1 (1989), S. 167-179 
    ISSN: 1432-2110
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A method for reconstructing radially varying conductivity profiles in cylindrical conductors is described. Solenoidal driving and sensing coils surround the cylindrical sample and an AC magnetic field applied by the driving solenoid induces axisymmetric eddy currents in the sample. It is shown how a radially varying conductivity profile can be recovered from measurements of the complex impedance recorded as a function of frequency, where impedance here is defined as the ratio of the induced electromotive force (EMF) in the sensing coil to the current in the driving coil. An iterative nonlinear least-squares algorithm is employed to reconstruct the profiles. Demonstrations of the reconstruction method are presented based on both simulated and experimentally recorded impedance data.
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  • 6
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