Jensen-Shannon Divergence of Two Eddy Current Distributions Induced by Circular and Fractal Koch Excitation Coils

Document Type : Original Article


School of Mechanical and Electrical Engineering, Lanzhou university of technology, Lanzhou, China


Eddy current distribution is important to the performance of planar eddy current probes. In this paper, the Jensen-Shannon divergences of tangential intersection angle spectrum and radial direction energy spectrum were proposed to evaluate the difference between eddy current distributions generated by circular and fractal Koch excitation coils. By the simulation for the circular and Koch shape excitation coils, it works out that the difference of the eddy current distributions between the two kinds of coils becomes larger and larger with an increase in the values of the two Jensen-Shannon divergences. At the same time, the correlation between the change of Jensen-Shannon divergence and the detectability of the short crack in the special direction was discussed through simulation and experiment results. It is found that, relative to the crack in 0° direction, the detectability of the Koch and circular differential pickup probes to the crack in 90° direction has a correlation with the Jensen-Shannon divergence of tangential intersection angle spectrum. The width of each signal generated by the two probes has a correlation with the Jensen-Shannon divergence of radial direction energy spectrum.


Main Subjects

  1. Garcia-Martin, J., Gomez-Gil, J., and Vazquez-Sanchez, E., “Non-destructive techniques based on eddy current testing”, Sensors, Vol. 11, (2011), 2525-2565. DOI: 10.3390/s110302525
  2. Gilles-Pascaud, C., Decitre, J.M., Vacher, F., Fermon, C., Pannetier, M., and Cattiaux, G., “Eddy current flexible probes for complex geometries”, AIP Conference Proceedings, (2006), 399-406. DOI: 10.1063/1.2184556
  3. Martinos, J., and Martinos, T., “Experimental development flexible eddy current planar probe”, Non-Destructive Testing, (2015), 1-3.
  4. Ding, T.H., Chen, X.L., and Huang, Y.P., “Ultra-Thin flexible eddy current sensor array for gap measurements”, Tsinghua Science and Technology, Vol. 9, No. 6, (2004), 667-671.
  5. Meyendorf, N., Grundy, D., Baaklini, G.Y., Washabaugh, A., Schlicker, D., Michel, B., Shay, I., and Goldfine, N., “Health monitoring using MWM-array and IDED-array sensor networks”, Advanced Sensor Technologies for Nondestructive Evaluation and Structural Health Monitoring, Vol. 5770, (2005), 14-23. DOI: 10.1117/12.606069
  6. Zilberstein, V., Walrath, K., Grundy, D., Schlicker, D., Goldfine, N., Abramovici, E., and Yentzer, T., “MWM eddy-current arrays for crack initiation and growth monitoring”, International Journal of Fatigue, 25, (2003), 1147-1155. DOI: 10.1016/j.ijfatigue.2003.08.010
  7. Ding, H., He, Y.T., and Jiao, S.B., “Rosette eddy current sensor for structural health monitoring”, Applied Mechanics and Materials, 330, (2013), 430-436. DOI: 10.4028/
  8. Fan, X.H., Chen, T., He, Y.T., Du, J.Q., Ma, B.L., and Song, Y.J., “An excitation coil layout method for improving the sensitivity of a rosette flexible eddy current array sensor”, Smart Materials and Structures, Vol. 29, (2020), 1-16. DOI: 10.1088/1361-665X/ab5455
  9. Sun, Z.G., Cai, D., Zou, C., Zhang, W.Z., and Chen, Q., “A flexible arrayed eddy current sensor for inspection of hollow axle inner surfaces”, Sensors, Vol. 16, (2016), 1-9. DOI: 10.3390/s16070952
  10. Zhang, H.Y., Ma, L.Y., and Xie, F.Q., “A method of steel ball surface quality inspection based on flexible arrayed eddy current sensor”, Measurement, Vol. 144, (2019), 192-202. DOI: 10.1016/j.measurement.2019.05.056
