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Abstract

A mathematical method for nonlinear surrogate synthesis of frame surface eddy current probes providing a uniform eddy current density distribution in the testing object area is proposed. A metamodel of a frame movable eddy-current probe with a planar excitation system structure, used in the algorithm for surrogate optimal synthesis was created. The examples of a nonlinear synthesis of excitation systems with the application of the modern metaheuristic stochastic algorithms for finding the global extremum are considered. The numerical findings of the problem analyses are presented. The efficiency of the synthesized excitation structures was demonstrated on the basis of the eddy current density distribution graphs on the surface of the control zone of the object in comparison with classical analogues.
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Bibliography

[1] Rosado, L. S., Gonzalez, J. C., Santos, T. G., Ramos, P. M., & Pieda, M. (2013). Geometric optimization of a differential planar eddy currents probe for non-destructive testing. Sensors and Actuators A: Physical., 197, 96–105. https://doi.org/10.1016/j.sna.2013.04.010
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[3] Su, Z.,Ye, C., Tamburrino, A., Udpa, L.,&Udpa, S. (2016). Optimization of coil design for eddy current testing of multi-layer structures. International Journal of Applied Electromagnetics and Mechanics, 52(1–2), 315–322. https://doi.org/10.3233/JAE-162030
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[5] Ye, C., Udpa, L., & Udpa, S. (2016). Optimization and Validation of Rotating Current Excitation with GMR Array Sensors for Riveted Structures Inspection. Sensors, 16(9), 1512. https://doi.org/10.3390/s16091512
[6] Rekanos, I. T., Antonopoulos, C. S., & Tsiboukis, T. D. (1999). Shape design of cylindrical probe coils for the induction of specified eddy current distributions. IEEE Transactions Magnetics, 35(3), 1797–1800. https://doi.org/10.1109/20.767380
[7] Li, Y., Ren, S., Yan, B., Zainal Abidin, I. M., & Wang, Y. (2017). Imaging of subsurface corrosion using gradient-field pulsed eddy current probes with uniform field excitation. Sensors, 17, 1747. https://doi.org/10.3390/s17081747
[8] Hashimoto, M., Kosaka, D., Ooshima, K., & Nagata, Y. (2002). Numerical analysis of eddy current testing for tubes using uniform eddy current distribution. International Journal of Applied Electromagnetics and Mechanics, 15(1–4), 27–32. https://doi.org/10.3233/JAE-2002-511
[9] Repelianto, A. S., Kasai, N., Sekino, K., & Matsunaga, M. (2019). A Uniform Eddy Current Probe with a Double-Excitation Coil for Flaw Detection on Aluminium Plates. Metals, 9(10), 1116. https://doi.org/10.3390/met9101116
[10] Halchenko, V. Ya., Trembovetskaya, R. V., & Tychkov, V. V. (2020). Surface eddy current probes: excitation systems of the optimal electromagnetic field (review). Devices and Methods of Measurements, 11(2), 91–104. https://doi.org/10.21122/2220-9506-2020-11-2-91-104
[11] Trembovetska, R. V., Halchenko, V. Ya., Tychkov, V. V., & Storchak, A. V. (2020). Linear Synthesis of Uniform Anaxial Eddy Current Probes with a Volumetric Structure of the Excitation System. International Journal “NDT Days”, 3(4), 184–190. https://www.bg-s-ndt.org/journal/ vol3/JNDTD-v3-n4-a01.pdf (in Russian)
[12] Halchenko, V. Ya., Yakimov, A. N., & Ostapuschenko, D. L. (2010). Global optimum search of functions with using of multiagent swarm optimization hybrid with evolutional composition formation of population. Information Technology, 10, 9–16. http://novtex.ru/IT/it2010/It1010.pdf (in Russian)
[13] Itaya, T., Ishida, K., Kubota, Y., Tanaka, A., & Takehira, N. (2016). Visualization of Eddy Current Distributions for Arbitrarily Shaped Coils Parallel to a Moving Conductor Slab. Progress In Electromagnetics Research M, 47, 1–12. https://doi.org/10.2528/PIERM16011204
[14] Itaya, T., Ishida, K., Tanaka, A., Takehira, N., & Miki, T. (2012). Eddy Current Distribution for a Rectangular Coil Arranged Parallel to a Moving Conductor Stab. IET Science, Measurement & Technology, 6(2), 43–51. https://doi.org/10.1049/iet-smt.2011.0015
[15] Kozieł, S., & Bekasiewicz, A. (2017). Multi-objective design of antennas using surrogate models, World Scientific Publishing Europe Ltd. [16] Forrester, A. I. J., Sóbester, A., & Keane, A. J. (2008). Engineering design via surrogate modelling: a practical guide. Chichester: Wiley.
[17] Burnaev, E. V., Erofeev, P., Zaitsev, A., Kononenko, D., & Kapushev E. (2015). Surrogate modeling and optimization of the airplane wing profile based on Gaussian processes. http://itas2012.iitp.ru/pdf/ 1569602325.pdf (in Russian)
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[19] Halchenko, V. Ya., Trembovetska, R. V., Tychkov, V. V., & Storchak, A. V. (2019). Nonlinear surrogate synthesis of the surface circular eddy current probes. Przegla˛d Elektrotechniczny, 9, 76–82. https://doi.org/10.15199/48.2019.09.15
[20] Halchenko,V. Ya., Trembovetska, R. V.,&Tychkov, V. V. (2019). Linear synthesis of non-axial surface eddy current probes. International Journal “NDT Days”, 2(3), 259–268. https://www.ndt.net/article/ NDTDays2019/papers/JNDTD-v2-n3-a03.pdf (in Russian)
[21] Trembovetska, R. V., Halchenko, V. Y., & Tychkov, V. V. (2019). Multiparameter hybrid neural network metamodel of eddy current probes with volumetric structure of excitation system. International Scientific Journal Mathematical Modeling, 4(3), 113–116. https://stumejournals.com/journals/ mm/2019/4/113
[22] Koshevoy, N. D., Gordienko, V. A., & Sukhobrus, Ye. A. (2014). Optimization for the design matrix realization value with the aim to investigate technological processes. Telecommunications and radio engineering, 73(15), 1383–1386. https://doi.org/10.1615/TelecomRadEng.V73.i15.60 (in Russian)
[23] Halchenko, V. Ya., Trembovetska, R. V., Tychkov, V. V., & Storchak, A. V. (2020). The Construction of Effective Multidimensional Computer Designs of Experiments Based on a Quasi-random Additive Recursive Rd–sequence. Applied Computer Systems, 25(1), 70–76. https://doi.org/10.2478/ acss-2020-0009
[24] Brink, H., Richards, J., & Fetherolf, M. (2017). Real-World Machine Learning. Manning Publications Co.
[25] Kuznetsov, B. I., Nikitina, T. B.,& Bovdui, I. V. (2020). Active shielding of magnetic field of overhead power line with phase conductors of triangle arrangement. Tekhnichna elektrodynamika, 4, 25–28. https://doi.org/10.15407/techned2020.04.025
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Authors and Affiliations

