Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp
Статьи журнала - Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование
Все статьи: 785
The existence of a unique solution to a mixed control problem for Sobolev-type equations
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This article studies a mixed control problem for Sobolev-type equations in the case of a relatively radial operator. We use the Showalter-Sidorov initial condition. The difference in the statement of our problem from those studied previously by other researchers amounts to the form of the quality functional, which, in the authors' opinion, is more adequate to model applications in economics and technology. We prove an existence and uniqueness theorem for the solution to this problem.
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The flux recovering at the ecosystem-atmosphere boundary by inverse modelling
Статья научная
We consider the heat and mass transfer models in the quasistationary case, i. e., all coefficients and the data of the problem depends on time while the time derivative in the equation is absent. Under consideration is the inverse problem of recovering the surface flux through the values of a solution at some collection of points lying inside the domain. The flux is sought in the form of a finite segment of the Fourier series with unknown Fourier coefficients depending on time. The problem of determining the Fourier coefficient is reduced to a system of algebraic equations with the use of special solutions to the adjoint problem. The equation is considered in a cylidrical space domain. We prove the existence and uniqueness theorems for solutions of the corresponding direct problem. The results are employed in the proof of the corresponding results for the inverse problem. The corresponding numerical algorithm in the three-dimensional case is constructed and the results of the numerical experiments are exhibited. It is demonstrated that the algorithm is stable under random perturbations of the data. The finite element method is used. The results can be used in the problem of the determination of the fluxes of green house gases from soils from the concentration measurements.
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Статья научная
This paper describes a method of use of equations in M.F. Shul'gin's form in Lagrangian variables for steady motion stability and stabilization problems of systems with geometric constraints. These equations of motion are free from Lagrange multipliers; we substantiate their advantage for solving stability and stabilization problems. Depended coordinates corresponding to zero solutions of characteristic equation are allocated in the disturbed equations of motion. These variables are necessarily present in systems with geometric constraints for any control method. It is suggested to present equations of motion in Routh variables for finding stabilizing control coefficients; Lagrangian variables are more useful for constructing an estimation system of object state. In addition to previous results, we evaluate the ability to reduce the dimension of measured output signal obtained in conformity with the chosen modelling method. Suppose the state of system is under observations and the dimension of measurement vector is as little as possible. Stabilizing linear control law is fulfilled as feedback by the estimation of state. We can determine uniquely the coefficients of linear control law and estimation system can be determined uniquely by solving of the corresponding linear-quadratic problems for the separated controllable subsystems using the method of N.N. Krasovsky. The valid conclusion about asymptotical stability of the original equations is deduced using the previously proved theorem. This theorem is based on the nonlinear stability theory methods and analysis of limitations imposed by the geometric constraints on the initial disturbances.
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The mathematical modelling of the production of construction mixtures with prescribed properties
Статья научная
We propose a method for the mathematical modelling of the preparation of construction mixes with prescribed properties. The method rests on the optimal control theory for Leontieff-type systems. Leontieff-type equations originally arose as generalizations of the well-known input-output model of economics taking supplies into account. Then they were used with success in dynamical measurements, therefore giving rise to the theory of optimal measurements. In the introduction we describe the ideology of the proposed model. As an illustration, we use an example of preparing of simple concrete mixes. In the first section we model the production process of similar construction mixtures (for instance, concrete mixtures) depending on investments. As a result, we determine the price of a unit of the product. In the second section we lay the foundation for the forthcoming construction of numerical algorithms and software, as well as conduction of simulations. Apart from that, we explain the prescribed properties of construction mixes being optimal with respect to expenses.
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The multipoint initial-final value condition for the Navier - Stokes linear model
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The Navier - Stokes system models the dynamics of a viscous incompressible fluid. The problem of existence of solutions of the Cauchy - Dirichlet problem for this system is included in the list of the most serious problems of this century. In this paper it is proposed to consider the multipoint initial-final conditions instead of the Cauchy conditions. It should be noted that nowadays the study of solvabilityof initial-final value problems is a new and actively developing direction of the Sobolev type equations theory. The main result of the paper is the proof of unique solvability of the stated problem for the system of Navier - Stokes equations.
