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: 838
Mathematical modelling of industrial equipment operation based on Markov processes
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The existence of an almost unlimited number of methods for evaluating the productivity of industrial equipment contributes to the uncertainty of choosing the most effective approach. At the same time, the presence of many possible states of equipment (from working to repair and other downtime) complicates the problem of modelling the operation of such a system. The problem of modelling does not lose its relevance, first of all, for large industrial companies. The article presents the methodological features of modelling the operation of industrial equipment based on the Markov method. This approach is used as a base for estimating the probabilities of equipment transitions between states, as well as for predicting the final state of operation of such a system. In terms of practical application, we consider an example of the functioning of the same type of industrial equipment in the framework of three possible states (functional, broken, and also in the mode of forced repair). Based on the results of calculations, we carry out assessment of the reality of the state transitions of equipment, designed rate of these transitions, as well as the predicted level of productivity equipment system after the period "''. The reliability of the research results is confirmed by their practical implementation. The obtained results are recommended to be used by the management and analysts of industrial companies in the process of making operational decisions and in the development of equipment repair strategies.
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Mathematical modelling of moisture distribution in porous media
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We propose the mathematical model for distribution of moisture in porous material during the industrial wetting process for a number of assumptions. The model is presented in form of a boundary problem for ordinary differential equation. In current article we discuss possible methods of the solution of this problem, highlight some problems, which can occur during the solution. At the end of the paper, we present some numerical results of modelling wetting process for different materials and calculation of the parameters. The model under discussion allows to understand better the influence of parameters of the problem in order to optimize the wetting process in industry.
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Quantitative approaches based on mathematical modelling are used to justify a set of measures aimed at justifying a set of preventive measures to protect the life and health of older people in the context of COVID-19 pandemic. Analysis of the state of development of actuarial mathematical models of mortality in the COVID-19 epidemic shows the need to construct models that reflect the dynamics of the studied ratios of infection rates, morbidity, recovery and mortality in the dynamics of the pandemic, taking into account the influence of external factors on this process. Most of the known mathematical models for predicting the spread and consequences of COVID-19 are compartmental models that implement sequential transitions between states with the allocation of groups of individuals with different affiliation to the progression/decline of the spread of infection. To compensate for the shortcomings of the compartmental models due to the assumption of population homogeneity and the lack of adequate approaches to the scalability of the simulation results, models based on the Monte Carlo method and the concept of multi-agent systems are used. The development of modelling methods is associated with the need to expand information support for healthcare professionals and health care organizers with the possibility of online configuration of parameters of mathematical models and the use of data from «cloud services» with visualization of the results of modelling.
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Статья научная
The article is devoted to mathematical modelling of processes, occurring in the flowing part of the vortex flowmeter, by the finite element method. The urgency of the current study is due to the lack of research in this area. The analysis of research literature devoted to the study of non-stationary vortex shedding processes and other hydrogasdynamics effects occurring in the flowing part of the vortex flowmeter and similar devices has been performed. A brief description of the vortex generation process behind the bluff body placed in a circular cross-section pipe as well as the basic criteria for functional products are presented. Various mathematical models for describing turbulent flows in pipes with an object or obstruction were investigated. The available software packages suitable for modelling unsteady turbulent flows were analyzed. The ANSYS software package, in particular CFX module for fluid and gas, as well as various approaches to mathematical modelling were used to simulate the flowing part of the vortex flowmeter. The article provides a brief description of the basic computational domain settings, mesh formation and initial and boundary conditions setting. To verify the numerical calculations, physical experiments on fluid and gas test benches were performed. For this purpose the samples corresponding to the numerical model have been manufactured and tested. The research findings led us to conclude that in terms of accuracy and calculation time the optimal approach to numerical simulation of vortex generation processes (Karman vortex street) in the vortex flowmeter is the use of the Reynolds-averaged Navier - Stokes equations (or RANS equations) closed by means of a two-equation model of turbulence, known as the k-e model, which is confirmed by comparison with the experimental data.
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Статья научная
Development of periodic disturbances on free surface of water film falling down vertical plane for Reynolds' number Reє[5;10] is investigated. The investigation is implemented in a scope of the nonlinear differential equation for evolution of free surface of falling down liquid film. The equation is solved by a finite differencies method at rectangular uniformly spaced grid. By researching the growth of unit inaccuracy, the conditions on parameters of computation grid for inaccuracies to be not increasing are obtained. As a result, waveforms of water film, time spent to form the regular wave mode and amplitudes of periodic disturbances are calculated. Calculated amplitudes and experimental ones are compared.
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Mathematical terrain modelling with the help of modified Gaussian functions
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Based on a fundamentally new approach, we present a complete mathematical model for estimating the mass of water in the flooded coastal relief, taking into account the water in the basin of the reservoir in a given region. Taking into account stochastic studies, we construct an approximate model of the relief of the reservoir basin bottom, as well as the relief of a possible section of the flooding of this basin coastline. The modelling is based on the empirical data of measurements of the reservoir depths, as well as on the study on the architecture of the lines of the coastal maps of the possible flooding zone. Based on the measurements of the depths and bumps of the bottom surface, we verify the hypothesis that the use of the two-dimensional Gauss distribution is adequate. Numerous confirmation of this hypothesis on the basis of empirical measurements allows to use localized elliptic Gauss surfaces as a model function in order to construct an approximate model of hillocks and valleys. At the same time, the coordinates of local extremes of the depths, as well as the values of these extremes are constant. In order to simulate the surfaces of the underwater slopes, we construct planes according to depth measurements. This simulation is not a real copy, but is stochastic in nature and allows to take into account the main goal of the model, i.e. a full adequate estimation of the water mass of the flooded coastal relief included the water in the basin of the reservoir in the region. The equation of the model of the entire flooded region includes all local functions constructed for the mounds and troughs of the reservoir, as well as the functions of the planes of the slope models. For an approximate construction of the surface equations of the coastal zone, we use maps with detailed level lines as empirical data.
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Статья научная
Application of projective normalization (a special case of orthocorrection and perspective correction) to photographs of documents for their further optical recognition is generally accepted. In this case, inaccuracies of normalization can lead to recognition errors. To date, a number of normalization accuracy criteria are presented in the literature, but their conformity with recognition quality was not investigated. In this paper, for the case of a fixed structured document, we justify a uniform probabilistic model of recognition errors, according to which the probability of correct recognition of a character abruptly falls to zero with an increase in the coordinate discrepancy of this character. For this model, we prove that the image normalization accuracy criterion, which is equal to the maximal coordinate discrepancy in the text fields of a document, monotonously depends on the probability of correct recognition of the entire document. Also, we show that the problem on computing the maximal coordinate discrepancy is not reduced to the nearest known one, i.e. the linear-fractional programming problem. Finally, for the first time, we obtain an analytical solution to the problem on computing the maximal coordinate discrepancy on a union of polygons.
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Method for analyzing the structure of noisy images of administrative documents
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The problem of extracting content elements (fields) from the images of administrative documents via descriptions of anchoring elements is considered. Administrative documents contain static elements and content elements (filled information). The static objects of the document model are the lines of the document structure and the words. Sets of objects united by properties and relationships are described. The text descriptor can contain attributes that distinguish it from similar descriptors. We suggest using combined descriptors of line segments and words. We showed experimentally that the extraction of object sets improves the recognition accuracy of the document fields by 17% and the accuracy of information extraction by 16%. For optical character recognition, we employed SDK Smart Document Engine in the experiment.
