Andrianov I. K. (Комсомольский-на-Амуре государственный технический университет), Chepurnova E. K. (Комсомольский-на-Амуре государственный технический университет)
doi: 10.18698/2309-3684-2024-2-316
The study considers the problem of optimizing the crack detection system of gas turbine blades. The shell of the capsule of the damage detection system, which is under the influence of internal pressure, is considered as an object of research. The task of the study was devoted to the mathematical modeling of optimal pressure in capsules of the damage detection system. As part of solving the research problem, a mathematical formulation of the problem of optimizing the nonlinear pressure function was carried out in the presence of restrictions on variable parameters: wall thickness and outer diameter of the cylindrical capsule shell. The construction of the optimization objective function was carried out on the basis of the equilibrium condition of the shell element in the area of crack opening of the turbine blade, the limit state criterion using the Tresk-Saint-Venant strength theory. The research methodology was based on the approximate decomposition of the function into a Taylor series, the Lagrange multiplier method, and the Kuhn-Tucker theorem. When solving the problem of conditional optimization, the cases of violation of the regularity conditions of the limiting functions are analyzed. According to the calculation results, the minimum value of the required pressure for the destruction of the capsule shell in case of opening of the crack banks of the turbine blade is achieved at the maximum value of the outer diameter of the shell and the minimum thickness of its wall. According to the test calculation data, the area of acceptable solutions to the optimization problem is graphically presented, and the lines of the level of the target function of pressure optimization are shown. The constructed mathematical model and calculation algorithm will automate the process of calculating the required pressure in the capsules of the turbine blade crack detection system and obtain an estimate of the minimum pressure value in the presence of restrictions on the absolute and relative values of the capsule shell wall thickness, the outer diameter of the capsule.
Андрианов И.К., Чепурнова Е.К. Математическая модель условной оптимизации давления в системе обнаружения трещин лопаток газовых турбин. Математическое моделирование и численные методы, 2024, № 2, с. 3–16.
Dimitrienko Y. I. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University), Dimitrienko A. Y. (Lomonosov Moscow State University)
doi: 10.18698/2309-3684-2024-2-1734
The paper is devoted to modeling the deformation of composite materials with finite deformations. The so-called universal models of constitutive relations for composite components are considered, defining several classes of nonlinear relationship between the Piola-Kirchhoff stress tensor and the strain gradient within different energy pairs of stress-strain tensors. The method of asymptotic averaging is applied and local problems are formulated to solve the problem of determining the averaged properties of composites with finite deformations. A variational formulation of the original deformation problem, the so-called local problems on a periodicity cell and the averaged problem for a composite is considered, which makes it possible to use FEM for the numerical solution of these classes of problems. A software module has been developed as part of the SMCM software package, which implements the proposed numerical algorithm. An example of the numerical solution of problems on a periodicity cell for a 3D orthogonally reinforced composite is given, taking into account large deformations of the matrix and fibers, and composite deformation diagrams are calculated for various variants of universal models of constitutive relations.
Димитриенко Ю.И., Каримов С.Б., Димитриенко А.Ю. Моделирование конечных деформаций композиционных материалов на основе универсальных моделей Аn и метода асимптотического осреднения. Математическое моделирование и численные методы, 2024, № 2, с. 17–34.
Abdikarimov N. I. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.), Navruzov K. N. (Ургенчский государственный университет Адрес: 220100, Узбекистан, город Ургенч, улица Х. Олимжона, 14.)
doi: 10.18698/2309-3684-2024-2-3545
The problems of oscillatory flow of an elastic-viscous fluid in a flat channel for a given harmonic oscillation of fluid flow are solved based on the generalized Maxwell model. The “impedance” function was determined, and with the help of this function the dependence of the hydrodynamic resistance on the dimensionless oscillation frequency was studied for various values of the elastic Deborah number and the concentration of the Newtonian fluid. It is shown that in the oscillatory flow of an elastic-viscous fluid, the hydrodynamic resistance decreases depending on the Deborah number. This effect makes it possible to estimate the hydrodynamic resistance for a given law of change in the longitudinal velocity averaged over the cross section of the channel, with oscillatory flow and, thereby, allows us to determine the dissipation of the energy of the medium, which is important in the regulation of hydraulic and pneumatic systems.
Абдикаримов Н.И., Наврузов К.Н. Математическое моделирование гидродинамических сопротивлений при колебательном течении упруговязкой жидкости в плоском канале. Математическое моделирование и численные методы, 2024, № 2, с. 35–45.
519.7 Modeling and efficiency analysis of perceptual hash functions for segmented image search
Valishin A. A. (Bauman Moscow State Technical University), Zaprivoda A. V. (Bauman Moscow State Technical University), Tsukhlo S. S. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-4667
This research paper explores the use of perceptual hash functions to improve the retrieval efficiency of aerial photography and satellite remote sensing images segmented by a convolutional neural network. This paper describes three hashing algorithms. The first algorithm is based on the use of a low-pass filter and is aimed at reducing image detail in order to highlight the most stable image features. The second algorithm uses a two-dimensional discrete cosine transform to create an image hash. The third algorithm is based on the Radon transform, which allows you to extract information about the directions of lines in the image, as well as provide maximum invariance to the rotation transformation of the input image. The article also tests these algorithms, including analysis of their invariance to transformations for rotation, scaling and shifting of the source image. Test results show that the algorithm based on the Radon transform exhibits good rotation invariance, but is sensitive to the quality of segmentation, which can lead to frequent collisions when searching for similar images. Algorithms using a two-dimensional discrete cosine transform and an algorithm using a low-pass filter turned out to be more stable and have a smaller spread of values. However, it should be noted that algorithms using a low-pass filter and 2D discrete cosine transform may not be applicable to rotated images. Based on the results of analysis and comparison of the performance of the algorithms, it is recommended to give preference to either the second or third algorithm, because each of them has its own advantages and disadvantages, and the decision to use a specific algorithm in the task of finding the most similar image must take into account the specific conditions and limitations of the problem, as well as the requirements for the quality of image comparison.
