Determination of Crack Depth Profile in Cylindrical Metallic Structures, Using Alternating Current Field Measurement Data

  • Ali Akbari-Khezri
  • Seyed Hossein Hesamedin SadeghiEmail author


The paper proposes an efficient technique for reconstructing the depth profile of a surface-breaking crack in a cylindrical metal from the output signal of an alternating current field measurement (ACFM) probe. The proposed technique utilizes a pattern search algorithm that seeks to improve the predicted depth profile in each iteration by minimizing an error function. The error function quantifying the difference between the predicted and measured ACFM signals in each iteration is obtained, using a fast pseudo-analytic ACFM probe output simulator. The main feature of the proposed technique is that it requires a small pattern size that includes only a finite number of measurement points along the crack opening, improving the computational efficiency without compromising convergence rate. The efficiency of the proposed method is demonstrated by comparing the proposed method and a Genetic Algorithm for reconstructing depth profiles of several simulated and machine-made cracks with no predetermined geometries.


Cylindrical metal Surface crack Depth profile Eddy current Pattern search 



  1. 1.
    Cui, L., Lim, S.I., Shi, M., Liu, Y., Soh, C.K.: Detection and monitoring of axial cracks on cylindrical structures using torsional wave generated by piezoelectric macro-fiber composite. In: Proceedings Volume 8348, Health Monitoring of Structural and Biological Systems (2012).
  2. 2.
    Cui, L., Liu, Y., Soh, C.K.: Macro-Fiber Composite-Based Structural Health Monitoring System for Axial Cracks in Cylindrical Structures. J. Intell. Mater. Syst. Struct. 25(3), 332–341 (2014)CrossRefGoogle Scholar
  3. 3.
    Greco, A.: Bearing Reliability—White Etching Cracks (WEC). Argonne National Laboratory, Energy Systems Division, NREL Gearbox Reliability Collaborative, Lemont (2013)Google Scholar
  4. 4.
    Baray, D.E., McBride, D.: Nondestructive Testing Techniques. Wiley, New York (1992)Google Scholar
  5. 5.
    Sadeghi, S.H.H., Mirshekar-Syahkal, D.: Scattering of an induced surface electromagnetic field by fatigue cracks in ferromagnetic metals. IEEE Trans. Magn. 28(2), 1008–1016 (1992)CrossRefGoogle Scholar
  6. 6.
    Livingston, R.A.: Standards for evaluating the performance of nondestructive testing (NDT) for preservation. In: American Society for Testing and Materials, pp. 119–125 (1996)Google Scholar
  7. 7.
    Salemi, A.H., Sadeghi, S.H.H., Moini, R.: The effect of sensor lift-off on crack depth measurement by the surface magnetic field measurement technique. Rev. QNDE 21, 977–983 (2002)Google Scholar
  8. 8.
    Ravan, M., Sadeghi, S.H.H., Moini, R.: Neural network approach for determination of fatigue crack depth profile in a metal, using alternating current field measurement data. IET Sci. Meas. Technol. 2, 32–38 (2008)CrossRefGoogle Scholar
  9. 9.
    Xiaoyunl, S., Donghui, L., Kai, Z., Liweil, G., Ran, Z., Jianye, L.: Neural network with adaptive Genetic Algorithm for eddy current nondestructive testing. In: IEEE Proceedings of the 5th World Congress on Intelligent and Automation, pp. 2034–2037 (2004)Google Scholar
  10. 10.
    Chady, T., Enkizono, M., Sikora, R.: Neural network models of eddy current multi-frequency system for nondestructive testing. IEEE Trans. Magn. 36, 1724–1727 (2000)CrossRefGoogle Scholar
  11. 11.
    Preda, G., Popa, R.C., Demachi, K., Miya, K.: Neural network for inverse mapping in eddy current testing. IEEE Int. Jt Conf. Neural Netw. 6, 4033–4036 (1999)CrossRefGoogle Scholar
  12. 12.
    Hoole, S.: Artificial neural network in the solution of inverse electromagnetic field problem. IEEE Trans. Magn. 29, 1931–1934 (1993)CrossRefGoogle Scholar
  13. 13.
    Livni, R., Shalev-Shwartz, S., Shamir, O.: On the computational efficiency of training neural networks. In: Advances in Neural Information Processing Systems, pp. 855–863 (2014)Google Scholar
