surface eddy current probe, eddy currents density distribution, excitation structure, mathematical model, optimal synthesis, computer experiment plan, LPτ–sequence, RBF–metamodel, neural networks committee


Introduction. The work is devoted to metamodels creation of surface circular concentric eddy current probe. Formulation of the problem. In the problem of surface circular concentric eddy current probe synthesis in the general formulation, apriori given desired eddy currents density distribution in the control zone was used. The realization of the optimal synthesis problem involves a multiple solution to the analysis problem for each current structure of numerical calculations excitation, which are very costly in terms of computational and time costs, which makes it impossible to solve the synthesis problem in the classical formulation. By solving the critical resource intensiveness problem, there is the surrogate optimization technology using of that uses the surface circular concentric eddy current probe metamodel, which is much simpler in realization and is an approximation of the exact electrodynamic model. Goal. Creation of surface circular concentric eddy current probe RBF-metamodels, which can be used to calculate eddy currents density distribution in the control zone and suitable for use in optimal synthesis problems. Method. To develop an approximation model, a mathematical apparatus for artificial neural networks, namely, RBF–networks, has been used, whose accuracy has been increased with the help of the neural networks committee. Correction of errors in the committee was reduced by applying the bagging procedure. During the network training the regularization technique is used, which avoids re-learning the neural network. The computer experiment plan was performed using the Sobol LPt–sequences. The obtained multivariable regression model quality evaluation was performed by checking the response surface reproducibility correctness in the entire region of variables variation. Results. The modelling of eddy currents density distribution calculations on exact electrodynamic mathematical models in the experimental plan points are carried out. For the immovable and moving surface circular concentric eddy current probe, RBF–metamodels were constructed with varying spatial coordinates and radius. Scientific novelty. Software was developed for eddy currents density distribution calculation in the surface circular concentric eddy current probe control zone taking into account the speed effect on exact electrodynamic mathematical models and for forming experiment plan points using the Sobol LPt–sequences. The geometric surface circular concentric eddy current probe excitation structures models with homogeneous sensitivity for their optimal synthesis taking into account the speed effect are proposed. Improved computing technology for constructing metamodels. The RBF-metamodels of the surface circular concentric eddy current probe are built and based on the speed effect. Practical significance. The work results can be used in the surface circular concentric eddy current probe synthesis with an apriori given eddy currents density distribution in the control zone. 


Stelblev Yu.I. Synthesis of the given characteristics of eddy current converters. Defectoscopy, 1984, no.11, pp. 12-20. (Rus).

Stelblev Yu.I. Synthesis of eddy current transformers with a given structure of the excitatory field in the control zone. Defectoscopy, 1986, no.4, pp. 58-64. (Rus).

Halchenko V.Ya., Pavlov O.K., Vorobyov M.O. Nonlinear synthesis of magnetic fields of excitation of eddy-current converters of flaw detectors. Methods and instruments of quality control, 2002, no.8, pp. 3-5. (Ukr).

Gal’chenko V.Ya., Vorob’ev M.A. Structural Synthesis of Attachable Eddy-Current Probes with a Given Distribution of the Probing Field in the Test Zone. Russian Journal of Nondestructive Testing, 2005, vol.41, no.1, pp. 29-33. doi: 10.1007/s11181-005-0124-7.

Su Z., Ye C., Tamburrino A., Udpa L., Udpa S. Optimization of coil design for eddy current testing of multi-layer structures. International Journal of Applied Electromagnetics and Mechanics, 2016, vol.52, no.1-2, pp. 315-322. doi: 10.3233/JAE-162030.

Su Z., Efremov A., Safdarnejad M., Tamburrino A., Udpa L., Udpa S.S. Optimization of coil design for near uniform interrogating field generation. AIP Conference Proceedings, 2015, vol.1650, no.1, pp. 405-413. doi: 10.1063/1.4914636.

Stawicki K., Gratkowski S. Optimization of Exciter Coils in Eddy Current Transducer for Testing Thick Conducting Plates. International Symposium on Electromagnetic Fields in Electrical Engineering; Electromagnetic fields in mechatronics, electrical and electronic engineering: ISEF'05; 2005; Baiona, Spain in studies in applied electromagnetics and mechanics; 27; Oxford, Amsterdam, IOS Press, 2006. pp. 497-502.

Itaya T., Ishida K., Kubota Y., Tanaka A., Takehira N. Visualization of eddy current distributions for arbitrarily shaped coils parallel to a moving conductor slab. Progress In Electromagnetics Research M, 2016, vol.47, pp. 1-12. doi: 10.2528/PIERM16011204.

