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Modeling the differential eddy current probe for steam generator tubing inspections using Z parameters
N DT Abstracts geometry of a flaw in a conducting surface from an eddy current image. Image restoration is formulated as a maximum likelihood estimation problem and is solved using constrained iterative gradient descent. A novel frequency-domain constraint relaxation algorithm is used to control the iterative restoration process. The technique is applied to eddy current images generated by sampling the output of an absolute transducer on a dense grid, creating smoothly blurred images of crack- like flaws. The principal conclusions drawn from this work are: (I) Representing a nonlinear system with layers of linear blurs and non- linear point transformations is general, permitting efficient gradient descent on any analytic system function. (2) Smooth blurring functions in the gradient improve the stability of the algorithm. (3) The accuracy of the estimate is improved dramatically by restoring portions of estimate spectrum which corresponds to the highest signal-to-noise ratio band in the observation spectrum first.
48977
NDE
for
Nuclear
States),
NE-Vol.
6-10
6. ASME
Heat Oct.
Exchangers,
1991.
San
pp. 1-7. Edited
Diego, by D.A.
(1991)
Steam generator tubing inspections using a differential probe typically utilize the probe impedance as the primary indication of incipient failure. This paper proposes a 2 parameter model for the differential probe inside the steam tube. Z parameters reveal information about the tube and the flaw which is neglected using the normal voltage difference method. The voltage difference response can still bc calculated using the Z parameters but the Z parameters can not be derived from the voltage difference. With the Z parameter model, the flaw-dependent components can be separated out from the non-flaw components in the probe signal. This paper investigates how the Z parameter components can bc used to distinguish flaws on the outside of the tube (OD) from flaws on the inside of the tube (ID) and also to estimate the flaw penetration (depth) into the tube. An axisymmetric finite element computer code is used as a basis for testing the model and analytical expressions are developed to closely approximate the results.
Numerical and experimental analysis of eddy current testing for a tube with cracks Vol. 28, No. 2, pp. 1469-1472
48970
A new method to calculate impedance signal in Eddy Current Testing
Journal of Physics D. Applied Physics, Vol. 25, No. 2, pp. 319-326 (14 Feb. 1992) An analytical calculation is presented for the response of an air-cored eddy-current probe to a surface-breaking metal fatigue crack in a flat plate. modelled as a region of zero conductivity, infinitely long and uniformly deep, in a homogeneous, conducting half-space. The problem is formulated in terms of the magnetic scalar potential, subject to surface impedance boundary conditions, with a line source to represent the crack. Solutions are found using spatial Fourier transforms. The theory is valid for both ferromagnetic and non-magnetic metals, providing that the electromagnetic penetration depth is small compared with the crack depth. The signal is expressed in terms of two integrals which in general must be evaluated numerically. Specific computations have been performed for a circular, single-coil probe.
Jenkins, S.A.; Sahbagh, L.D.
Simulations in eddy current NDE NDE - The Vehicle to the Future, Orlando, Florida (United States), 30 Mar. - 3 Apr. 1992. pp. 120-I 22. ASNT (1992) A model capable of accurately matching experimental eddy current results is important and could be a key to understanding the detected signal in terms of the underlying flaw geometry. A computer model has been developed based on an implementation of a volume integral formulation for solving Maxwell’s equations. The theoretical model uses integral equations with dyadic Green’s function kernels for flaw calculations at many skin depths and frequencies. Discrete approximations of the integral equations are solved using a highly efficient algorithm based on recent developments in numerical techniques and their application to solving large problems in
48725
Macecek, M.
Advanced eddy current array defect imaging Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15-20 Jul. 1990. Vol. IOA, pp. 9951002. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN O-306-43903-4. This research has attempted to simplify and advance existing state of the art technology by trying to achieve an eddy current equivalent of the C-scan display, i.e. a raster scan of area of interest indicating flaws with eddy current arrays. Digitai eddy current methodologies were explored as the only way to advance the technique and bring it in line with data recognition and signal processing techniques currently in use in the field. Consideration was given to various graphics and display techniques to best display flaws of interest (i.e. cracks, corrosions).
electromagnetics. In this paper, we give the results of a volume integral code used in modelling eddy current probe responses to slots (flaws), and solve a number of benchmark problems.
Lynch, D.J.; Mahmnod, A.; Phil&,
Lewis, A.M.
A theoretical model of the response of an eddy-current probe to a surface breaking fatigue crack in a flat teat-piece
(ECT) for a tube with surface cracks is developed using the two dimensional T-method (current vector potential method). Three dimensional current flow around a surface crack is approximated by introducing quasi conductivity in the crack region. Further a final matrix relating the current vector potentials on the crack surface with neighboring potentials is obtained by decreasing the width of the crack to zero and then the elements in the crack region are not necessary any longer. The numerical results show good agreement with the experimental ones, which indicates the validity of the method proposed here and the possibility to design more efficient probe of the ECT using the code.
