DOI QR코드

DOI QR Code

A study on estimating the interlayer boundary of the subsurface using a artificial neural network with electrical impedance tomography

  • 투고 : 2021.12.06
  • 심사 : 2021.12.20
  • 발행 : 2021.12.31

초록

Subsurface topology estimation is an important factor in the geophysical survey. Electrical impedance tomography is one of the popular methods used for subsurface imaging. The EIT inverse problem is highly nonlinear and ill-posed; therefore, reconstructed conductivity distribution suffers from low spatial resolution. The subsurface region can be approximated as piece-wise separate regions with constant conductivity in each region; therefore, the conductivity estimation problem is transformed to estimate the shape and location of the layer boundary interface. Each layer interface boundary is treated as an open boundary that is described using front points. The subsurface domain contains multi-layers with very complex configurations, and, in such situations, conventional methods such as the modified Newton Raphson method fail to provide the desired solution. Therefore, in this work, we have implemented a 7-layer artificial neural network (ANN) as an inverse problem algorithm to estimate the front points that describe the multi-layer interface boundaries. An ANN model consisting of input, output, and five fully connected hidden layers are trained for interlayer boundary reconstruction using training data that consists of pairs of voltage measurements of the subsurface domain with three-layer configuration and the corresponding front points of interface boundaries. The results from the proposed ANN model are compared with the gravitational search algorithm (GSA) for interlayer boundary estimation, and the results show that ANN is successful in estimating the layer boundaries with good accuracy.

키워드

과제정보

This research was supported by the 2021 scientific promotion program funded by Jeju National University Manuscript received

