Skip to main content

Part of the book series: Scientific Computation ((SCIENTCOMP))

  • 1539 Accesses

Abstract

In this chapter, we describe the mathematical development of a general axisymmetric model for VIC-3D®. This model is capable of analyzing tubes with tube supports and roll-expanded transition zones. Features such as magnetite and sludge,are included, and materials may be either ferromagnetic or nonmagnetic. The model described in this chapter will include only differential (or absolute) bobbin coils.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Burrows, M.L.: A theory of eddy-current flaw detection. PhD Thesis, University of Michigan, University Microfilms, Inc., Ann Arbor, Michigan (1964)

    Google Scholar 

  2. Förster, F., Breitfeld, H.: Theoretische und Experimentelle Grundlagen der zerstörungsfreien WerkstoffprĂ¼fung mit Wirbelstromverfahren, (Parts I and II). Z. Metallkd. 43(5), 163–180 (1952)

    Google Scholar 

  3. Förster, F., Breitfeld, H., Stambke, K.: Theoretishe und Experimentelle Grundlagen der zerstörungsfreien WerkstoffprĂ¼fung mit Wirbelstromverfahren, (Parts III–VII). Z. Metallkd. 45(5), 166–199 and 221–226 (1954)

    Google Scholar 

  4. Dodd, C.V., Deeds, W.E.: Analytical solutions to eddy-current probe coil problems. J. Appl. Phys. 39(6), 2829–2838 (1968)

    Google Scholar 

  5. Luquire, J.W., Deeds, W.E., Dodd, C.V.: Alternating current distribution between planar conductors. J. Appl. Phys. 41(10), 3983–3991 (1970)

    Google Scholar 

  6. Cheng, C.C., Dodd, C.V., Deeds, W.E.: General analysis of probe coils near stratified conductors. Int. J. Nondestr. Test. 3, 109–130 (1971)

    Google Scholar 

  7. Nestor, C.W., Jr., Dodd, C.V., Deeds, W.E.: Analysis and computer programs for eddy current coils concentric with multiple cylindrical conductors. Report No. ORNL-5220, Oak Ridge National Laboratory, Oak Ridge, TN 37830, July 1979

    Google Scholar 

  8. Deeds, W.E., Dodd, C.V., Scott, G.W.: Computer-aided design of multifrequency eddy-current tests for layered conductors with multiple property variations. Report No. ORNL/TM-6858, Oak Ridge National Laboratory, Oak Ridge, TN 37830, October 1979

    Google Scholar 

  9. Miller, E.K.: Model-based parameter estimation in electromagnetics: III–applications to EM integral equations. Appl. Comput. Electrom. 10(3), 9–29 (1995)

    Google Scholar 

  10. Murphy, K., Sabbagh, H.A.: A boundary-integral code for electromagnetic nondestructive evaluation. In: Conference Proceedings: 12th Annual Review of Progress in Applied Computational Electromagnetics, Applied Computational Electromagnetics Society, 18–22 March 1996, pp. 171–178

    Google Scholar 

  11. Xie, H., Song, J., Yang, M., Nakagawa, N.: A novel boundary integral equation for surface crack model. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 29, pp. 329–336. American Institute of Physics, Melville (2010)

    Google Scholar 

  12. Harrington, R.F.: Field Computation by Moment Methods. The Macmillan Company, New York (1968)

    Google Scholar 

  13. Berreman, D.W.: Optics in Stratified and Anisotropic Media: 4 × 4-Matrix Formulation. J. Opt. Soc. Am. 62(4), 502–510 (April 1972)