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Статья научная
We propose a procedure to determine the strain rate sensitivity index of a superplastic material from the results of bulge forming of a long thin rectangular membrane under constant pressure of inertia gas. In contrast to other known procedures, the method suggested takes into consideration the presence of entry radius in the matrix set used. The mathematical model of the technological process is developed based on the main assumptions of the thin shell theory. To validate the procedure suggested the finite element analysis is fulfilled using the software package ANSYS 10 ED. Experimental approbation of the method suggested is carried out on the titanium alloys Ti-6Al-4V, a good agreement is achieved. It is shown that taking into account the influence of the entry radius allows to improve considerably the accuracy for finite element modelling. We draw the conclusion that the procedure developed may be recommended for practical usage to determine the superplastic parameters of thin sheet superplastic materials.
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Статья научная
The paper presents the results on numerical modelling of the quality of opto-electronic detectors. In order to demonstrate a successful application of the proposed method of the object base extension, we use examples of hierarchy analysis of generalized quality index and integrated quality-price index. The proposed methodology allows reliable analysis the number of objects up to 21-24, that is enough for the most practical cases of examination.
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Model of conveyer with the regulable speed
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This article is devoted to mathematical modelling of the production flow lines of the conveyor-type. Here is an analytical method for calculating the parameters of a production line with a regulated speed of the movement of the subjects of the labour along the conveyor developed. The description of the parameters of the state of the production line is made in the one-moment approximation using partial differential equations. There has been derived a solution that determines the state of the parameters of the production line for a given technological position as a function of the time. The transitional period during which the initial condition of the distributing of the subjects of the labour along a conveyor has the influence on the state parameters of a production line is certain. The developed method of the calculation of the flow parameters of the production line allows designing control systems of the production line of the conveyor-type with a regulated rate of the movement of the subjects of the labour.
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Model of porous material sintering
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The mathematical model of inert porous materials sintering was proposed. As an initial data, the model uses the initial distribution of pore surface elements and time-temperature conditions of sintering. Sintering is modelled by the system of kinetic equations describing shrinkage of a material depending on its initial properties and a time-temperature condition of the process. Experiments on aluminum oxide powder sintering have been carried out in several time-temperature conditions in which linear shrinkage was traced in time. The initial powder particles size distribution was previously measured. A value of main parameters used in the model was determined according to the sample linear shrinkage data measured at the 10 C/min heating rate. Time dependences of linear shrinkage were calculated for the heating rates of 5 and 15 C/min. Comparison of the calculated dependences with experimental data for heating rates 5 and 15 С/min has shown the good qualitative and quantitative concordance.
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Статья научная
In this paper we studied the possibilities of adaptation of Scilab freeware computer mathematic package to the solution of special calculation problems are studied. We modeled and calculated the family of adaptive devices of automation, control and protection for smart/intellectual electric grids including renewable energy sources. We studied the possibilities of Scilab package for sequential calculating using a big number of algebraic functions, solving the systems of linear algebraic equations, analyzing of results, solving the tasks of optimization, building 2D and 3D function diagrams, etc. All calculated solutions obtained from Scilab, were analysed in comparison with the similar solutions calculated in MathCAD. The results confirm the relevance of using the Scilab package for these purposes and demonstrate some of its advantages in education, scientific research and electric engineering calculations.
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Modelling of "green" investments risks
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The practical lack of methods for quantitative assessment of capital-intensive renewable energy projects taking into account the present uncertainty leads to an increase in the riskiness and reduce the amount of "green" investment in the economy. It resolves the urgency of the developing approaches to the renewable energy projects assessment. The article presents the diagnostics of specific risks and assessment of limiting the investor market share in the renewable energy projects with the optimal risk level. The proposed authors' approach to risks formalization of renewable energy deals is based on the introduction of dummy-variable, evaluation of coefficients' significance, tendency and strength of relation of risks indicators. This approach yields an indicative assessment of the deals' riskiness taking into account sectoral specifics. The developed method to limiting the investor market share is based on the principles of the economic capital theory. It allows for consolidating the current states of investor, project and economy. Research veracity is confirmed by the practical implementation. The results of the study can be used by the management of energy companies, investors and analysts in making financial decisions.