49234
(United
Steininger.
Hashizume, H.; Yamada, Y.; Miya, K.; Toda, S.; Mnrimota. K.; Araki, Y.; Satake, K.; Shimizu, N.;
49509
Techniques
California
497 10
IEEE Transactions on Magnetics, (Mar. 1992)
Nguyen, Q.H.; Philipp, L.D.; Lynch, D.J.; Mahmood, A.
Modeling the differential eddy current probe for steam generator tubing inspections using Z parameters
L.D.; Nguyen, Q.H.
A normalization scheme for comparing eddy current differential probe signals using a finite element formulation Research in Nondestructive Evaluation, Vol. 3, No. 4, pp. 221-234
48721
(1991). A First-orderfinite element formulation is used to model an eddy current differential bobbin coil probe scanning a tube with axisymmetric flaws. A multifrequency signal normalization scheme is developed to allow direct comparison between experimental measurements of the differential bobbin coil probe signal and finite element calculations of the probe coil impedance. Results demonstrate that both magnitude and phase of the differential bobbin coil impedance are useful in characterizing flaws in turbine for multifrequency scans.
49229
Rummel, W.D.; Moulder, J.C.; Nakagawa,
N.
The comparative responses of cracks and slots in eddy current measurements Review of Progress in Quantitative I\;ondestructive Evaluation, La Jolla, California (United States), 15-20 Jul. 1990. Vol. 10 A. pp. 277-283. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN o-306-43903-4. Historically saw cuts and electrodischarge machined (EDC) slots have been used for the calibration of eddy current equipment and measurement of output acceptance levels, and consistency has been assumed. Some factors are identified which have contributed to conflicting conclusions regarding the equivalency of eddy current response to EDM slots and fatigue cracks of equivalent size. I: is shown that probability of detection plots can produce erroneous conclusions unless careful atten!ion is paid to system calibration, signal/noise analyses and acceptance criteria. Signals from EDM slots are nearly always greater than those from fatigue cracks by factors between two and five, becoming nearly equal only at the lowest frequencies. Indeed the eddy current response signals of EDM slots, and saw cuts are not equivalent to those from cracks of equal size and so should not be used exclusively for evaluating crack detection capabilities or validating the performance levels of eddy current inspcc:ctionprocedures.
Cahouet, J.; Coutanceau, N.; Verite, J.C.
Problem 8: analysis of the eddy current N.D.T. signals European Team Workshop and International Seminar in Electromagnetic Field Analysis, Oxford (United Kingdom), 23-25 Apr. 1990. pp. 17-19. Edited by Y. Crutzen, N.J. Diserens, C.R.I. Emson and D. Rodgers. EUR 12988 EN. Commission of the European Communities (1992). The Trifou code gave excellent results for this problem concerning eddy current non destructive testing. We present in this paper an analysis of the defect signals.
178
48977
NDE
for
Nuclear
States),
NE-Vol.
6-10
6. ASME
Heat Oct.
Exchangers,
1991.
San
pp. 1-7. Edited
Diego, by D.A.
(1991)
Steam generator tubing inspections using a differential probe typically utilize the probe impedance as the primary indication of incipient failure. This paper proposes a 2 parameter model for the differential probe inside the steam tube. Z parameters reveal information about the tube and the flaw which is neglected using the normal voltage difference method. The voltage difference response can still bc calculated using the Z parameters but the Z parameters can not be derived from the voltage difference. With the Z parameter model, the flaw-dependent components can be separated out from the non-flaw components in the probe signal. This paper investigates how the Z parameter components can bc used to distinguish flaws on the outside of the tube (OD) from flaws on the inside of the tube (ID) and also to estimate the flaw penetration (depth) into the tube. An axisymmetric finite element computer code is used as a basis for testing the model and analytical expressions are developed to closely approximate the results.
Numerical and experimental analysis of eddy current testing for a tube with cracks Vol. 28, No. 2, pp. 1469-1472
48970
A new method to calculate impedance signal in Eddy Current Testing
Journal of Physics D. Applied Physics, Vol. 25, No. 2, pp. 319-326 (14 Feb. 1992) An analytical calculation is presented for the response of an air-cored eddy-current probe to a surface-breaking metal fatigue crack in a flat plate. modelled as a region of zero conductivity, infinitely long and uniformly deep, in a homogeneous, conducting half-space. The problem is formulated in terms of the magnetic scalar potential, subject to surface impedance boundary conditions, with a line source to represent the crack. Solutions are found using spatial Fourier transforms. The theory is valid for both ferromagnetic and non-magnetic metals, providing that the electromagnetic penetration depth is small compared with the crack depth. The signal is expressed in terms of two integrals which in general must be evaluated numerically. Specific computations have been performed for a circular, single-coil probe.
Jenkins, S.A.; Sahbagh, L.D.