    Google Scholar 

  14. Altman, C., Schatzberg, A.: Appl. Phys. B 28, 327–333 (1982)

    Google Scholar 

  15. Altman, C., Schatzberg, A.: Appl. Phys. B 26, 147–153 (1981)

    Google Scholar 

  16. Altman, C., Schatzberg, A., Suchy, K.: IEEE Trans. Antenn. Propag. AP-32(11) (November 1984)

    Google Scholar 

  17. Schatzberg, A., Altman, C.: J. Plasma Phys. 26(Part 2), 333–344 (1981)

    Google Scholar 

  18. Suchy, K., Altman, C.: J. Plasma Phys. 13(Part 3), 437–449 (1975)

    Google Scholar 

  19. Krowne, C.M.: IEEE Antennas and Propagation Symposium Digest, Boston, MA, 25–29 June 1984, pp. 569–572

    Google Scholar 

  20. Krowne, C.M.: IEEE Trans. Microw. Theor. Tech. MTT-32(12), 1617–1625 (December 1984)

    Google Scholar 

  21. Krowne, C.M.: IEEE Trans. Antenn. Propag. AP-32(11), 1224–1230 (November 1984).

    Google Scholar 

  22. Roberts, T.M., Sabbagh, H.A., Sabbagh, L.D.: Electromagnetic interactions with an anisotropic slab. IEEE Trans. Magn. 24(6), 3193–3200 (November 1988)

    Google Scholar 

  23. Roberts, T.M., Sabbagh, H.A., Sabbagh, L.D.: Electromagnetic scattering for a class of anisotropic layered media. J. Math. Phys. 29, 2675–2681 (December 1988)

    Google Scholar 

  24. Roberts, T.M.: Explicit eigenmodes for anisotropic media. IEEE Trans. Magn. 26(6), 3064–3071 (November 1990)

    Google Scholar 

  25. Bowler, J.R., Sabbagh, L.D., Sabbagh, H.A.: A theoretical and computational model of eddy-current probes incorporating volume integral and conjugate gradient methods. IEEE Trans. Magn. 25(3), pp. 2650–2664 (May 1989)

    Google Scholar 

  26. Sabbagh, H.A., Bowler, J.R., Sabbagh, L.D.: A model of eddy-current probes with ferrite cores. Nondestr. Test. Eval. 5(1), 67–79 (1989)

    Google Scholar 

  27. Sabbagh, H.A.: A model of eddy-current probes with ferrite cores. IEEE Trans. Magn. MAG-23(3), 1888–1904 (May 1987)

    Google Scholar 

  28. Sabbagh, H.A., Sabbagh, L.D., Bowler, J.R.: A volume-integral code for eddy-current nondestructive evaluation. Int. J. Comput. Math. Elec. Electron. Eng. 9(Suppl. A), 67–70 (1990)

    Google Scholar 

  29. Bowler, J.R., Sabbagh, L.D., Sabbagh, H.A.: Eddy-current probe impedance due to a surface slot in a conductor. IEEE Trans. Magn. 26(2), 889–892 (March 1990)

    Google Scholar 

  30. Rao, S.M., Wilton, D.R., Glisson, A.W.: Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antenn. Propag. AP-30(3), 409–418 (May 1982)

    Google Scholar 

  31. Aubin, J-P.: Approximation of Elliptic Boundary-Value Problems. Wiley-Interscience, New York (1972)

    Google Scholar 

  32. Glisson, A.W., Wilton, D.R.: Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces. IEEE Trans. Antenn. Propag. AP-29, 593–603 (1980)

    Google Scholar 

  33. Wertgen, W., Jansen, R.H.: Efficient direct and iterative electrodynamic analysis of geometrically complex MIC and MMIC structures. Int. J. Numer. Model. Electron. Network. Dev. Field. 2(3), 153–186 (September 1989)

    Google Scholar 

  34. Yaghjian, A.D.: Electric dyadic Green’s functions in the source region. Proc. IEEE. 68, 248–263 (February 1980)

    Google Scholar 

  35. Burke, G.J., Dease, C.G., Didwall, E.M., Lytle, R.J.: Numerical modeling of subsurface communication. UCID-20439 Rev. 1, Lawrence Livermore National Laboratory, August 1985

    Google Scholar 

  36. Catedra, M.F., Gago, E., Nuño, L.: A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform. IEEE Trans. Antenn. Propag. 37(5), 528–537 (May 1989)

    Google Scholar 

  37. Peter, A., Zwamborn, M., van den Berg, P.M., Mooibroek, J., Koenis, F.T.C.: Computation of three-dimensional electromagnetic-field distributions in a human body using the weak form of the CGFFT method. Appl. Comput. Electrom. 7(2), 26–42 (Winter 1992)

    Google Scholar 

  38. Zwamborn, P., van den Berg, P.M.: The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems. IEEE Trans. Microw. Theor. Tech. 40(9), 1757–1766 (September 1992)

    Google Scholar 

  39. Sabbagh, H.A.: Splines and their reciprocal-bases in volume-integral equations. IEEE Trans. Magn. 29(6), 4142–4152 (November 1993)

    Google Scholar 

  40. http://www.sabbagh.com

  41. Dongarra, J.J., Moler, C.B., Bunch, J.R., Stewart, G.W.: LINPACK Users’ Guide. Society for Industrial and Applied Mathematics, Philadelphia (1979)

    Google Scholar 

  42. Hestenes, M.: Conjugate Direction Methods in Optimization. Springer, New York (1980)

    Google Scholar 

  43. Sarkar, T.P.: Application of the Conjugate Gradient Method in Electromagnetics and Signal Processing. Elsevier, New York (1991)

    Google Scholar 

  44. Catedra, M.F., Torres, R.P., Basterrechea, J., Gago, E.: The CG-FFT Method: Application of Signal Processing Techniques to Electromagnetics. Artech House, Boston (1995)

    Google Scholar 

  45. Peterson, A., Ray, S., Mittra, R.: Computational Methods for Electromagnetics. IEEE, New York (1998)

    Google Scholar 

  46. Chew, W.C., Jin, J.M., Michielsssen, E., Song, J.M.: Fast and Efficient Algorithms in Computational Electromagnetics. Artech House, Boston (2001)

    Google Scholar 

  47. Harrington, R.F.: Time-Harmonic Electromagnetic Fields. McGraw-Hill, New York (1961)

    Google Scholar 

  48. Collin, R.E.: Field Theory of Guided Waves. McGraw-Hill, New York (1960)

    Google Scholar 

  49. Sabbagh, H.A., Sabbagh, E.H., Murphy, R.K.: Recent advances in modeling eddy-current probes. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 21, pp. 423–429. American Institute of Physics, Melville (2002)

    Google Scholar 

  50. Wozencraft, J.M., Jacobs, I.M.: Principles of Communication Engineering. Wiley, New York (1965)

    Google Scholar 

  51. Umashankar, K.R., Nimmagadda, S., Taflove, A.: Numerical analysis of electromagnetic scattering by electrically large objects using spatial decomposition technique. IEEE Trans. Antenn. Propag. 40(8), 867–877 (August 1992)

    Google Scholar 

  52. Murphy, K., Sabbagh, H.A., Treece, J.C.: Thickness measurements with eddy-current probes: a simple inversion problem. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 13, pp. 927–934. Plenum Press, New York (1994)

    Google Scholar 

  53. Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice-Hall, Inc., Englewood Cliffs (1974)

    Google Scholar 

  54. Murphy, K., Sabbagh, H.A., Treece, J.C.: Some inversion problems in nondestructive evaluation. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 14, pp. 857–861. Plenum Press, New York (1995)

    Google Scholar 

  55. Baltzersen, O.: Model-based inversion of plate thickness and liftoff from eddy current probe coil measurements. Mat. Eval. 51, 72–76 (1993)

    Google Scholar 

  56. Förster, F. Libby, H.: Electromagnetic Testing, 2nd edn, pp. 178–179. The American Society or Nondestructive Testing, Columbus (1986)

    Google Scholar 

  57. Sabbagh, H.A., Murphy, R.K. Sabbagh, E.H.: Advances in modeling eddy-current NDE of ferromagnetic bodies. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 22, pp. 383–389. American Institute of Physics, Melville (2003)

    Google Scholar 

  58. Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods. Part I: clustering methods. Math. Program. 39, 27–56 (1987)

    Google Scholar 

  59. Rinnooy Kan, A.H.G., Timmer, G.T.: Stochastic global optimization methods Part II: multi level methods. Math. Program. 39, 57–78 (1987)