  14. 14.
    Kam-Chuen, J., Giles, C.L., Horne, B.G.: An analysis of noise in recurrent neural networks: convergence and generalization. IEEE Trans. Neural Netw. 7, 1424–1428 (1996)CrossRefGoogle Scholar
  15. 15.
    Oristaglio, M., Worthington, M.: Inversion of surface and borehole electromagnetic data for 2D electrical conductivity model. Geophys. Prospect. 28, 633 (1980)CrossRefGoogle Scholar
  16. 16.
    Hoole, S., Subramaniam, S., Saldanha, R., Coulomb, J.: Inverse problem methodology and finite elements in the identification of cracks, sources, materials, and their geometry in inaccessible locations. IEEE Trans. Magn. 27, 3433–3443 (1991)CrossRefGoogle Scholar
  17. 17.
    Bowler, J.R.: Thin-skin eddy-current inversion for the determination of crack shape. Inst. Phys. Inverse Probl. 18(6), 1891–1905 (2002)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Norton, S.J., Bowler, J.R.: Theory of eddy-current inversion. J. Appl. Phys. 73, 501–512 (1993)CrossRefGoogle Scholar
  19. 19.
    Li, Y, et al.: An adjoint equation based method for 3D eddy current NDE signal inversion. In: Electromagnetic Nondestructive Evaluation (V), pp. 89–96. Amsterdam (2001)Google Scholar
  20. 20.
    Huang, H., Takagi, T., Fukutomi, H., Tani, J.: Forward and inverse analysis of ECT signals based on reduced vector potential method using a database. In: Electromagnetic Nondestructive Evaluation (II), pp. 313–321. Amsterdam (1998)Google Scholar
  21. 21.
    Hvattum, L.M., Glover, F.: Finding local optima of high-dimensional functions using direct search methods. Eur. J. Oper. Res. 195, 31–45 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zaoui, F., Marchand, C., Pavo, J.: Stochastic crack inversion by an integral approach. In: Electromagnetic Nondestructive Evaluation (V), pp. 129–136. Amsterdam (2001)Google Scholar
  23. 23.
    Ioan, D., Mihai, M., Duca, A.: Use of evolution agents to solve ENDE inverse problems. In: Electromagnetic Nondestructive Evaluation (V), pp. 59–66. Amsterdam (2001)Google Scholar
  24. 24.
    Hooke, R., Jeeves, T.A.: Direct search solution of numerical and statistical problems. J. Assoc. Comput. Mach. (ACM) 8(2), 212–229 (1961)CrossRefGoogle Scholar
  25. 25.
    Koziel, S., Yang, X.S.: Computational Optimization, Methods and Algorithms. Springer, Berlin (2011)CrossRefGoogle Scholar
  26. 26.
    Akbari-Khezri, A., Sadeghi, S.H.H., Moini, R., et al.: An efficient modeling technique for analysis of AC field measurement probe output signals to improve cracks detection and sizing in cylindrical metallic structures. J. Nondestruct. Eval. 35, 9 (2016). CrossRefGoogle Scholar
  27. 27.
    Akbari-Khezri, A., Sadeghi, S.H.H., Moini, R.: Field distribution around surface cracks in metallic cylindrical structures excited by high-frequency current-carrying coils of arbitrary shape. IEEE Trans. Magn. 51(2), 1–10 (2015)CrossRefGoogle Scholar
  28. 28.
    Pattern search for unconstrained NLP. Accessed 27 Aug 2015
  29. 29.
    Wang, X., Zhou, N.: Pattern search firefly algorithm for solving systems of nonlinear equations. In: 7th International Symposium on Computational Intelligence and Design (2014)Google Scholar
  30. 30.
  31. 31.
    Khalaj-Amineh, R., Ravan, M., Sadeghi, S.H.H., Moini, R.: Removal of probe lift-off effects on crack detection and sizing in metals by the AC field measurement technique. IEEE Trans. Magn. 44(8), 2066–2073 (2008)CrossRefGoogle Scholar
  32. 32.
    Sadeghi, S.H.H., Toosi, B., Moini, R.: On the suitability of induction coils for crack detection and sizing in metals by the surface magnetic field measurement technique. NDT E Int. 34(7), 493–504 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ali Akbari-Khezri
    • 1
  • Seyed Hossein Hesamedin Sadeghi
    • 1
    Email author
  1. 1.Department of Electrical EngineeringAmirkabir University of TechnologyTehranIran

Personalised recommendations