## Volume №2(26) / 2022

#### Articles in journal

Mathematical models of the intertheory of sign systems are developed in terms of the vector fiber bundle (stratification) of feature spaces of differential geometry as part of the general complexes theory, using philosophical and system-semiotic representations of linguistic knowledge. The manifestation of metatheoretic (MT) laws from the equations of the individual signs formation to the analysis and synthesis of scientific texts and system theories is investigated. The universal equation proposed allows us to compare various objects and phenomena and use it as a device for quantitative and qualitative analysis. For each kind of sign and non-sign systems, specific conceptual and terminological base is created and a set of axioms of the connection of concepts is determined, i.e. a special system intertheory is formed. The semiotic intertheory studies the properties of linear order in the form of pure knowledge on laws abstracted from the contextual environment. The axioms of semiotics postulate the existence of different forms of sign systems of fiber bundles with a linearly ordered structure: the feature space for fibration, the base of fiber bundle, the vector space of bundle with fiber, and the connectedness of signs (symbols complex). Using the vectorization procedures and their generalization to a signs series, sign systems of different complexity are produced. An analogy of the text structure with cartographic and technical reality constructions is made. Sign changes occur with geometric transformations in various coordinate systems with the preservation of recognition capacity. The properties of simple signs extend to the properties of sign systems and MT-models of geographical and technical reality. The triadic form of the organization of MTknowledge allows us to consider the signified object as the sum of the subject (concept) of research and signifier, which is logical connected with the philosophical model of transcendental argumentation. Order structures are modeled by a unit interval [0,1], which allows us to transfer the known properties of real and hyper-real numbers to complex sign systems (complexes) on complex sign systems (complexes) of semiotics, linguistics and other sciences of complex phenomena, and to present scientific texts of natural language in terms of the formal metalanguage of transformations and relations of algebraic systems. As a result, signs (schemes) are everything that reproduces and preserves linear order, that they are bounded, indexed, fractal and hierarchical organized, homotopical similar, etc.

The article is devoted to the development and application of mathematical models to study the effect of intentional mistuning on the durability of the impellers of power turbomachines by the finite element method (FEM). A numerical study of the introduction of intentional mistuning and optimization of the life characteristics of power turbomachines based on the created or developed mathematical models of the dynamic load of turbomachine blades and the assessment of life characteristics has been carried out. Using the obtained mathematical models and the numerical FEM method in this work makes it possible to increase the efficiency and reliability of new designs at the stage of designing and finishing the rotor parts of turbomachine impellers. It is confirmed that on the basis of the created mathematical models and a set of programs, it is possible to obtain the necessary accuracy of calculations and conduct computational experiments to assess the effect of deliberate mistuning of parameters in ideal cyclic symmetric systems and systems with mistuning. It is confirmed that on the basis of the created mathematical models and complex of programs, it is possible to obtain the necessary accuracy of calculations and conduct computational experiments to assess the effect of intentional mistuning in ideal cyclic symmetric systems and systems with mistuning. The ANSYS WORKBENCH software package and original author's programs were used to study the effect of intentional mistuning of the impellers of turbomachines. The object of the study is an academic impeller with 10 blades, which is manufactured at the Brandenburg University of Technology.

The paper investigates the influence of various parameters of the mathematical model of diffusion on the results of calculations of the convective diffusion of a dispersed impurity in a liquid. The need to study and model the diffusion processes of dispersed impurities is associated with the environmental problems of deepening the riverbed. Natural conditions in fishery reservoirs are adversely affected as a result of hydraulic engineering works. The extraction of sand and gravel mixtures in riverbeds leads to pollution of watercourses with suspended solids and, accordingly, to an increase in turbidity, which has a negative impact on aquatic ecosystems. This paper presents the results of a theoretical study of the diffusion of a solid impurity and evaluates the influence of both different approaches in modeling and the parameters of disperse media. The equations of the mathematical model are derived from the equation of convective diffusion in a two-dimensional non-stationary form. The watercourse is assumed to be rectilinear, of constant depth, with a constant average longitudinal velocity, while the transverse and vertical averaged velocities of the watercourse are assumed to be equal to zero. Let us direct the Ox axis along the coast towards the current, the Oz axis vertically upwards, and the Oy axis transverse to the flow. It is assumed that the point source maintains its intensity long enough to be able to solve the problem in the stationary approximation. After applying simplifications, a flat mathematical model of stationary diffusion is obtained. By the method of separation of variables in the form of a Fourier series, a solution was obtained for the set of equations of the mathematical model of diffusion of several fractions of particles. The solution is implemented in the form of a computer program. The influence of various model parameters (particle settling rate, accounting for particle sedimentation, and the linear size of particles of a dispersed impurity) on the results of calculations of the diffusion of a dispersed impurity in the longitudinal and transverse directions was determined using the method.