    Google Scholar 

  60. Byrd, R.H., Dert, C.L., Rinnooy Kan, A.H.G., Schnabel, R.B.: Concurrent stochastic methods for global optimization. Math. Program. 46, 1–29 (1990)

    Google Scholar 

  61. Nakhkash, M., Huang, Y., Fang, M.T.C.: Application of the multilevel single-linkage method to one-dimensional electromagnetic inverse scattering problem. IEEE Trans. Antenn. Propag. 47(11), 1658–1668 (November 1999)

    Google Scholar 

  62. Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, Baltimore (1983)

    Google Scholar 

  63. Rousseeuw, P., Yohai, V.: Robust regression by means of s-estimators. In: Robust and Nonlinear Time Series Analysis: Proceedings of a Workshop, pp. 256–272, 1984

    Google Scholar 

  64. Van Trees, H.L.: Detection, Estimation, and Modulation Theory: Part I. Wiley, New York (1968)

    Google Scholar 

  65. Kay, S.M.: Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice-Hall, Inc., Upper Saddle River (1993)

    Google Scholar 

  66. Devaney, A.J., Tsihrintzis, G.A.: Maximum likelihood estimation of object location in diffraction tomography. IEEE Trans. Signal Process. 39(3), 672–682 ( March 1991)

    Google Scholar 

  67. Herman, G.T., Lent, A., Hurwitz, H.: A storage-efficient algorithm for finding the regularized solution of a large, inconsistent system of equations. J. Inst. Math. Appl. 25, 361–366 (1980)

    Google Scholar 

  68. Censor, Y.: Row-action methods for huge and sparse systems and their applications. SIAM Rev. 23, 444–446 (October 1981)

    Google Scholar 

  69. Herman, G.T., Meyer, L.B.: Algebraic reconstruction techniques can be made computationally efficient. IEEE Trans. Med. Imag. 12(3), 600–609 (September 1993)

    Google Scholar 

  70. Sabbagh, H.A., Sabbagh, L.D., Vernon, S.N.: Verification of an eddy-current flaw inversion algorithm. IEEE Trans. Magn. 22(6), 1881–1886 (November 1986)

    Google Scholar 

  71. Papoulis, A.: A new algorithm in spectral analysis and band-limited extrapolation. IEEE Trans. Circ. Syst. CAS-22, 735–742 (1975)

    Google Scholar 

  72. Youla, D.C.: Generalized image restoration by the method of alternating orthogonal projections. IEEE Trans. Circ. Syst. CAS-25, 694–702 (1978)

    Google Scholar 

  73. Youla, D.C., Webb, H.: Image restoration by the method of convex projections: Part 1-Theory. IEEE Trans. Med. Imag. MI-1, 81–94 (October 1982)

    Google Scholar 

  74. Sezan, M.I., Stark, H.: Image restoration by the method of convex projections: Part 2-applications and numerical results. IEEE Trans. Med. Imag. MI-1, 95–101 (October 1982)

    Google Scholar 

  75. Oskoui-Fard, P., Stark, H.: Tomographic image reconstruction using the theory of convex projections. IEEE Trans. Med. Imag. 7(1), 45–58 (March 1988)

    Google Scholar 

  76. Bucci, O.M., D’Elia, G., Mazzarella, G., Panariello, G.: Antenna pattern synthesis: a new general approach. Proc. IEEE. 82(3), 358–371 (March 1994)

    Google Scholar 

  77. Oh, S., Marks II, R.J., Atlas, L.E.: Kernel synthesis for generalized time-frequency distributions using the method of alternating projections onto convex sets. IEEE Trans. Signal Process. 42(7), 1653–1661 (July 1994)

    Google Scholar 

  78. Lent, A., Tuy, H.: An iterative method for the extrapolation of band limited functions. J. Math. Anal. Appl. 83, 554–565 (1981)

    Google Scholar 

  79. Kaczmarz, S.: Angenaherte auflosung von systemen linearer gleichungen. Bull. Pol. Acad. Sci. Lett. A, 6–8A, 355–357 (1937)

