Числовий метод комплексного аналізу розв’язання задач ідентифікації за даними томографії прикладених квазіпотенціалів: Fìz.-mat. model. ìnf. tehnol. 2017, 25:14-26

• Datum: 2018
• Hauptverfasser: Bomba, Andriy, Boichura, Mykhailo
• Format: Artikel
• Sprache: Ukrainisch
• Veröffentlicht: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2018
• Schlagworte: томографія прикладених квазіпотенціалів; квазіконформні відображення; ідентифікація; нелінійні задачі; числові методи; ідентифікація параметрів; метод перебору
• Online Zugang: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/23
• Назва журналу: Physico-mathematical modeling and informational technologies

The article deals with the problem of identification parameters of a piecewise homogeneous medium with using the applied quasipotential tomographic data when the data about the conductivity coefficient is incomplete. The method of image reconstruction, according to which solving of the analysis problem is reduced to the using numerical quasiconformal mappings methods and the synthesis problem is reduced to the solution the parametric identification problem when all possible variants of the conductivity distribution is considered. The reconstructed image of the conductivity distribution inside the investigated object on the basis of performed numerical calculations is constructed. The received results were analyzed. The proposed approach to reconstruction slightly increases the total number of iterations in some cases, but significantly simplifies the intermediate iterative problems solving. References Holder, D. (2005). Electrical Impedance Tomography. Methods, History and Applications. London: Institute of Physics. Hou, T. C., Lynch, J. P. (2009). Electrical Impedance Tomographic Methods for Sensing Strain Fields and Crack Damage in Cementitious Structures. Journal of Intelligent Material Systems and Structures, 20, 1363-1379. DOI https://doi.org/10.1177/1045389X08096052 Rybin, A. I., Movchanyuk, A. V., Lugovskoj, A. F. (2012). Primenenie impedansnoj tomografii v mehatronnyh sistemah s ultrazvukovymi kavitatorami. Visnik Nacionalnogo tehnichnogo universitetu Ukrayini «Kiyivskij politehnichnij institut». Seriya Mashinobuduvannya, 64, 67-75. Chambers, J. E., Wilkinson, P. B., Wardrop, D. (2012). Bedrock detection beneath river terrace deposits using three-dimensional electrical resistivity tomography. Geomorphology, 177-178, 17-25. DOI https://doi.org/10.1016/j.geomorph.2012.03.034 Linderholm, P., Marescot, L., Loke, M., Renaud, P. (2008). Cell Culture Imaging Using Microimpedance Tomography. IEEE Transactions on Biomedical Engineering, 55(1), 138-146. DOI https://doi.org/10.1109/tbme.2007.910649 Ingham, M., Pringle, D., Eicken, H. (2008). Cross-borehole resistivity tomography of sea ice. Cold Regions Science and Technology, 52(3), 263-277. DOI https://doi.org/10.1016/j.coldregions.2007.05.002 Bayford, R., Tizzard, A. (2012). Bioimpedance imaging: an overview of potential clinical applications. Analyst, 137, 4635-4643. DOI https://doi.org/10.1039/c2an35874c Humplík, P., Cermak, P., Zid, T. (2016). Electrical impedance tomography for decay diagnostics of Norway spruce (Picea abies): possibilities and opportunities. Silva Fennica, 50(1), 1-13. DOI https://doi.org/10.14214/sf.1341 Bomba, A. Ya., Kroka, L. L. (2014). Chyslovi metody kompleksnoho analizu pry rozviazanni odnoho klasu neliniinykh eliptychnykh zadach za umov identyfikatsii parametriv. Matematychne ta kompiuterne modeliuvannia. Seriia: Fizyko-matematychni nauky: zb. nauk. pr., 10, 24-33. Bomba, A. Ya., Kroka, L. L. (2014). Chyslovyi metod kvazikonformnoho vidobrazhennia rozviazannia zadach identyfikatsii koefitsiienta elektrychnoi providnosti za danymy tomohrafii prykladenykh potentsialiv. Volynskyi matematychnyi visnyk. Seriia prykladna matematyka, 11(20), 24-33. Bomba, A. Ya., Boichura, M. V. (2016). One numerical complex analysis method for parameters identification of piecewise homogeneous conductivity media with using applied quasipotential tomographic data. Matematychne ta kompiuterne modeliuvannia. Seriia: Tekhnichni nauky: zb. nauk. prats., 14, 5-17. DOI https://doi.org/10.32626/2308-5916.2019-19.11-17 Terebus, A. V. (2011). Prostorovi modelni analohy kraiovykh zadach na kvazikonformni vidobrazhennia. Volynskyi matematychnyi visnyk. Seriia “Prykladna matematyka”, 8(17), 191-205. Horb, M. S., Husieva, O. V. (2013). Vybir matematychnoi modeli obiektu doslidzhennia v elektroimpedansnii tomohrafii. Visnyk NTUU “KPI”. Seriia —Radiotekhnika. Radioaparatobuduvannia, 52, 120-128. DOI https://doi.org/10.20535/radap.2018.75 Bomba, A. Ya., Kashtan, S. S., Pryhornytskyi, D. O., Yaroshchak, S. V. (2013). Metody kompleksnoho analizu : monohrafiia. Rivne:NUVHP. Ortega, Dzh., Rejnboldt, V. (1975). Iteracionnye metody resheniya nelinejnyh sistem uravnenij so mnogimi neizvestnymi. Moskva: Mir.