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The aim of this work is to carry out numerical calculation of electric fields in axisymmetric systems for cathode protection of underground structures against corrosion. As is known, cathode protection is a complex multi-parameter system, which has a number of features depending on the type and form of the protected structure, properties of the surrounding environment, etc. As a result, the modelling of protection parameters is quite complex and requires new more advanced computer technologies. In this work, we construct a mathematical model of the problem on the electric field distribution in an axisymmetric system for cathode electrochemical protection of underground structures. In addition, we propose an algorithm to solve the problem. The algorithm is based on the use of integral Green transformations and, in particular, the second Green integral formula. Also, we give an example of a computer implementation of the proposed algorithm in the case of a homogeneous half-space. The Scilab application package is used to implement the example.
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Статья научная
The paper considers a boundary-value problem for a hybrid system of differential equations, which represents a generalized mathematical model for a system of interconnected rigid bodies attached to the rod by elastic-damping links. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. For the theoretical foundations of our approach to investigation of the boundary value problem for the hybrid system of differential equations we propose a method of finding eigenvalues for the boundary-value problem. The comparative analysis of the results of numerical computations conducted with the use of the proposed method and the results obtained by other techniques known from the literature have proved the validity and the universal character of the proposed approach.
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Modelling of the axisymmetric precision electrochemical shaping
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The problem on modelling of a precision shaping and boundary conditions are formulated according to Faraday's law and with applying of stepwise dependence current efficiency on current density. The problem is reduced to the solution of a boundary problem for definition of two analytical functions of the complex variable. The first function is a conformal mapping of region of parametrical variable on the physical plane. In order to determine this function we use the Schwartz's integral and a spline interpolation. Unlike a plane problem for determination of potential and stream function of an axisymmetric field, the integration transformations of the second analytical function are used. The analytical function is defined in the form of a sum of two addends. The first addend takes into account the singularities of the function so that the second addend has no singularities. The second function is defined by the Schwartz's integral. Interpolation by spline functions is carried out, where the spline coefficients are derivatives of these functions by means of which the intensity vector components are calculated. We propose the method to solve the axisymmetric stationary problems, which differs from the known methods by the accuracy. By means of the method, we obtain the numerical results, describing the workpiece form. The error estimation of the obtained results is carried out. Also, we show qualitative coincidence with results of plane problem solution.
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Modelling of the time series digressions by the example of the ups of the Ural
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The article oversees forecasting model for deviations of the balancing market index and day-ahead market index according to the maximum similarity sample for different levels of approximation in the context of positive and negative time-series value. The model is being tested on the factual data of the Integrated Power system of the Ural, Wholesale market for electricity and power of the Russian Federation. The offered model is based on the sample of maximum similarity of the daily digressions by "Day-ahead" market from balancing market index in the history data of 2009 - 2014 that was acquired from an official web-site of the wholesale electric power market. Testing of the mathematical model gave the prediction error of 3,3%. The offered toolkit for forecasting of the main day-ahead and balancing market parameters is recommended to use for operational work of the industrial enterprise.
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Modelling the flow of character recognition results in video stream
Статья научная
The paper considers problems of developing stochastic models consistent with results of character image recognition in video stream. A set of assumptions that define the models structure and properties is stated. A class of distributions, namely the Dirichlet distribution and its generalizations, that set a description of the model components is pointed out; and methods for statistical estimation of the distribution parameters are given. To rank the models, the Akaike information criterion is used. The proposed theoretical distributions are verified vs sample data.
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Modelling the human papilloma virus transmission in a bisexually active host community
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In this article, we construct a mathematical model describing the transmission dynamics of Human Papilloma Virus (HPV) in a bisexually active host community. Comprehensive mathematical techniques are used to qualitatively and quantitatively analyze the model. We analyze the local and global stabilities of the model's equilibria and show that if the basic reproduction number is less than unity, then the model is locally and globally asymptotically stable at the HPV-free static states. Also, if the basic reproduction number is less than unity, then the HPV-endemic static state is globally asymptotically stable. Numerical simulations are carried out and graphical illustrations are presented to validate the theoretical results.
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