    Google Scholar 

  80. Tanabe, K.: Projection method for solving a singular system. Numer. Math. 17, 203–214 (1971)

    Google Scholar 

  81. Hounsfield, G.N.: A method of and apparatus for examination of a body by radiation such as x-ray or gamma radiation. Patent Specification 1283915, The Patent Office (1972)

    Google Scholar 

  82. Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Imaging. IEEE Press, New York (1988)

    Google Scholar 

  83. Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill, San Francisco (1968)

    Google Scholar 

  84. Pratt, W.K.: Digital Image Processing. Wiley, New York (1978).

    Google Scholar 

  85. Sabbagh, L.D., Sabbagh, H.A., Klopfenstein, J.S.: Image enhancement via extrapolation techniques: a two dimensional iterative scheme and a direct matrix inversion scheme. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 5, pp. 473–483. Plenum Press, New York (1986)

    Google Scholar 

  86. Sabbagh, L.D., Sabbagh, H.A.: Inversion of eddy current data and the reconstruction of flaws Part 2: inversion of data. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 6, pp. 619–626. Plenum Press, New York (1987)

    Google Scholar 

  87. Sabbagh, L.D., Sabbagh, H.A.: Eddy-current modeling and flaw reconstruction. J. Nondestr. Eval. 7(1/2), 95–110 (1988)

    Google Scholar 

  88. Sabbagh, H.A., Sabbagh, L.D.: An eddy-current model for three-dimensional inversion. IEEE Trans. Magn. MAG-22(4), 282–291 (July 1986)

    Google Scholar 

  89. Sabbagh, L.D., Sabbagh, H.A.: Eddy current modeling and signal processing in NDE. In: Chen, C.H. (ed.) Signal Processing and Pattern Recognition in Nondestructive Evaluation of Materials: NATO ASI Series, vol. F44, pp. 145–154. Springer, Berlin (1988)

    Google Scholar 

  90. Theodoulidis, T.P., Poulakis, N., Bowler, J.R.: Developments in modeling eddy current coil interactions with a right-angled conductive wedge. In: Takahashi, S., Kikuchi, H. (eds.) Electromagnetic Nondestructive Evaluation X, pp 41–48. IOS Press, Amsterdam (2007)

    Google Scholar 

  91. Sabbagh, H.A., Sabbagh, L.D., Roberts, T.M.: An eddy-current model and algorithm for three-dimensional nondestructive evaluation of advanced composites. IEEE Trans. Magn. 24(6), 3201–3212 (November 1988)

    Google Scholar 

  92. Murphy, K., Sabbagh, H.A. Treece, J.C.: Verification of a model of eddy-current probes with ferrite cores. In: Thompson, D.O., Chimenti, D.E. (eds) Review of Progress in Quantitative Nondestructive Evaluation, vol. 13, pp. 1089–1093. Plenum Press, New York (1994)

    Google Scholar 

  93. Mittleman, D.M., Jacobsen, R.H., Buss, M.C.: T-ray imaging. IEEE J. Sel. Top. Quant. Electron. 2(3), 679–692 (September 1996)

    Google Scholar 

  94. Sze, S.M.: Physics of Semiconductor Devices. Wiley, New York (1969)

    Google Scholar 

  95. Sabbagh, H.A., Murphy, R.K., Woo, L.W., Sabbagh, E.H., Krzywosz, K.: Recent advances in modeling eddy-current probe-flaw interactions. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 15, pp. 331–338. Plenum Press, New York (1996)

    Google Scholar 

  96. Burke, S.K., Ditchburn, R.J.: Mutual impedance of planar eddy-current driver-pickup spiral coils. Res. Nondestr. Eval. 19, 1–19 (2008)

    Google Scholar 

  97. Moré, J.J., Garbow, B.S., Hillstrom, K.E.: USER GUIDE FOR MINPACK-1. ANL-80-74, Argonne National Laboratory, August 1980