  11. Xiao, M., Ju, F., Ning, P., He, Z.Q., Li, K.Y., Zhou, C., and Zhang, Y.Z., “Effects of filler type and aging on self-sensing capacity of cement paste using eddy current-based nondestructive detection”, Measurement, Vol. 182, (2021), 1-9. DOI: 10.1016/j.measurement.2021.109708
  12. Yin, X.K., Zhang, X.R., Li, Y.Y., Zhu, T., Hutchins, D., Li, W., Chen, G.M., “A combined inductive and capacitive non-destructive evaluation technique using a single spiral coil sensor”, IEEE Sensors Journal, Vol. 21, No. 16, (2021), 18187-18195. DOI: 10.1109/JSEN.2021.3084204
  13. She, S.B., He, Y.Z., Chen, Y.F., and Chady, T., “Flexible floral eddy current probe for detecting flaws in metal plate”, IEEE Sensors Journal, Vol. 20, No. 18, (2020), 10521-10529. DOI: 10.1109/JSEN.2020.2995472
  14. She, S.B., Liu, Y.Z., Zhang, S.J., Wen, Z.Z., Zhou, Z.J., Liu, X.K., Sui, Z.H., Ren, D.T., Zhang, F., and He, Y.Z., “Flexible differential butterfly-shape eddy current array sensor for defect detection of screw thread”, IEEE Sensors Journal, DOI: 10.1109/JSEN.2021.3093550.
  15. Chen, G.L., Cao, Z., and Zhang, W.M., “A novel planar differential Koch fractal eddy current probe with parallel wound topological structure”, Journal of Sensors, (2021), 1-13. DOI: 10.1155/2021/6671189
  16. Chen, G.L., Zhang, W.M., and Pang, W.H., “Koch curve fractal geometry excitation probe for EC non-destructive testing”, Measurement, Vol. 124, (2018), 470-478. DOI: 10.1016/j.measurement.2018.04.031
  17. Xie, R.F., Chen, D.X., Pan, M.C., Tian, W.G., Wu, X.Z., Zhou, W.H., and Tang, Y., “Fatigue crack length sizing using a novel flexible eddy current sensor array”, Sensors, Vol. 15, (2015) 32138-32151. DOI: 10.3390/s151229911
  18. Zhang, W.P., Wang, C.L., Xie, F.Q., and Zhang, H.Y., “Defect imaging curved surface based on flexible eddy current array sensor”, Measurement, Vol. 151, (2020), 1-10. DOI: 10.1016/j.measurement.2019.107280
  19. Aouf, A., Bouchala, T., Abdou, A., and Abdelhadi, B., “Eddy current probe configuration for full rail top surface inspection”, Instrumentation Mesure Métrologie, Vol. 20, No. 2, (2021), 65-72. DOI: 10.18280/i2m.200201
  20. Chen, K.F., Gao, B., Tian, G.Y., Yang, Y.P., Yang, C.R., and Ma, Q.P., “Differential coupling double-layer coil for EC testing with high lift-off”, IEEE Sensors Journal, Vol. 21, No. 16, (2021), 18146-18155. DOI: 10.1109/JSEN.2021.3076880
  21. Fan, X.H., Chen, T., He, Y.T., and Du, J.Q., “Influence of spatial winding distribution of flexible eddy current sensor on quantitative monitoring of subsurface cracks”, Measurement, Vol. 178, (2021), 1-15. DOI: 10.1016/j.measurement.2021.109382
  22. Zhang, N., Ye, C.F., Peng, L., and Tao, Y., “Eddy current probe with three-phase excitation and integrated array tunnel magnetoresistance sensors”, IEEE Transactions on Industrial Electronics, Vol. 68, No. 6, (2021), 5325-5336. DOI: 10.1109/TIE.2020.2989704
  23. Chen, G.L., and Cao, Z., “Quantitative evaluation of eddy current distribution by relative entropy and cross entropy”, Measurement and Control, Vol. 54, (2021), 1-6. DOI: 10.1177/0020294020984201
  24. Zhang, W.M., Chen, G.L., and Pang, W.H., “Shannon information entropy of eddy current density distribution”, Nondestructive Testing and Evaluation, Vol. 32, (2016), 152-165. DOI: 10.1080/10589759.2016.1184266
  25. Chen, G.L., “Two novel information entropy indices for analysis of the eddy current distribution”, Entropy, Vol. 20, (2018), 1-8. DOI: 10.3390/e20090699
  26. Chen, G.L., and Zhang, W.M., “Angular spectral density and information entropy for eddy current distribution”, Entropy, Vol. 18, (2016), 1-11. DOI:3390/e18110392
  27. Lin, J.H., “Divergence measures based on the Shannon entropy”, IEEE Transactions on Information Theory, Vol. 37, No. 1, (1991), 145-151. DOI: 10.1109/18.61115