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The optimal control problem for output material flow on conveyor belt with input accumulating bunker
Статья научная
The article is devoted to the synthesis of optimal control of conveyor belt with the accumulating input bunker. Much attention is given to the model of the conveyor belt with a constant speed of the belt. Simulation of the conveyor belt is carried out in the one-moment approximation using partial differential equations. The conveyor belt is represented as a distributed system. The used PDE-model of the conveyor belt allows to determine the state of the flow parameters for a given technological position as a function of time. We consider the optimal control problem for flow parameters of the conveyor belt. The problem consists in ensuring the minimum deviation of the output material flow from a given target amount. The control is carried out by the material flow amount, which comes from the accumulating bunker into the conveyor belt input. In the synthesis of optimal control, we take into account the limitations on the size of the accumulating bunker, as well as on both max and min amounts of control. We construct optimal control of the material flow amount coming from the accumulating bunker. Also, we determine the conditions to switch control modes, and estimate time period between the moments of the switching.
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The optimal design of pressure swing adsorption process of air oxygen enrichment under uncertainty
Статья научная
The paper formulates and studies the problem of optimal (by the criterion of profits from oxygen production) design of a pressure swing adsorption (PSA) unit for air oxygen enrichment under partial uncertainty of the source data (the air composition, temperature, atmospheric pressure) with limitations on oxygen purity, unit capacity, and resource saving granular adsorbent. A heuristic iterative algorithm was developed for solving an optimal design problem under partial uncertainty of the source data. An auxiliary optimization problem related to the class of nonlinear programming problems (assuming the approximation of continuous control functions at the stages of the adsorption-desorption cycle by step-functions) was formulated and then solved by the sequential quadratic programming method. The problem of optimal design was solved for the range of PSA units with a capacity of 1 to 4 l/min allowing to obtain oxygen with a purity of 40 to 90% vol. According to the findings, we analyze the most promising operational and design parameters ensuring the maximum profit in the operation of the PSA unit, taking into account the saving of the granular adsorbent. It was established that the introduction of limitations on the gas flow rate in the frontal layer of the PSA unit adsorbent allows to increase the reliability of its operation and the adsorbent service life.
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We consider the problem of identifying the trajectory of a mobile point source described by the Delta function in a one-dimensional linear convective transport equation under a given additional boundary condition. To solve this problem, the Delta function is approximated by a continuous function and a discrete analog of the problem is constructed using finite-difference approximations in the form of an implicit difference scheme. To solve the resulting difference problem, we propose a special representation that allows to split the problem into two mutually independent linear first-order difference problems at each discrete value of a time variable. The result is an explicit formula for determining the position of a mobile point source for each discrete value of a time variable. Based on the proposed computational algorithm, numerical experiments were performed for model problems.
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The rate of convergence of hypersingular equations numerical computation
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Numerical methods for solving hypersingular equations based on Chebyshev polynomials of the second kind with a weight taking into account the Meixner physical conditions on the edge are developed. We obtained estimates of the rate of convergence using the analytical form of the matrix of an integral operator with a logarithmic singularity. Authors considered a delta function model, and its inapplicability in diffraction problems and vibrator antennas are shown. Previously, a numerical-analytical method for solving the excitation problems of vibrator antennas was proposed, but in the present work, the rationale for the numerical-analytical method is given for the first time. Unlike the reduction method, the numerical-analytical method demonstrates reliable convergence, not only in diffraction problems but also in antenna excitation problems. The specific feature of the excitation problems is that the right-hand side of the hypersingular equation is localized in a small region, in comparison with the characteristic dimensions of the antenna. Mathematically, this means that the right-hand side of the hypersingular equation decomposes into a slowly-convergent series. A similar property is also possessed by the solution of the equation. That is why the method of reduction is not effective enough. An example of a numerical solution is considered. Estimates of the rate of convergence are obtained. The applicability of developed methods for investigating a wide range of diffraction problems is shown.
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Статья научная
This article focuses on the application of wavelet theory to the problem of modelling the processes of manufacturing the shells of fibrous composite materials (CM). The basic methods for preparing such shells are two related ones: filament winding, when the strip made of CM is laid out on the outstretched surface, and laying out, when the tape is placed by dint of pressing rollers. In both cases, laying the tape is carried out in accordance with the program of moving spreader. To create such a program the mathematical model of the process of placing the tape is needed. The article describes semi orthogonal wavelet systems on the segment that are based on B-spline of arbitrary order. The matrices which compose the filter bank for such wavelet systems are represented. Some algorithms for geometric modelling are reviewed and summarized from the point of view of the wavelet theory. The results are applied to the mathematical modelling and software of manufacturing process of shells made of fibrous composite materials. As an example, consider the process of making the ventilator blade.
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Статья научная
In this paper, the problem of training the Viola-Jones detector for 3D objects is considered on the example of an inflatable life raft PSN-10. The detector is trained on a fully synthetic training dataset. The paper discusses in detail the methods of modelling an inflatable life raft, water surface, various weather conditions. As a feature space, we use edge Haar-like features, which allow training the detector that is resistant to various lighting conditions. To increase the computational efficiency, the L1 norm is used to calculate the magnitude of the image gradient. The performance of the trained detector is estimated on real data obtained during the rescue operation of the trawler "Dalniy Vostok". The proposed method for training the Viola-Jones detectors can be successfully used as a component of hardware and software "assistants" of the UAV.
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Статья научная
We study a mathematical model of coastal waves in the shallow water approximation. The model contains two empirical parameters. The first one controls turbulent dissipation. The second one is responsible for the turbulent viscosity and is determined by the turbulent Reynolds number. We study travelling waves solutions to this model. The existence of an analytical and numerical solution to the problem in the form of a traveling wave is shown. The singular points of the system are described. It is shown that there exists a critical value of the Reylnols number corresponding to the transition from a monotonic profile to an oscillatory one. The paper is organized as follows. First, we present the governing system of ordinary differential equations (ODE) for travelling waves. Second, the Lyapunov function for the corresponding ODE system is derived. Finally, the behavior of the solution to the ODE system is discussed.
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Статья научная
The paper presents a new two-stage parametric identification procedure for constructing a navigation satellite motion model. At the first stage of the procedure, the parameters of the radiation pressure model are estimated using the maximum likelihood method and the multiple adaptive unscented Kalman filter. At the second stage, the parameters of the unaccounted perturbations model are estimated based on the results of residual differences measurements. The obtained results lead to significant improvement of prediction quality of the satellite trajectory.
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Two-stage stochastic facility location model with quantile criterion and choosing reliability level
Статья научная
A two-stage discrete model for the location of facilities is considered. At the first stage, a set of facilities to be opened is selected. At the second stage, additional facilities may be opened due to the realization of random demand for products. Customers preferences are taken into account in choosing the facility in which they will be served. The quantile of losses (income with the opposite sign) is used as a criterion function of the model. Several optimization problems are stated. In the first problem, a set of facilities to be opened is selected for a given value of the reliability level. In the second problem, along with the set of facilities to be opened, the reliability level of the quantile criterion is selected. At the same time, restrictions on the level of reliability and the value of the quantile criterion are introduced. Two approaches to setting these constraints are proposed. To solve the problems stated, the method of sample approximations is used. A theorem on sufficient conditions for the convergence of the proposed method is proved. We formulate mathematical programming problems, the solutions of which under certain conditions are solutions to the obtained approximating problems. Numerical results are presented.
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Статья научная
Level control of coupled tank systems with non-linearity and instability is one of important issues in the industry process. Control of unstable systems is a challenging task for industries. In this paper we have controlled unstable water flow in a coupled two tank problem in real plant with disturbances. Here we have implemented the Online Neuro Fuzzy Controller (ONFC) with a new learning rate. The Online Neuro Fuzzy Controller is an adaptive control with a simple structure which is capable of processing non-linear, time-varying, uncertain systems. The efficiency and low computational cost of this technology have enabled successful implementations in many industrial plants. Simulations of a coupled tank system with ONFC are done in Python programming language. The gradient descent method is used to update the parameters.