    Google Scholar 

  98. Collin, R.E.: Foundations for Microwave Engineering, Chap. 4. McGraw-Hill Book Company, New York (1966)

  99. Sabbagh, H.A., Sabbagh, E.H., Murphy, R.K., Nyenhuis, J.: Assessing thermal barrier coatings by eddy current inversion. Mater. Eval. 59(11), 1307–1312 (November 2001)

    Google Scholar 

  100. Sabbagh, H.A., Sabbagh, E.H., Murphy, R.K., Nyenhuis, J.: Assessing thermal barrier coatings by eddy current inversion. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 21, pp. 722–727. American Institute of Physics, Melville (2002)

    Google Scholar 

  101. Wang, S. Solid-State Electronics. McGraw-Hill Book Company, New York (1966)

    Google Scholar 

  102. Knopp, J.S., Aldrin, J.C., Misra, P.: Considerations in the validation and application of models for eddy current inspection of cracks around fastener holes. J. Nondestr. Eval. 25(3), 123–138 (2006)

    Google Scholar 

  103. Carpenter, D.C.: Use of the finite element method in simulation and visualization of electromagnetic nondestructive testing applications. Mater. Eval. 58(7), 877–881 (2000)

    Google Scholar 

  104. Palanisamy, R., Lord, W.: Prediction of eddy current probe signal trajectories. IEEE Trans. Magn. 16(5), 1083–1085 (1980)

    Google Scholar 

  105. Knopp, J.S., Aldrin, J.C., Sabbagh, H.A., Jata, K.V.: Estimation theory metrics in electromagnetic NDE, electromagnetic nondestructive evaluation workshop proceedings, Seoul, Korea, 10–12 June 2008

    Google Scholar 

  106. Trefethen, L.N. Bau, D.: Numerical Linear Algebra. SIAM, Philadelphia (1997)

    Google Scholar 

  107. Sabbagh, H.A., Murphy, R.K., Sabbagh, E.H. Aldrin, J.C., Knopp, J., Blodgett, M.: Computational electromagnetics and model-based inversion: a modern paradigm for eddy-current nondestructive evaluation. Appl. Comput. Electrom. 24(6), 533–540 (December 2009)

    Google Scholar 

  108. Sabbagh, E.M.: Circuit Analysis. Ronald Press Company, New York (1961)

    Google Scholar 

  109. Ramo, S., Whinnery, J.R., Van Duzer, T.: Fields and Waves in Communication Electronics. Wiley, New York (1965)

    Google Scholar 

  110. Vernon, S.N.: The universal impedance diagram of the ferrite pot core eddy current transducer. IEEE Trans. Magn. 25(3), 2639–2645 (May 1989)

    Google Scholar 

  111. Bowler, J.R., Sabbagh, L.D., Sabbagh, H.A.: The reduced impedance function for cup-core eddy-current probes. IEEE Trans. Magn. 25(3), 2646–2649 (May 1989)

    Google Scholar 

  112. ’Validation of Direct and Inverse Models of SEACURE Ferritic Tubes With Benchmark Data,’ PID069961, Technical Update, October 2010, Electrical Power Research Institute. Prepared by Victor Technologies, LLC

    Google Scholar 

  113. Todorov, E., Levesque, S., Ames, N., Krzywosz, K.: Measurement of magnetic properites of ferromagnetic tubes for heat exchangers. Trans. Am. Nucl. Soc. 104, 297–298 (26–30 June 2011, Hollywood, Florida)

    Google Scholar 

  114. Scully, J.R.: Hidden corrosion, What Should Be Measured to Improve Emerging Anticipate and Manage Strategies, 32nd Annual Review of Progress In Quantitative Non-destructive Evaluation, QNDE-Brunswick, Maine (2005)

    Google Scholar 

  115. Tian, Y., Tamburrino, A., Udpa, S.S., Udpa, L.: Time-of-flight measurements from eddy current tests. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 22, pp. 593–600. American Institute of Physics, Melville (2003)

