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

The problem of reconstruction of internal structure of the non-uniform dielectric materials located in the closed waveguide measuring systems is considered in the paper. The solution of this problem is of great practical interest because the received solution can be applied in many field of science and engineering where monitoring of internal structure of materials is required. Application of the developed technique is of special interest for reconstruction of internal structure of the material subjected to the microwave oven to processing. For a solution the method based on use of mathematical apparatus of the artificial neural networks (ANN) is offered. The essence of a method consists in the following: creating the model of the measuring system comprising the studied sample; modeling of this measuring system by means of the specialized software (QuickWave-3D); further the mathematical model of measuring system is realized in the form of ANN which is trained with use of the results received as a result of modeling; after training of ANN it is capable to determine parameters of a dielectric sample and the discontinuity which is placed in this sample, using as input parameters the measured values of reflection and transmission coefficients of the electromagnetic field in ports of the 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 sets of output parameters responsible for sample and discontinuity, and after that the scattering matrix of turnstile junction is calculated. After completion of modeling we receive a numerical data set which will be used for training of a neural network. Training of a neural network is made repeatedly for the purpose of definition of optimum quantity of training points in the training set (a data set of numerical data). Every time, after completion of training, the test run of the trained ANN on test data is carried out for calculation of an average relative error of reconstruction. Quality of training of a neural network is estimated by value of the average relative error of reconstruction calculated for a test data set provided that test pairs of input and output parameters are not included into the training set (a numerical data set on which ANN was trained). After the neural network is sufficiently trained, it can be used for reconstruction of parameters of a sample and discontinuity using results of measurements of reflection and transmission coefficients in ports of measuring system. To illustrate the performance of the proposed method, the numerical results of the reconstruction of parameters of a sample and he-terogeneity on four data sets differing from each other by geometrical form of the discontinuity are given in article. For all four data sets the relative error of reconstruction of parameters of a sample and discontinuity does not exceed 6% in case of optimum chosen quantity of training points.

 

1. Brovko A.V., Murphy E.K., and Yakovlev V.V. Waveguide microwave imaging: neural network reconstruction of functional 2-D permittivity profiles // IEEE Transactions on Microwave Theory and Techniques. 2009. V. 57. № 2. P. 406−414.
2. Brovko A.V. Metod opredelenija trekhmernogo profilja diehlektricheskojj pronicaemosti obrazca s ispolzovaniem nejjrosetevojj matematicheskojj modeli // Radiotekhnika. 2015. № 10. S. 115−120.
3. Brovko A.V., Murphy E.K., Rother M., Schuchmann H.P., Yakovlev V.V. Waveguide microwave imaging: spherical inclusion in a dielectric sample // IEEE Microwave and Wireless Comp. Lett. 2008. V. 18. № 9. P. 647−649.
4. QuickWave-3DTM, QWED Sp. z o.o., ul. Nowowiejska 28, lok. 32, 02-010 Warsaw, Poland. http://www.qwed.com.pl/.
5. Gubanov V.S. Obobshhennyjj metod naimenshikh kvadratov M.: Izd-vo fiziko-matematicheskojj lit-ry MGU. 1997. 318 s.
6. Dolinina O.N., Ermakov A.V. Metod povyshenija ehffektivnosti obrabotki videoinformacii s ispolzovaniem GRID-vychislenijj // Vestnik SGTU. 2010. T. 50. № 4. Vyp. 2. S. 131−133.