Itaya T., Miki T., Takehira N., Tanaka A., Ishida K. Eddy current distribution for a rectangular coil arranged parallel to a moving conductor slab. IET Science, Measurement & Technology, 2012, vol.6, no.2, pp. 43-51. doi: 10.1049/iet-smt.2011.0015.

Ishida K., Itaya T., Tanaka A., Takehira N. Magnetic Field Analysis of an Arbitrary Shaped Coil Using Shape Functions. IEEE Transactions on Magnetics, 2009, vol.45, no.1, pp. 104-112. doi: 10.1109/TMAG.2008.2005119.

Panas S., Kriezis E.E. Eddy current distribution due to a rectangular current frame moving above a conducting slab. Archiv für Elektrotechnik, 1986, vol.69, no.3, pp. 185-191. doi: 10.1007/BF01574623.

Thollon F., Lebrun B., Burais N., Jayet Y. Numerical and experimental study of eddy current probes in NDT of structures with deep flaws. NDT & E International, 1995, vol.28, no.2, pp. 97-102. doi: 10.1016/0963-8695(94)00010-h.

Theodoulidis T., Bowler J.R. Interaction of an Eddy-Current Coil With a Right-Angled Conductive Wedge. IEEE Transactions on Magnetics, 2010, vol.46, no.4, pp. 1034-1042. doi: 10.1109/TMAG.2009.2036724.

Trembovetska R.V., Halchenko V.Ya., Tychkov V.V. The MLP-Metamodels Application In The Surrogate Optimization Tasks. Young Scientist, 2018, vol.6, no.2, pp. 32-39. (Ukr).

Halchenko V.Ya., Trembovetska R.V., Tychkov V.V. Neural network metamodel of a cylindrical overhead eddy current converter as a component of surrogate optimal synthesis. Bulletin of Kherson National Technical University, 2018, no.3(66), vol.1, pp. 32-38. (Ukr).

Galchenko V.Ya., Trembovetska R.V., Tychkov V.V. Application of metamodels for solving problems of synthesis of eddy current converters with a homogeneous distribution of current density in the control zone. Zbіrnik tez dopovіdej XVII Mіzhnarodnoї naukovo-tehnіchnoї konferencії «Priladobuduvannja: stan і perspektivi» [Materials of the XVII Int. Sci.-Pract. Conf. «Instrumentation: state and prospects»]. Kyiv, NTUU «KPI», 15-16 May, 2018, pp. 146-147. (Ukr).

Halchenko V.Y., Trembovetska R.V., Tychkov V.V. The neurocomputing using of the development metamodels stage in the optimal surrogate antennas synthesis process. Visnyk NTUU KPI SeriiaRadiotekhnika Radioaparatobuduvannia, 2018, no.74, pp. 60-72. doi: 10.20535/radap.2018.74.60-72.

Kuznetsov B.I., Nikitina T.B., Tatarchenko M.O., Khomenko V.V. Multicriterion anisotropic regulators synthesis by multimass electromechanical systems. Tekhnichna Elektrodynamika, 2014, no.4, pp. 105-107. (Rus).

Kuznetsov B.I., Nikitina T.B., Voloshko A.V., Bovdyj I.V., Vinichenko E.V., Kobilyanskiy B.B. Single-circuit active screening of magnetic field generated by several overhead transmission lines in residential area. Electrical engineering & electromechanics, 2018, no.1, pp. 41-45. doi: 10.20998/2074-272X.2018.1.06.

Haykin Simon. Neironnye seti: polnyi kurs [Neural Networks: A Complete Course]. Moscow, Williams Publ. House, 2006. 1104 p. (Rus).

Sobol I.M., Statnikov R.B. Vybor optimal'nyh parametrov v zadachah so mnogimi kriterijami [Choosing Optimal Parameters in Problems with Many Criteria]. Moscow, Drofa Publ., 2006. 175 p. (Rus).

Radchenko S.G. Metodologija regressionnogo analiza: monografija [Methodology of regression analysis: monograph]. Kyiv, Korniychuk Publ., 2011. 376 p. (Rus).



How to Cite

Halchenko, V. Y., Trembovetska, R. V., & Tychkov, V. V. (2019). DEVELOPMENT OF EXCITATION STRUCTURE RBF-METAMODELS OF MOVING CONCENTRIC EDDY CURRENT PROBE. Electrical Engineering & Electromechanics, (2), 28–38.



Theoretical Electrical Engineering