Simulations in eddy current NDE NDE - The Vehicle to the Future, Orlando, Florida (United States), 30 Mar. - 3 Apr. 1992. pp. 120-I 22. ASNT (1992) A model capable of accurately matching experimental eddy current results is important and could be a key to understanding the detected signal in terms of the underlying flaw geometry. A computer model has been developed based on an implementation of a volume integral formulation for solving Maxwell’s equations. The theoretical model uses integral equations with dyadic Green’s function kernels for flaw calculations at many skin depths and frequencies. Discrete approximations of the integral equations are solved using a highly efficient algorithm based on recent developments in numerical techniques and their application to solving large problems in
48725
Macecek, M.
Advanced eddy current array defect imaging Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15-20 Jul. 1990. Vol. IOA, pp. 9951002. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN O-306-43903-4. This research has attempted to simplify and advance existing state of the art technology by trying to achieve an eddy current equivalent of the C-scan display, i.e. a raster scan of area of interest indicating flaws with eddy current arrays. Digitai eddy current methodologies were explored as the only way to advance the technique and bring it in line with data recognition and signal processing techniques currently in use in the field. Consideration was given to various graphics and display techniques to best display flaws of interest (i.e. cracks, corrosions).
electromagnetics. In this paper, we give the results of a volume integral code used in modelling eddy current probe responses to slots (flaws), and solve a number of benchmark problems.
Lynch, D.J.; Mahmnod, A.; Phil&,
Lewis, A.M.
A theoretical model of the response of an eddy-current probe to a surface breaking fatigue crack in a flat teat-piece
(ECT) for a tube with surface cracks is developed using the two dimensional T-method (current vector potential method). Three dimensional current flow around a surface crack is approximated by introducing quasi conductivity in the crack region. Further a final matrix relating the current vector potentials on the crack surface with neighboring potentials is obtained by decreasing the width of the crack to zero and then the elements in the crack region are not necessary any longer. The numerical results show good agreement with the experimental ones, which indicates the validity of the method proposed here and the possibility to design more efficient probe of the ECT using the code.
49234
(United
Steininger.
Hashizume, H.; Yamada, Y.; Miya, K.; Toda, S.; Mnrimota. K.; Araki, Y.; Satake, K.; Shimizu, N.;
49509
Techniques
California
497 10
IEEE Transactions on Magnetics, (Mar. 1992)
Nguyen, Q.H.; Philipp, L.D.; Lynch, D.J.; Mahmood, A.
Modeling the differential eddy current probe for steam generator tubing inspections using Z parameters
L.D.; Nguyen, Q.H.
A normalization scheme for comparing eddy current differential probe signals using a finite element formulation Research in Nondestructive Evaluation, Vol. 3, No. 4, pp. 221-234
48721
(1991). A First-orderfinite element formulation is used to model an eddy current differential bobbin coil probe scanning a tube with axisymmetric flaws. A multifrequency signal normalization scheme is developed to allow direct comparison between experimental measurements of the differential bobbin coil probe signal and finite element calculations of the probe coil impedance. Results demonstrate that both magnitude and phase of the differential bobbin coil impedance are useful in characterizing flaws in turbine for multifrequency scans.
49229
Rummel, W.D.; Moulder, J.C.; Nakagawa,
N.
The comparative responses of cracks and slots in eddy current measurements Review of Progress in Quantitative I\;ondestructive Evaluation, La Jolla, California (United States), 15-20 Jul. 1990. Vol. 10 A. pp. 277-283. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN o-306-43903-4. Historically saw cuts and electrodischarge machined (EDC) slots have been used for the calibration of eddy current equipment and measurement of output acceptance levels, and consistency has been assumed. Some factors are identified which have contributed to conflicting conclusions regarding the equivalency of eddy current response to EDM slots and fatigue cracks of equivalent size. I: is shown that probability of detection plots can produce erroneous conclusions unless careful atten!ion is paid to system calibration, signal/noise analyses and acceptance criteria. Signals from EDM slots are nearly always greater than those from fatigue cracks by factors between two and five, becoming nearly equal only at the lowest frequencies. Indeed the eddy current response signals of EDM slots, and saw cuts are not equivalent to those from cracks of equal size and so should not be used exclusively for evaluating crack detection capabilities or validating the performance levels of eddy current inspcc:ctionprocedures.
Cahouet, J.; Coutanceau, N.; Verite, J.C.
Problem 8: analysis of the eddy current N.D.T. signals European Team Workshop and International Seminar in Electromagnetic Field Analysis, Oxford (United Kingdom), 23-25 Apr. 1990. pp. 17-19. Edited by Y. Crutzen, N.J. Diserens, C.R.I. Emson and D. Rodgers. EUR 12988 EN. Commission of the European Communities (1992). The Trifou code gave excellent results for this problem concerning eddy current non destructive testing. We present in this paper an analysis of the defect signals.
178