Defect Shape Recovering by Parameter Estimation Arising in Eddy Current Testing

  • Kojima, Fumio (Graduate School of Science and Technology, Kobe University)
  • Published : 2003.12.30

Abstract

This paper is concerned with a computational method for recovering a crack shape of steam generator tubes of nuclear plants. Problems on the shape identification are discussed arising in the characterization of a structural defect in a conductor using data of eddy current inspection. A surface defect on the generator tube ran be detected as a probe impedance trajectory by scanning a pancake type coil. First, a mathematical model of the inspection process is derived from the Maxwell's equation. Second, the input and output relation is given by the approximate model by virtue of the hybrid use of the finite element and boundary element method. In that model, the crack shape is characterized by the unknown coefficients of the B-spline function which approximates the crack shape geometry. Finally, a parameter estimation technique is proposed for recovering the crack shape using data from the probe coil. The computational experiments were successfully tested with the laboratory data.

Keywords

References

  1. Banks, H.T. and Kojima, F. (1989) Boundary Shape Identification Problems in Two-dimensional Domains related to Thermal Testing of Materials, Quart. Appl. Math., Vol. 47, pp. 273-293
  2. Banks, H.T., Kojima, F. and Winfree W.P. (1990) Boundary Estimation Problems arising in Thermal Tomography, Inverse Problems, Vol. 6, pp. 121-132
  3. Bowler, J.R. Jenkins. S.A., Sabbagh, L.D., and Sabbagh, H.A. (1991) Eddy-current Probe Impedance due to a Volumetric Flaw, J. Appl. Phys., Vol. 70, No. 3, pp. 1107-1114
  4. Bowler, J.R. (1995) Eddy Current Inversion using Gradient Method, Studies in Applied Electromagnetics and Mechanics, Vol. 8, lOS Press, Amsterdam, the Netherlands, pp. 31-40
  5. Broyden, C.G. (1970) The Convergence of a Class of Double-Rank Minimization Algorithm, J. Institute of Mathematics and Its Applications, Vol. 6, pp. 76-90
  6. Carter. R.G. (1987) Safeguarding Hessian Approximations in Trust Region Algorism, Technical Report, TR87-12, Department of Mathematical Sciences, Rice University
  7. de Boor, C. (1978) Practical Guide to Splines, Springer, New York
  8. Harrison, D.J., Jones L.D., and Burke S.K. (1996) Benchmark Problems for Defect Size and Shape Determination in Eddy-current Nondestructive Evaluation, J. Nondestructive Evaluation, Vol. 15, No. 1, pp. 21-34
  9. Kojima, F. (1996) Computational Methods for Inverse Problems in Engineering Sciences. International Journal of Applied Electromagnetics and Mechanics, Vol. 7, pp. 1-16
  10. Matsuoka, F (1987) Calculation of a Three Dimensional Eddy Current by the FEM-BEM Coupling Method. Proc. IUTAM Conf. on Electmmagnetomccluinicol Interactions in Deformable Solids and Strnciurcs, North-Holland pp. 169-174
  11. Pironneau, O (1983) Optimal Shape Design for Elliptic Systems, Springer, New York
  12. Sabbagh, H.A. and L.D. Sabbagh (1986) An Eddy-current Model for Three-dimensional Inversion IEEE Trans. on Magnetics, Vol. MAG-22, No. 4, pp. 282-290
  13. Takagi, T. et al. (1994) Benchmark Models of Eddy Current Testing for Steam Generator Tube: Experiment and Numerical Analysis, Int. J. Applied Electromagnetics in Materials, Vol. 5, pp. 149-162
  14. Takagi, T. et al. (1995) ECT research activities in JSAEM - Benchmark models of eddy current testing for steam generator tube (Part 1), Studies in Applied Electromagnetics and Mechanics, Vol. 8, lOS Press, Amsterdam, the Netherlands, pp. 253-264
  15. Takagi, T. et al. (1996). Electromagnetic NDE research activities in JSAEM, Studies in Applied Electromagnetics and Mechanics, Vol. 12, lOS Press, Amsterdam, the Netherlands, pp. 9-16