Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS

Тел.: +7 (495) 625-9241


Neural network model and numerical method for determining a volume fraction of firm particles in powder material


A.V. Brovko – Ph. D. (Phys.-Math.), Associate Professor, Department «Applied Information Technologies», Yuri Gagarin State Technical University of Saratov E-mail: R.S. Pakharev – Post-graduate Student, Department «Applied Information Technologies», Yuri Gagarin State Technical University of Saratov E-mail:

The paper presents the method of determining a volume fraction of firm particles in the powder material located in the closed waveguide measuring system. The considered method is of great practical interest as the received decision can be applied in many field of science and equipment where monitoring of internal structure of materials is required. The use of this method is of special interest for restoration of internal structure of the material subjected to the microwave oven processing. The method is based on the use of mathematical apparatus of the artificial neural networks (ANN). The method is based on simple measurements of parameters of a matrix of dispersion (coefficients of reflection and passing) of the waveguide system containing the research sample with the subsequent application of ANN trained on data of numerical modeling of electromagnetic system. The measured parameters are coefficients of reflection and passing of two-port waveguide system. During modeling of measuring system, the training sets (couple of entrance and corresponding to them output data sets) are generated as random data set. Then, every time, a matrix of dispersion of turnstile connection is calculated. After completion of modeling, we receive a numerical data set which will be used for training of a neural network. After the neural network is rather trained, it can be used for restoration of parameters of a cubic sample by results of measurements of coefficients of reflection and passing of the electromagnetic field in ports of measuring system. Quality of training of a neural network is estimated by a value of the relative error of reconstruction calculated for a test data set pro-vided that test pairs of input and output parameters aren\'t included into the training set (a numerical data set on which ANN was trained). To illustrate the performance of the proposed method, the paper presents numerical results of the reconstruction of parameters of cubic samples consisting of mix of particles of solid material of a rectangular or cylindrical form with air. The restored parameters of material can be determined with the use of elementary electromagnetic measurements in simple waveguide system with the relative error, which isn\'t exceeding 5%.


  1. Clark D.E., Sutton W.H. Microwave processing of materials // Annual Review of Material Science. 1996. V. 26. P. 299−331.
  2. Oghbaei M., Mirzaee O. Microwave versus conventional sintering: A review of fundamentals, advantages and applications // Journal of Alloys and Compounds. 2010. V. 494. № 1−2. P. 175−189.
  3. Bykov Y.V., Rybakov K.I., and Semenov V.E. High-temperature microwave processing of materials // Journal of Physics D: Applied Physics. 2001. V. 34. № 13. P. R55−R75.
  4. Duan Y., Sorescu D.C., and Johnson J.K. Finite element approach to microwave sintering of oxide materials // Proc. COMSOL Users Conference. Boston. 2006.
  5. Bouvard D., Charmond S., and Carry C.P. Multiphysics simulation of microwave sintering in monomode cavity // Ceramic Transactions. 2010. V. 209. P. 173−180.
  6. Rybakov K.I., Olevsky E.A., and Krikun E.V. Microwave sintering: fundamentals and modeling // Journal of the American Ceramic Society. 2013. V. 96. № 4. P. 1003−1020.
  7. Sihvola A. Electromagnetic mixing formulas and applications // IEE Electromagnetic Waves Series. London: The Institute of Electrical Engineers. 1999.
  8. Murphy E.K., Yakovlev V.V. RBF network optimization of complex microwave systems represented by small FDTD modeling data sets // IEEE Transactions on Microwave Theory and Techniques. 2006. V. 54. № 7. P. 3069−3083.
  9. Kirby M. Geometric Data Analysis. New York: Wiley. 2001.
  10. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Singular Value Decomposition // In «Numerical Recipes in C». Cambridge: Cambridge University Press. 1992.
  11. Yakovlev V.V., Allan S.M., Fall M.L., and Shulman H.S. Computational study of thermal runaway in microwave processing of zirconia // In «Microwave and RF Power Applications» / Ed. by Tao J.E. Cépaduès Éditions. 2011. P. 303−306.
  12. QuickWave-3DTM, QWED Sp. z o.o., ul. Nowowiejska 28, lok. 32, 02-010 Warsaw, Poland. URL =
  13. Dolinina O.N., Kuzmin A.K. Otladka nejjrosetevojj ehkspertnojj sistemy dlja oftalmologii // Vestnik Saratovskogo gosudarstvennogo tekhnicheskogo universiteta. 2011. T. 4. № 4 (62). S. 248−252.


June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio