Vestnik of Ryazan State
Radio Engineering University

UDC 004.8: 004.94

METHOD OF PRELIMINARY SELECTION
OF MULTILAYER NEURAL NETWORK ARCHITECTURE
FOR POLYHARMONIC SIGNAL APPROXIMATION

V. V. Frolov, Dr. Sc. (Tech.), associate professor, professor, V. N. Karazin Kharkiv National University,Kharkov, Ukraine;
orcid.org/0000-0002-2770-3385, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
G. N. Zholtkevych, Dr. Sc. (Tech.), full professor, V. N. Karazin Kharkiv National University, Kharkov,Ukraine;
orcid.org/0000-0002-7515-2143, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
O. Yu. Prikhodko, Ph.D. (Tech.), associate professor, BSTU named after V. G. Shukhov, Belgorod, Russia;
orcid.org/0000-0002-6452-0465, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Yu. V. Skuryatin, Ph.D. (Tech.), associate professor, BSTU named after V. G. Shukhov, Belgorod, Russia;
orcid.org/0000-0001-5555-8691, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

The proposed method for preliminary selection of the architecture for narrowing multi-layer arti-ficial
neural network of direct propagation without feedback with sigmoid activation functions is based on determining
the number of layers by the shape of a polyharmonic signal. The authors have pro-posed to characterize
signal shape by the number of inflection points. The article has experimentally proved that the number
of layers in multilayer network correlates with the number of inflection points according to the criterion of
minimizing absolute error when compared with a universal approxima-tor. The total number of neurons in a
multilayer network is determined from the condition that it can-not exceed the number of neurons in a universal
approximator. The essence of the method lies in the comparative analysis of absolute error for singlelayer
and multi-layer network. Resulting configura-tion of multilayer network can be used as an initial one
for further optimization of the structure.

Key words: artificial neural network, activation function, approximation, genetic algorithm, feedforward

neural network without feedbacks, discrete optimization, median, mean square, absolute error.

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UDC 004.942

I. Y. Klochkova, teacher of the department, Ryazan Guards Higher Airborne Command School, Ryazan, Russia;
orcid.org/0000-0002-4265-6759, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

A mathematical model of parachutist movement describing the stage of descent on open parachute is considered.
The aim of the work is to study the system of ordinary differential equations describing the speed of
parachutist movements for the presence and stability of equilibrium states. Initially, the system of differential
equations determines the relationship between the acceleration of parachute and the velocity for each
of three space coordinates. Various variations of this system of differential equations are considered. Theorems
on the number and stability of equality states are proved.
Numerical coefficients values for the system of differential equations based on real data of jumps obtained
using a special program installed on parachutist mobile device by regression analysis method are
obtained. The equilibrium states for each jump, their stability, practical significance and maximum value of
the speed at the time of landing are determined. Theoretical parachutist trajectory for the obtained system of
differential equation is constructed; its comparison with actual trajectory is carried out.

Key words: mathematical model of parachutist movement, equilibrium state, regression analysis, correlation

coefficient, parachutist trajectory, parachutist landing speed.

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UDC 550.343.6

ABOUT A POSSIBLE MATHEMATICAL METHOD
STUDYING THE DYNAMICS OF DANGEROUS PROCESSES
GEODYNAMIC ORIGIN

A. O. Faddeev, Dr. Sc. (Tech.), Associate Professor, Ryazan, Russia;
orcid.org/0000-0002-7259-1693, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
S. A. Pavlova, Ph.D. (Tech.), associate professor, Chair of Mathematics and Information Technologies
of Management, Academy of law management of the Federal penal service of Russia, Ryazan, Russia;
orcid.org/0000-0001-8634-9163, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

The aim of the study is to analyze the mathematical method of studying the dynamics of danger-ous
processes of geodynamic origin; the influence of factors that can lead to overvoltages in earth crust is considered.
When analyzing the method under consideration, two-dimensional graphs of changes in solar wind density
and magnetic induction of MMP were constructed to determine significant impact of space-earth connections;
when preparing the initial fields of quantities used in the construction of SWAN diagrams, the Fourier
spectrum was constructed in a two-dimensional Cartesian coordinate system for each series of values;
the most significant frequencies, which were used to calculate ampli-tude-frequency spectrum were identified;
spatial SWANN diagrams were constructed.

Key words: Geodynamic stability; seismic activity, SWANN diagrams, solar wind, interplanetary magnetic

field.

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UDC 004.932: 519.64

FREQUENCY METHOD OF FILTERING PERIODIC INTERFERENCE
OF DIGITAL IMAGES

A. I. Novikov, Dr. Sc. (Tech.), associate Professor department of higher mathematics, RSREU, Ryazan, Russia;
orcid.org/0000-0002-8166-8234, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
A. V. Pronkin, post-graduate student of the Department of electronic computing machines, RSREU, Ryazan, Russia;
orcid.org/0000-0003-2832-7462, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
N. O. Shamin, student RSREU, Ryazan, Russia;
orcid.org/0000-0001-9175-9095, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

The aim of the work is to develop and experimentally test a method for filtering periodic interference of
a digital image based on two-dimensional discrete Fourier transform (DFT). Periodic interference in the
image in the form of rectilinear bands, or in the form of lines of a more complex structure, but at the same
time periodic, corresponds to the local maxima of the amplitude spectrum obtained as a result of performing
direct DFT. To filter periodic interference, it is necessary to detect local maxima, reset Fourier coefficients
in the vicinity of local maxima and apply inverse DFT to a modified matrix of Fourier coefficients. A simple
method for detecting local maxima on amplitude spectrum and an approximate method for forming regions
of zeroing the Fourier coefficients in the vicinity of local maxima are proposed. Studies of the results of filtering
periodic interference of various shapes, intensities and, in particular, in conditions of additive discrete
white noise have been carried out.

Key words: periodic interference, filtering, discrete Fourier transform, amplitude spectrum, local extremum,

estimation of mathematical expectation

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