    Google Scholar 

  116. Liu, Z., Safizadeh, M.-S. Forsyth, D.S., Lepine, B.A.: Data fusion method for the optimal mixing of multi-frequency eddy current signals. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 22, pp. 577–584. American Institute of Physics, Melville (2003)

    Google Scholar 

  117. Liu, X., Deng, Y., Zeng, Z., Udpa, L., Knopp, J.: Model based inversion technique of GMR signals using element-free Galerkin method. In: Conference Proceedings: 24th Annual Review of Progress in Applied Computational Electromagnetics, Applied Computational Electromagnetics Society, pp. 221–226 (2008)

    Google Scholar 

  118. Gray, J.N., Gray, T.A., Nakagawa, N., Thompson, R.B.: Models for predicting NDE reliability, nondestructive evaluation and quality control, Metals Handbook 17, pp 702–715. ASM International, Ohio, 1989

    Google Scholar 

  119. Thompson, R.B.: Using Physical Models of the Testing Process in Determination of Probability of Detection. Mater. Eval. 69(7), 861–865 (2001)

    Google Scholar 

  120. Thompson, R. B.: A unified approach to the model-assisted determination of probability of detection. Mater. Eval. 66, 667–673 (2008)

    Google Scholar 

  121. U.S. Department of Defense, Handbook, Nondestructive Evaluation System Reliability Assessment, MIL-HDBK-1823A, 7 April 2009

    Google Scholar 

  122. Smith, K.D., Thompson, R.B., Brasche, L.: Model-Based POD: Successes and Opportunities, 1st Meeting of the MAPOD Working Group, Albuquerque, New Mexico, 23–24 September 2004. Web site: http://www.cnde.iastate.edu/MAPOD/

  123. Harding, C., Hugo, G., Bowles, S.: Model-assisted Probability of Detection Validation of Automated Ultrasonic Scanning for Crack Detection at Fastener Holes, Proceedings of the 10th Joint FAA/DoD/NASA Conference on Aging Aircraft, Palm Springs, CA, 16–19 April 2007

    Google Scholar 

  124. Aldrin, J.C., Knopp, J.S., Lindgren E.A., Jata, K.V.: Model-assisted probability of detection (MAPOD) evaluation for eddy current inspection of fastener sites. Rev. progr. Quant. Nondestr. Eval. 28, AIP, 1784–1791 (2009)

    Google Scholar 

  125. Aldrin, J.C., Medina, E.A., Lindgren, E.A., Buynak, C., Knopp, J.: Case studies for model-assisted probabilistic reliability assessment for structural health monitoring systems. Rev. progr. Quant. Nondestr. Eval. 30, AIP, 1589–1596 (2011)

    Google Scholar 

  126. Aldrin, J.C., Medina, E.A., Lindgren, E.A., Buynak, C.F., Knopp, J.S.: Protocol for reliability assessment of structural health monitoring systems incorporating model-assisted probability of detection (MAPOD) approach. In: Chang, F.-K. (ed.) Proceedings of the 8th International Workshop on Structural Health Monitoring, Stanford, 13–15 September 2011

    Google Scholar 

  127. Aldrin, J.C., Medina, E.A., Santiago, J., Lindgren, E.A., Buynak, C.F., Knopp, J.S.: Demonstration study for reliability assessment of SHM systems incorporating model-assisted probability of detection approach. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 31, pp. 1543–1550. American Institute of Physics, Melville (2012)

    Google Scholar 

  128. Aldrin, J.C., Sabbagh, H.A., Murphy, R.K., Sabbagh, E.H., Knopp, J.S., Lindgren, E.A., Cherry, M.R.: Demonstration of model-assisted probability of detection evaluation methodology for eddy-current nondestructive evaluation. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 31, pp. 1733–1740. American Institute of Physics, Melville (2012)

    Google Scholar 

  129. Oberkampf, W.L., Roy, C.J.: Verification and Validation in Scientific Computing. Cambridge University Press, New York (2010)