참고문헌

  1. P. Kearey, M. Brooks, and I. Hill, An introduction to geophysical exploration. John Wiley & Sons, vol.4, 2002.
  2. R. Philp and P. Crisp, "Surface geochemical methods used for oil and gas prospecting-a review," Journal of Geochemical Exploration, vol.17, no.1, pp.1-34, 1982. DOI: 10.1016/0375-6742(82)90017-6
  3. R. Saad, M. Nawawi, and E. Mohamad, "Groundwater detection in alluvium using 2-d electrical resistivity tomography (ert)," Electronic Journal of Geotechnical Engineering, vol.17, pp.369-376, 2012.
  4. D. B. Hoover, D. P. Klein, D. C. Campbell, and E. du Bray, "Geophysical methods in exploration and mineral environmental investigations," Preliminary compilation of descriptive geoenvironmental mineral deposit models: USGS Open-File Report, vol.95, no.831, pp.1-27, 1995.
  5. N. Abdullahi, I. Osazuwa, P. Sule et al., "Application of integrated geophysical techniques in the investigation of groundwater contamination: A case study of municipal solid waste leachate," Ozean Journal of applied sciences, vol.4, no.1, pp.7-25, 2011.
  6. G. S. Baker, T. E. Jordan, J. Pardy et al., "An introduction to ground penetrating radar (gpr)," Special Papers-Geological Society of America, vol.432, p.1, 2007. DOI: 10.1130/2007.2432(01)
  7. W. Daily, A. Ramirez, D. LaBrecque, and J. Nitao, "Electrical resistivity tomography of vadose water movement," Water Resources Research, vol.28, no.5, pp.1429-1442, 1992. DOI: 10.1029/91WR03087
  8. K. Sudha, M. Israil, S. Mittal, and J. Rai, "Soil characterization using electrical resistivity tomography and geotechnical investigations," Journal of Applied Geophysics, vol.67, no.1, pp.74-79, 2009. DOI: 10.1016/j.jappgeo.2008.09.012
  9. T. J. Katsube, P. K. Keating, H. McNairn, Y. Das, R. DiLabio, V. Singhroy, S. Connell-Madore, M. E. Best, J. Hunter, R. Klassen et al., "Soil moisture and electrical conductivity prediction and their implication for landmine detection technologies," in Detection and Remediation Technologies for Mines and Minelike Targets IX, vol. 5415. International Society for Optics and Photonics, pp.691-704, 2004. DOI: 10.1117/12.542521.short?SSO=1
  10. T. J. Katsube, R. A. Klassen, Y. Das, R. Ernst, T. Calvert, G. Cross, J. Hunter, M. Best, R. DiLabio, and S. Connell, "Prediction and validation of soil electromagnetic characteristics for application in landmine detection," in Detection and Remediation Technologies for Mines and Minelike Targets VIII, vol.5089. International Society for Optics and Photonics, pp.1219-1230, 2003. DOI: 10.1117/12.486983.short
  11. W. Menke, "The resolving power of cross-borehole tomography," Geophysical Research Letters, vol.11, no.2, pp.105-108, 1984. DOI: 10.1029/GL011i002p00105
  12. M. Perri, G. Cassiani, I. Gervasio, R. Deiana, and A. Binley, "A saline tracer test monitored via both surface and cross-borehole electrical resistivity tomography: Comparison of time-lapse results," Journal of Applied Geophysics, vol.79, pp.6-16, 2012. DOI: 10.1016/j.jappgeo.2011.12.011
  13. J. G. Webster, Electrical impedance tomography. Taylor & Francis Group, 1990.
  14. M. Cheney, D. Isaacson, and J. C. Newell, "Electrical impedance tomography," SIAM review, vol.41, no.1, pp.85-101, 1999. DOI: 10.21037/atm.2017.12.06
  15. G. D'Antona, A. Ferrero, M. Lazzaroni, R. Ottoboni, and E. Samarani, "Active monitoring apparatus for underground pollutant detection based on electrical impedance tomography," in IMTC/2002. Proceedings of the 19th IEEE Instrumentation and Measurement Technology Conference (IEEE Cat. No. 00CH37276), vol.1. pp.577-579, 2002. DOI: 10.1109/IMTC.2002.1006906
  16. R. Stacey, K. Li, R. N. Horne et al., "Electrical impedance tomography (eit) technique for real-time saturation monitoring," in SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, 2006. DOI: 10.2118/103124-MS
  17. A. Adler, J. H. Arnold, R. Bayford, A. Borsic, B. Brown, P. Dixon, T. J. Faes, I. Frerichs, H. Gagnon, Y. Garber et al., "Greit: a unifed approach to 2d linear eit reconstruction of lung images," Physiological measurement, vol.30, no.6, p.S35, 2009. DOI: 10.1088/0967-3334/30/6/S03