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Weighted Trudinger - Moser inequalities and applications
Статья научная
Trudinger - Moser inequalities provide continuous embeddings in the borderline cases of the standard Sobolev embeddings, in which the embeddings into Lebesgue Lp spaces break down. One is led to consider their natural generalization, which are embeddings into Orlicz spaces with corresponding maximal growth functions which are of exponential type. Some parameters come up in the description of these growth functions. The parameter ranges for which embeddings exist increase by the use of weights in the Sobolev norm, and one is led to consider weighted TM inequalities. Some interesting cases are presented for special weights in dimension two, with applications to mean field equations of Liouville type.
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«Эффективность» нитей в многопроцессорных системах с общей памятью
Статья научная
Традиционно предполагается, что вычисление, разбитое на несколько нитей определённым образом, выполняется в системах с общей памятью (SMP или NUMA) быстрее, чем это же вычисление, но разбитое на несколько процессов. В представляемой работе высказана гипотеза о том, что такое предположение может быть неверным для вычислений с большими объёмами данных, главным образом по двум причинам. Во-первых, поддержка единого адресного пространства для нитей может быть существенно более накладной, чем суммарные затраты на переключение контекста выполнения между процессами. Во-вторых, даже если вычисление не требует интенсивного управления памятью, естественное ограничение на объём хранимого в TLB описания рабочего множества страниц, и в случае нитей приводит к необходимости частого обновления этого кэша трансляций. В статье описаны эксперименты и их результаты, которые подтверждают адекватность этой гипотезы.
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Статья научная
В работе рассматривается возможность применения агентно-ориентированной системы имитационного моделирования для решения ряда проблем, возникающих при создании экзафлопсных компьютеров, содержащих десятки и сотни миллионов вычислительных узлов. Предлагается двухуровневая децентрализованная схема управления вычислениями и соответствующая имитационная модель, в которой все вычислительные узлы поделены между областями вычислений, которые контролируются своими локальными управляющими агентами. Головной управляющий агент распределяет между областями поток больших задач и контролирует общие ресурсы. В качестве примера масштабируемого алгоритма рассматривается метод Монте-Карло, перспективный для компьютерного моделирования на экзафлопсных компьютерах. В этом методе существенно то, что чем больше объем выборки из независимых реализаций, тем выше точность оценивания. В работе предлагается генератор базовых псевдослучайных чисел, пригодный для больших расчетов по методу Монте-Карло. При распределении вычислений по узлам допускается возможность реализации различных объемов выборки на различных узлах с использованием статистически оптимального способа осреднения результатов. Объем памяти, доступный каждому вычислительному узлу, и его быстродействие должны быть достаточными для эффективного моделирования реализаций. Данный алгоритм распределенного статистического моделирования асинхронен, и при использовании предлагаемого генератора базовых псевдослучайных чисел масштабируется практически на неограниченное число узлов. Примером масштабируемого приложения распределенного статистического моделирования для современных компьютеров терафлопсного уровня производительности является библиотека PARMONC. Кроме того, в работе рассматривается вариант реализации мультиагентного моделирования для прогнозирования сбоев и отказов вычислительных узлов. Предлагается архитектура динамической системы прогнозирования сбоев, которая состоит из агентов различного назначения, каждый из которых выполняет свою функцию для достижения общей цели.
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Адаптация метода Куропатенко для расчета ударных волн в эйлеровых координатах
Статья научная
В настоящее время отсутствует реализация хорошо зарекомендовавшего себя численного метода Куропатенко в эйлеровых координатах. Такая реализация имеет высокий потенциал для решения определенного круга задач. Данная работа посвящена адаптации метода Куропатенко для расчетов ударных волн в эйлеровых координатах. Представлена идея метода, приведены разностные уравнения и вычислительный алгоритм для идеальной среды. Работоспособность предложенного численного метода продемонстрирована на результатах решения задач о распаде произвольного разрыва и о распространении стационарной ударной волны, приведены отклонения газодинамических величин от аналитических решений. Хорошее согласие численных решений с аналитическими подтверждает адекватность построенного алгоритма и метода в целом.
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