    Google Scholar 

  130. Knopp, Knopp, J.S., Aldrin, J.C., Blodgett, M.P.: Efficient Propagation of Uncertainty in Simulations via the Probabilistic Collocation Method. In: Chady, T., Gratkowski, S., Takagi, T., Udpa, S.S. (eds) Electromagnetic Nondestructive Evaluation (XIV), pp. 141–148 IOS Press, Amsterdam (2011)

    Google Scholar 

  131. Frey, H.C.: Quantitative analysis of uncertainty and variability in environmental policy making. Fellowship Program for Environmental Science and Engineering, American Association for the Advancement of Science, Washington, DC (1992)

    Google Scholar 

  132. Mahadevan, S., Rebba, R.: Validation of reliability computational models using Bayes networks. Reliab. Eng. Syst. Saf. 87, 223–232 (2005)

    Google Scholar 

  133. Knopp, J.S., Aldrin, J.C., Lindgren, E., Annis, C.: Investigation of a model-assisted approach to probability of detection evaluation. Rev. Prog. Quant. Nondestr. Eval. 26, 1775–1782 (2007)

    Google Scholar 

  134. Aldrin, J.C., Knopp, J.S.: Modeling and simulation for nondestructive testing with applications to aerospace structures. Mater. Eval. 66(1), 53–59 (2008)

    Google Scholar 

  135. Knopp, J.S., Aldrin, J.C., Misra, P.: Considerations in the validation and application of models for eddy current inspection of cracks around fastener holes. J. Nondestr. Eval. 25(3), 123–138 (2006)

    Google Scholar 

  136. Dominguez, N., Feuillard, V., Jenson, F., Willaume, P.: Simulation assisted POD of a phased array ultrasonic inspection in manufacturing. Rev. Progr. Quant. Nondestr. Eval. 31, AIP, 1765–1772 (2012)

    Google Scholar 

  137. Kennedy, M.C., O’Hagan, A.: Bayesian calibration of computer models. J. R. Stat. Soc. B 63, 425–464 (2001)

    Google Scholar 

  138. Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. CRC, London (2003)

    Google Scholar 

  139. Christensen, R., Johnson, W., Branscum, A.: Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians. CRC, Boca Raton (2010)

    Google Scholar 

  140. Meeker, W.Q., Escobar, L.A.: Introduction to the use of Bayesian methods for reliability data. In: Statistical Methods for Reliability Data, pp. 343–368. Wiley, New York (1998)

    Google Scholar 

  141. Thompson, R.B.: A Bayesian approach to the inversion of NDE and SHM data. Rev. Progr. Quant. Nondestr. Eval. 29, AIP, 679–686 (2010)

    Google Scholar 

  142. Leemans, D.V., Forsyth, D.: Bayesian approaches to using field test data in determining the probability of detection. Mater. Eval. 62, 855–859 (2004)

    Google Scholar 

  143. Knopp, J.S., Zeng, L.: Statistical analysis of hit/miss data. Mater. Eval. 71(3), 323–329 (2013)

    Google Scholar 

  144. Li, M., Meeker, W.Q., Hovey, P.: Joint estimation of NDE inspection capability and flaw-size distribution for in-service aircraft inspections. Res. Nondestr. Eval. 23, 104–123 (2012)

    Google Scholar 

  145. Aldrin, J.C., Knopp, J.S., Sabbagh, H.A.: Bayesian methods in probability of detection estimation and model-assisted probability of detection evaluation. In: Thompson, D.O., Chimenti, D.E. (eds.) Review of Progress in Quantitative Nondestructive Evaluation, vol. 32, pp. 1733–1740. American Institute of Physics, Melville (2013)

    Google Scholar 

  146. Gelman, A., Hill, J.: Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  147. ASTM Standard E2782-11. Standard Guide for Measurement Systems Analysis (MSA). ASTM International, West Conshohocken, PA, DOI: 10.1520/E2782-11 (2011). www.astm.org

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Sabbagh, H.A., Murphy, R.K., Sabbagh, E.H., Aldrin, J.C., Knopp, J.S. (2013). Multilayered Media with Cylindrical Geometries. In: Computational Electromagnetics and Model-Based Inversion. Scientific Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8429-6_9

Download citation

Publish with us

Policies and ethics