  18. D. Holder, "Electrical impedance tomography (eit) of brain function," Brain Topography, vol.5, no.2, pp.87-93, 1992. DOI: 10.1007/BF01129035
  19. E. K. Murphy, A. Mahara, X. Wu, and R. J. Halter, "Phantom experiments using soft-prior regularization eit for breast cancer imaging," Physiological measurement, vol.38, no.6, p.1262, 2017. DOI: 10.1088/1361-6579/aa691b
  20. A. P. Bagshaw, A. D. Liston, R. H. Bayford, A. Tizzard, A. P. Gibson, A. T. Tidswell, M. K. Sparkes, H. Dehghani, C. D. Binnie, and D. S. Holder, "Electrical impedance tomography of human brain function using reconstruction algorithms based on the fnite element method," NeuroImage, vol.20, no.2, pp.752-764, 2003. DOI: 10.1016/S1053-8119(03)00301-X
  21. G. Xu, H. Wu, S. Yang, S. Liu, Y. Li, Q. Yang, W. Yan, and M. Wang, "3-d electrical impedance tomography forward problem with fnite element method," IEEE transactions on magnetics, vol.41, no.5, pp.1832-1835, 2005. DOI: 10.1109/TMAG.2005.846503
  22. E. Woo, P. Hua, J. Webster, and W. Tompkins, "Finite-element method in electrical impedance tomography," Medical and Biological Engineering and Computing, vol.32, no.5, pp.530-536, 1994. DOI: 10.1007/BF02515311
  23. J. C. de Munck, T. J. Faes, and R. M. Heethaar, "The boundary element method in the forward and inverse problem of electrical impedance tomography," IEEE transactions on Biomedical Engineering, vol.47, no.6, pp.792-800, 2000. DOI: 10.1109/10.844230
  24. M. Tarvainen, M. Vauhkonen, T. Savolainen, and J. P. Kaipio, "Boundary element method and internal electrodes in electrical impedance tomography," International journal for numerical methods in engineering, vol.50, no.4, pp.809-824, 2001. https://doi.org/10.1002/1097-0207(20010210)50:4<809::AID-NME52>3.0.CO;2-5
  25. R. Duraiswami, G. L. Chahine, and K. Sarkar, "Boundary element techniques for effcient 2-d and 3-d electrical impedance tomography," Chemical engineering science, vol.52, no.13, pp.2185-2196, 1997. https://doi.org/10.1016/S0009-2509(97)00044-4
  26. R. G. Aykroyd and B. A. Cattle, "A boundaryelement approach for the complete-electrode model of eit illustrated using simulated and real data," Inverse Problems in Science and Engineering, vol.15, no.5, pp.441-461, 2007. DOI: 10.1080/17415970600795337
  27. A. K. Khambampati, B. A. Lee, K. Y. Kim, and S. Kim, "An analytical boundary element integral approach to track the boundary of a moving cavity using electrical impedance tomography," Measurement Science and Technology, vol.23, no.3, p.035401, 2012. DOI: 10.1088/0957-0233/23/3/035401
  28. W. R. Lionheart, "Eit reconstruction algorithms: pitfalls, challenges and recent developments," Physiological measurement, vol.25, no.1, p.125, 2004. DOI: 10.1088/0967-3334/25/1/021
  29. E. Beretta, S. Micheletti, S. Perotto, and M. Santacesaria, "Reconstruction of a piecewise constant conductivity on a polygonal partition via shape optimization in eit," Journal of Computational Physics, vol.353, pp.264-280, 2018. https://doi.org/10.1016/j.jcp.2017.10.017
  30. S. Kim, U. Z. Ijaz, A. K. Khambampati, K. Y. Kim, M. C. Kim, and S. I. Chung, "Moving interfacial boundary estimation in stratifed ?ow of two immiscible liquids using electrical resistance tomography," Measurement Science and Technology, vol.18, no.5, p.1257, 2007. https://doi.org/10.1088/0957-0233/18/5/012
  31. A. K. Khambampati, S. K. Konki, Y. Han, S. Sharma, and K. Y. Kim, "An effcient method to determine the size of bladder using electrical impedance tomography," in TENCON 2018~2018 IEEE Region 10 Conference. IEEE, 2018, pp. 1933-1936.
  32. D. Liu, A. K. Khambampati, and J. Du, "A parametric level set method for electrical impedance tomography," IEEE transactions on medical imaging, vol.37, no.2, pp.451-460, 2017. https://doi.org/10.1109/tmi.2017.2756078