Валишин А.А., Запривода А.В., Цухло С.С. Моделирование и сравнительный анализ эффективности перцептивных хеш-функций для поиска сегментированных изображений. Математическое моделирование и численные методы, 2024, № 2, с. 46-67.
519.17 Pursuit problem in 3D-space with arbitrary initial aiming angles
Bodryakov V. Y. (Ural State Pedagogical University)
doi: 10.18698/2309-3684-2024-2-6884
An analytical solution of the pursuit problem in the “predator-prey” system in Euclide-an 3D space for arbitrary initial aiming angles was obtained in the article for the first time. In the process of pursuit, the prey moves uniformly and rectilinearly, the speed vector of the predator is constant in magnitude and is aimed at the prey. The exact solution of the problem is obtained in the form of a parametrically specified spatial pursuit curve. Exact expressions were obtained for other essential characteristics of the pursuit process (pursuit time, coordinates of the prey, length of the pursuit curve, etc.). A realistic computer simulation of the mutual movement of predator and prey in space and time was carried out; the characteristic parameters of the pursuit process are determined. The significant didactic potential of the solved problem of 3D pursuit for the training of future specialists in the field of mechanics and control is noted; the problem for students can serve as a meaningful basis to carry out research projects, courseworks and final qualifying works.
Бодряков В.Ю. Задача о преследовании в 3D-пространстве с произвольными начальными углами прицеливания. Математическое моделирование и численные методы, 2024, № 2, с. 68-84.
Mozzhorina T. Y. (Bauman Moscow State Technical University), Zakurazhnaya A. A. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-8599
In this paper, optimization of the control of the flight of a small spacecraft (spacecraft) on ion engines to the orbit of Venus is considered, taking into account the attraction of the Earth and the time of departure from the geostationary orbit. When solving the problem, the following assumptions were made: the orbits of the planets are circular, lying in the same plane. A detailed consideration of the influence of Venus when approaching the orbit of the planet was not considered. The problem is solved using the Pontryagin maximum principle by numerical targeting method. The spacecraft motion simulation was divided into 3 stages: acceleration of the spacecraft to a speed that allows overcoming the Earth's attraction with the help of short-term operation of the jet engine, optimization of control near the Earth at a distance of the spacecraft to the Earth of no more than 950 000 km and for the main interorbital flight between planets. The algorithm for solving the problem is implemented in the C++ programming language. Optimal control of the angle of action of the thrust vector is obtained. The analysis of the obtained results showed that, while minimizing the time to reach the orbit of Venus, in addition to significantly influencing the efficiency criterion of the longest interorbital section of the flight, the moment of the start (departure from Earth orbit) is fundamentally important.
Мозжорина Т.Ю., Закуражная А.А. Моделирование влияния времени схода с орбиты Земли на оптимальное управление перелетом малоразмерного КА на Венеру. Математическое моделирование и численные методы, 2024, № 2, с. 88–99.
Zakharov I. I. (Moscow State University of Civil Engineering), Aleroev T. S. (Moscow State University of Civil Engineering)
doi: 10.18698/2309-3684-2024-2-100111
This paper is devoted to an approximate method for solving the first boundary value problem for the inhomogeneous fractional-differential advection-diffusion (dispersion) equation. The aim of the work is to construct, and realize an effective approximate method for solving physical and mathematical problems. The boundary value problem is studied for the two-dimensional case. The problems of finding eigenvalues and constructing surfaces of solutions of the first boundary value problem for the inhomogeneous differential equation are considered. The method of estimating the accuracy of the approximate solution is shown. An algorithm for finding an approximate solution based on the analytical method of separation of variables (Fourier method) is described. The exact results of calculations, both numerical and graphical, are given for specific examples.
Захаров И.И., Алероев Т.С. Решение первой краевой задачи для неоднородного дробного дифференциального уравнения. Математическое моделирование и численные методы, 2024, № 2, с. 100-111.
Tlibekov A. T. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2024-2-112125
The comparison of existing and developed new methods of converting optimality criteria into a scalar function of the goal is performed. New converting methods are used in the problems of interpolation of experimental data by a modified fractional-power Newton–Puiseux series. Coefficients and degrees of a fractional-power series are calculated by evolutionary or infinite-step optimization methods, where the modules of the difference between experimental data and the values obtained by calculating the interpolation polynomial are used as optimality criteria. Under such conditions, the optimization task becomes multi-criteria, for which, during the search process, part of the optimality criteria increases, the rest decrease and reduce the scalar goal function and creating the illusion that the search is effective. For new converting methods, all optimality criteria in the search process are reduced. The errors obtained by interpolating the time of laser cutting of steel sheet and forecasting the production program of parts are shown. The use of modified fractional power series and new methods of converting optimality criteria for the implementation of the neural network learning function is proposed.
Тлибеков А.Х. Сравнительный анализ методов свертывания критериев оптимальности в задачах многокритериальной оптимизации. Математическое моделирование и численные методы, 2024, № 2, с. 112-125.