DETECTION OF AIR GAPS IN COPPER-MINE CEILING BY ELECTRICAL IMPEDANCE TOMOGRAPHY
Tomasz Rymarczyk
tomasz.rymarczyk@netrix.com.plNetrix S.A., Research and Development Center (Poland)
Paweł Tchórzewski
Netrix S.A., Research and Development Center (Poland)
Jan Sikora
Lublin University of Technology, Institute of Electronics and Information Technology; Electrotechnical Institute (Poland)
Abstract
In this paper, we investigate the inverse problem for the electric field so-called copper mine problem. In general, this task assumes detection of all air gaps. Gaps are localised above ceiling in a copper mine. Such task can be considered as application of the electrical impedance tomography. In order to solve forward problem there was used the boundary element method or the finite element method. The inverse problem is based on the level set method. There was considered extension of boundary element method (BEM). For simplicity zero order approximation has been chosen. The BEM has been connected with the infinite boundary elements. Hence, open domain problems with infinite boundary curves can be analysed. For such domain, we have solved the Dirichlet problem for two-dimensional Laplace’s equation. The proposed numerical model has been verified.
Keywords:
inverse problem, boundary element method, electrical impedance tomographyReferences
Brebbia C.A., Dominguez J.: Boundary Elements – An Introductory Course, WIT Press, UK, 1992
Google Scholar
Burger M.: Levenberg-Marquardt: Level set methods for inverse obstacle problems, Inverse Problem 20, 2004, 259–282.
Google Scholar
Ito K., Kunish K., Li Z.: The Level-Set Function Approach to an Inverse Interface Problem, 2001, Vol. 17, 11.
Google Scholar
Kythe P.K.: An introduction to Boundary Element Methods, CRC Press, USA, 1995.
Google Scholar
Li C., Xu C., Gui C., Fox M. D.: Level set evolution without re-initialization: A new variational formulation, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), volume 1, 2005, 430–436.
Google Scholar
Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York 2003.
Google Scholar
Osher, S., Fedkiw, R.: Level Set Methods: An Overview and Some Recent Results. J. Comput. Phys. 169, 2001, 463–502.
Google Scholar
Osher S., Sethian J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics 79, 1988.
Google Scholar
Pańczyk M.: Elementy nieskończone w metodzie elementów brzegowych, PhD thesis, Lublin University of Technology, 2009.
Google Scholar
Pańczyk M., Sikora J.: Geometry and physical quantity transformations in 2D boundary element method with infinite elements, Proceedings of Electrotechnical Institute 3, 2007, 233.
Google Scholar
Rymarczyk T.: Using electrical impedance tomography to monitoring flood banks, International Journal of Applied Electromagnetics and Mechanics 45, 2014, 489–494.
Google Scholar
Rymarczyk T.: Characterization of the shape of unknown objects by inverse numerical methods, Przegląd Elektrotechniczny, R. 88 NR 7b/2012, 138–140.
Google Scholar
Rymarczyk T., Sikora J., Waleska B.: Coupled Boundary Element Method and Level Set Function for Solving Inverse Problem in EIT, 7th World Congress on Industrial Process Tomography, WCIPT7, 2-5 September 2013, Krakow, Poland
Google Scholar
Rymarczyk T., Adamkiewicz P., Duda K., Szumowski J., Sikora J.: New Electrical Tomographic Method to Determine Dampness in Historical Buildings, Achieve of Electrical Engineering 65, 2/2016, 273–283.
Google Scholar
Sethian J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.
Google Scholar
Tai C., Chung E., Chan T.: Electrical impedance tomography using level set representation and total variational regularization. Journal of Computational Physics, vol. 205, no. 1, 2005, 357–372.
Google Scholar
Xia K., Zhang Z.: Three-dimensional finite/infinite elements analysis of fluid flow in porous media, Applied Mathematical Modelling, 30, 6, 2005.
Google Scholar
Authors
Tomasz Rymarczyktomasz.rymarczyk@netrix.com.pl
Netrix S.A., Research and Development Center Poland
Authors
Paweł TchórzewskiNetrix S.A., Research and Development Center Poland
Authors
Jan SikoraLublin University of Technology, Institute of Electronics and Information Technology; Electrotechnical Institute Poland
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