  33. D. Liu, D. Gu, D. Smyl, J. Deng, and J. Du, "B-spline-based sharp feature preserving shape reconstruction approach for electrical impedance tomography," IEEE transactions on medical imaging, vol.38, no.11, pp.2533-2544, 2019. https://doi.org/10.1109/tmi.2019.2905245
  34. S. K. Sharma, S. K. Konki, A. K. Khambampati, and K. Y. Kim, "Bladder boundary estimation by gravitational search algorithm using electrical impedance tomography," IEEE Transactions on Instrumentation and Measurement, vol.69, no.12, pp.9657-9667, 2020. https://doi.org/10.1109/tim.2020.3006326
  35. W. Liu, Z. Wang, X. Liu, N. Zeng, Y. Liu, and F. E. Alsaadi, "A survey of deep neural network architectures and their applications," Neurocomputing, vol.234, pp.11-26, 2017. DOI: 10.1016/j.neucom.2016.12.038
  36. S. K. Konki, A. K. Khambampati, S. K. Sharma, and K. Y. Kim, "A deep neural network for estimating the bladder boundary using electrical impedance tomography," Physiological Measurement, vol.41, no.11, p.115003, 2020. DOI: 10.1088/1361-6579/abaa56
  37. S. K. Sharma, A. K. Khambampati, and K. Y. Kim, "Estimating aquifer location using deep neural network with electrical impedance tomography," Journal of IKEEE, vol.24, no.4, pp.982-990, 2020. DOI: 10.7471/ikeee.2020.24.4.982
  38. H. Park, K. Park, S. Mo, and J. Kim, "Deep neural network based electrical impedance tomographic sensing methodology for large-area robotic tactile sensing," IEEE Transactions on Robotics, 2021. DOI: 10.1109/IROS40897.2019.8968532
  39. M. Vauhkonen, "Electrical impedance tomography and prior information [ph. d. thesis]," University of Kuopio, Kuopio, Finland, 1997. DOI: 10.1.1.208.9639 https://doi.org/10.1.1.208.9639
  40. O. C. Zienkiewicz and R. L. Taylor, Finite Element Method: Vol. 3: Fluid Dynamics. Elsevier Science & Technology Books, 2000.
  41. K.-S. Cheng, D. Isaacson, J. Newell, and D. G. Gisser, "Electrode models for electric current computed tomography," IEEE Transactions on Biomedical Engineering, vol.36, no.9, pp.918-924, 1989. DOI: 10.1109/10.35300
  42. E. Somersalo, M. Cheney, and D. Isaacson, "Existence and uniqueness for electrode models for electric current computed tomography," SIAM Journal on Applied Mathematics, vol.52, no.4, pp.1023-1040, 1992. DOI: 10.1137/0152060
  43. S. Brenner and R. Scott, The mathematical theory of fnite element methods. Springer Science & Business Media, vol.15, 2007.
  44. A. Adler and W. R. Lionheart, "Uses and abuses of eidors: an extensible software base for eit," Physiological measurement, vol.27, no.5, p.S25, 2006. DOI: 10.1088/0967-3334/27/5/S03
  45. A. K. Khambampati, Y. J. Hong, K. Y. Kim, and S. Kim, "A boundary element method to estimate the interfacial boundary of two immiscible stratifed liquids using electrical resistance tomography," Chemical Engineering Science, vol.95, pp.161-173, 2013. DOI: 10.1016/j.ces.2013.03.018
  46. E. Rashedi, H. Nezamabadi-Pour, and S. Saryazdi, "Gsa: a gravitational search algorithm," Information sciences, vol.179, no.13, pp.2232-2248, 2009. DOI: 10.1016/j.ins.2009.03.004
  47. M. M. Lau and K. H. Lim, "Review of adaptive activation function in deep neural network," in 2018 IEEE-EMBS Conference on Biomedical Engineering and Sciences (IECBES). IEEE, pp.686-690, 2018. DOI: 10.1109/IECBES.2018.8626714
  48. D. P. Kingma and J. Ba, "Adam: A method for stochastic optimization," arXiv preprint arXiv:1412.6980, 2014.
  49. J. McNeill, "Electrical conductivity of soils and rocks. geonics limited," Mississauga, Ontario, Technical Note TN-5, 1980.
  50. M. Abadi, P. Barham, J. Chen, Z. Chen, A. Davis, J. Dean, M. Devin, S. Ghemawat, G. Irving, M. Isard et al., "Tensor?ow: A system for large-scale machine learning," in 12th {USENIX} symposium on operating systems design and implementation ({OSDI} 16), pp.265283, 2016. DOI: 10.5555/3026877.3026899
  51. J. Lee Rodgers and W. A. Nicewander, "Thirteen ways to look at the correlation coeffcient," The American Statistician, vol.42, no.1, pp.59-66, 1988. DOI: 10.1080/00031305.1988.10475524