

Articles
by
Dmitry N. Tumakov 
Total Records (
2 ) for
Dmitry N. Tumakov 





Christina N. Stekhina
,
Dmitry N. Tumakov
and
Anastasia V. Anufrieva


We consider a semiopen elastic waveguide structure formed by a transversely isotropic layer which on the one hand is firmly fixed and on the other hand is linked with an isotropic halfspace. A general solution of differential equation system is obtained describing the propagation of elastic waves in a transversely isotropic medium. Using the boundary conditions and conjugation conditions at the junction of a strip and a halfspace as well as the explicit representations of the fields in each of the media, a characteristic equation for the eigenvalues (longitudinal permanents) is obtained concerning our waveguide structure. We considered separately the intervals of eigenvalues. The range in which the values of the longitudinal permanents form a discrete spectrum is specified. The dependence of the longitudinal permanents real values from oscillation frequencies is studied. It is noted that the waveguide modes may exist only if the substrate (halfspace) is acoustically more rigid material than the layer. It is concluded that the eigenvalues are bounded above and below by the values corresponding to wave numbers of the attached media. Also, the range is specified in which the modes are originated. It is noted that the characteristic curves are not intersected anywhere. The claculation results are presented for a transversely isotropic layer, filled with sandstone and coupled with rather solid material close to the foundation. 




Dmitry N. Tumakov
and
Diana M. Khairullina


The research studied the problem of a homogeneous layer refraction value recovering by Neural Network Method. The case with the known thickness is studied. We used three neuron activation functions: a linear, a sigmoidal and Gauss function. The network training is conducted by two methods: the method of back propagation and genetic algorithm. The desired value of refraction index is chosen as the average one between the results of independent neural networks trained according to the same initial data. This approach makes sense because the target functions of networks comprise the plurality of local extrema and each new network with a random initial vector of weights provides different but close results. The method of cross validation estimarted the accuracy of refractive index recovery for different activation functions and the methods of network training. The conclusion that the genetic algorithm provides better results than the gradient methods (in particular, the method of error backpropagation). It was shown that the number of neurons increase leads to a natural improvement of recoverable values accuracy for refractive index. The “best” objective functions are obtained for neural networks with sigmoidal and Gaussian activation function. It is expressed by more sustainable behavior of error at continuous change of other network settings. The plots of error dependence for the recovery of the refractive index on the sample size and the number of neurons are presented which confirm the findings. 