Volodymyr Ya. Halchenko
1
Ruslana Trembovetska
1
ORCID: ORCID
Volodymyr Tychkov
1
ORCID: ORCID

  1. Cherkasy State Technological University, Instrumentation, Mechatronics and Computer Technologies Department, Blvd. Shevchenka, 460, 18006, Cherkasy, Ukraine
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Abstract

Existing scientific studies devoted to the design of eddy-current probes with a priori given configuration of the electromagnetic excitation field, which provide a uniform eddy current density distribution, consider a wide class of such, but are limited to the case when the probe is stationary relative to the testing object. Therefore, the actual problem is the synthesis of moving tangential eddy current probes with a frame excitation system that provides a uniform eddy current density distribution in the testing object, the solution of which is proposed in this study.
A mathematical method for nonlinear surrogate synthesis of excitation systems for frame moving tangential surface eddy current probes, which implements a uniform eddy current density distribution of the testing zone object, is proposed. A metamodel of the volumetric structure of the excitation system of the frame tangential eddy current probe, applied in the process of surrogate optimal parametric synthesis, has been created. The examples of nonlinear synthesis of excitation systems using modern metaheuristic stochastic algorithms for finding the global extremum are considered. The numerical results of the obtained solutions of the problems are presented. The efficiency of the synthesized structures of excitation systems in comparison with classical analogs is shown on the graphs of the eddy current density distribution on the object surface in the testing zone.
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Bibliography

[1] Repelianto A.S., Development of uniform eddy current probes using multi excitation coils, Doctoral Dissertation, Graduate School of Environment and Information Sciences, Yokohama National University (2020).
[2] Halchenko V.Y., Trembovetskaya R.V., Tychkov V.V., Surface eddy current probes: excitation systems of the optimal electromagnetic field (review), Devices and Methods of Measurements, vol. 11, no. 2, pp. 91–104 (2020), DOI: 10.21122/2220-9506-2020-11-2-91-104.
[3] Huang L., Zou J., Zhang J., ZhouY., Deng F., A novel rectangular vertical probe with a conductive shell for eddy current testing, International Journal of Applied Electromagnetics and Mechanics, vol. 62, no. 1, pp. 191–205 (2019), DOI: 10.3233/JAE-190058.
[4] Halchenko V.Y., Trembovetskaya R.V., Tychkov V.V., Linear synthesis of non-axial surface eddy current probes, International Journal “NDT Days”, vol. 2, no. 3, pp. 259–268 (2019).
[5] Trembovetska R.V., Halchenko V.Y., Tychkov V.V., Storchak A.V., Linear synthesis of uniform anaxial eddy current probes with a volumetric structure of the excitation system, International Journal “NDT Days”, vol. 3, no. 4. pp. 184–190 (2020).
[6] Trembovetska R.V., Halchenko V.Y., Tychkov V.V., Bazilo C.V., Linear synthesis of frame eddy current probes with a planar excitation system, International Scientific Journal “Mathematical Modeling”, vol. 4, no. 3. pp. 86–90 (2020).
[7] 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, vol. 47, pp. 1–12 (2016), DOI: 10.2528/pierm16011204.
[8] Itaya T., Ishida K., Tanaka A., Takehira N., Miki T., A new analytical method for calculation of eddy current distribution and its application to a system of conductor-slab and rectangular coil, Progress in Electromagnetics Research Symposium, pp. 135–139 (2011).
[9] Halchenko V.Y., Trembovetska R.V., Tychkov V.V., Storchak A.V., Nonlinear surrogate synthesis of the surface circular eddy current probes, Przegląd Elektrotechniczny, no. 9, pp. 76–82 (2019), DOI: 10.15199/48.2019.09.15.
[10] Halchenko V.Y., Trembovetska R.V., Tychkov V.V., Development of excitation structure RBFmetamodels of moving concentric eddy current probe, Electrical Engineering & Electromechanics, no. 2, pp. 28–38 (2019), DOI: 10.20998/2074-272X.2019.2.05.
[11] Trembovetska R.V., Halchenko V.Y., Tychkov V.V., Studying the computational resource demands of mathematical models for moving surface eddy current probes for synthesis problems, Eastern- European Journal of Enterprise Technologies, vol. 95, no. 5/5, pp. 39–46 (2018), DOI: 10.15587/1729-4061.2018.143309.
[12] Forrester A.I.J., Sóbester A., Keane A.J., Engineering design via surrogate modelling: a practical guide, Chichester, Wiley (2008).
[13] Koziel S., Echeverrı’a-Ciaurri D., Leifsson L., Surrogate-based methods, Computational Optimization, Methods and Algorithms, Berlin, Springer-Verlag, pp. 33–59 (2011), https://link.springer.com/chapter/10.1007/978-3-642-20859-1_3
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[21] Kuznetsov B.I., Nikitina T.B., Bovdui I.V., Active shielding of magnetic field of overhead power line with phase conductors of triangle arrangement, Technical Electrodynamisc, no. 4, pp. 25–28 (2020), DOI: 10.15407/techned2020.04.025.
[22] Halchenko V.Y., Yakimov A.N., Ostapuschenko D.L., Global optimum search of functions with using of multiagent swarm optimization hybrid with evolutional composition formation of population, Information Technology, no. 10, pp. 9–16 (2010).
[23] Halchenko V.Y., Yakimov A.N., Ostapuschenko D.L., Method of Pareto-optimal parametric synthesis of axially symmetric magnetic systems taking into account the nonlinear magnetic properties of a ferromagnetic, Journal of Technical Physics, no. 7, pp. 1–7 (2012).
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Authors and Affiliations

Volodymyr Yakovych Halchenko
1
ORCID: ORCID
Ruslana Volodymyrivna Trembovetska
1
ORCID: ORCID
Volodymyr Volodymyrovych Tychkov
1
ORCID: ORCID

  1. Cherkasy State Technological University, Ukraine

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