The paper presents the results of applying growth models with saturation to solve prognostic problems and optimize the production of agricultural products based on parametric programming models. The problems of constructing asymptotic and logistic models for medium-term forecasting of agricultural production indicators were solved. The results of modeling by asymptotic and logistic models were compared; Parametric programming problems were created and applied using saturation growth models to optimize the production of agricultural products. At the same time, methods of mathematical modeling, forecasting, probability theory and mathematical statistics and parametric programming were used. As a result, multilevel asymptotic and logistic models are proposed for predicting the production and economic indicators of agricultural production using the example of grain crop yields. The upper level (peak trend) characterizes favorable conditions for the activity of

an agricultural producer, and the lower level (trough trend) describes unfavorable situations for obtaining products. It is shown that growth models with saturation have an advantage in accuracy and significance relative to linear and non-linear trend models that are not limited by an upper bound. In addition, such models are less limited by the amount of data-dependent lead time. When comparing the asymptotic and logistic models, their advantages and disadvantages are highlighted. The developed mathematical models are implemented on real objects. A multilevel model of parametric programming using a logistic function to optimize the production of agricultural products is proposed. Forecasts of crop yields and optimal plans for production until 2024 for favorable, average and unfavorable situations are given. The proposed algorithm for obtaining optimal solutions is aimed at improving the management of agricultural production.

This paper considers the MEOPT software package created by the authors for the numerical study of non-convex parametric identification tasks. The developed software includes libraries of optimization algorithms and test problems, tool and service modules, and metacomponents. The implemented libraries of optimization algorithms include methods of multidimensional and one-dimensional non-convex optimization. The software was created in the C language using the GCC compiler and supports operation on Windows, Linux and MacOS operating systems. To date, the prototypes of the main modules of the package have been completed. Performed technical testing of the first version of the software.

When designing and operating traction power supply systems (TPS), special attention is paid to the safety of the operation of transport power facilities. One of the determining factors of such impacts is the possibility of the appearance of induced stresses on extended metal structures located along the railway route. In modern conditions, characterized by the large-scale use of digitalization tools, the choice of such activities should be based on computer simulation. Therefore, it is necessary to develop algorithms for determining the induced voltages that are created by traction networks. For this, digital models can be used, which are based on the methods for determining the TPS modes implemented in the Fazonord software package. The article describes computer models that make it possible to determine the induced voltages on a pipeline equipped with insulating flanges, which are used for the purpose of electrochemical protection of a structure. The practical use of these models will make it possible to reasonably choose measures to reduce the negative effects of induced voltages on personnel servicing the structure.

Widespread use of distributed generation (DG) plants in electric power systems requires solving the complex problem of setting their regulators. The article proposes to use predictive control algorithms that can significantly simplify its solution. On the basis of a linear predictive link, various structures and models of predictive voltage and frequency controllers are considered, both for individual plant units and for group regulation.

The implementation of prognostic algorithms in the controllers of DG plants is possible on the basis of microprocessor systems. In this regard, it is required to study the impact of an unauthorized change as a result of a cyber-attack of the time constant of the predictive link on the operation of control systems for synchronous generators. The purpose of the presented study was to determine the operation of linear predictive algorithms in group voltage and frequency controllers with a change in the forecast time. The simulation was carried out in the MATLAB system, the results of which showed that with a sudden change in the forecast time, the group voltage and frequency controllers of the generators of a small hydroelectric power plant deteriorate in terms of control quality with a possible loss of stability. It is shown that to prevent such situations, it is necessary to use a hardware limitation of the prediction time, which ensures the inadmissibility of working with negative values of the time constants of the predictive links. In addition, limiting the forecast time constants to the value n, which determines the number of generators in the group, gives the best results in terms of the quality of control in the transient process.

This paper presents a versatile and simple methodology for calculating the lifetime of storage batteries in autonomous photovoltaic systems. A description is given of battery categorization and its importance in establishing potential configuration options. Battery operating modes are modeled using the chronological modeling method which defines the mode indicators with respect to every hour of the period under consideration. The notions of partial cycle and local minimum state of battery charge are introduced. These indicators are necessary for the correct estimate of the number of battery cycles to failure. After identifying the number of cycles to failure and the average annual number of cycles, it is possible to calculate storage battery lifetime. This methodology was used in 2015 when designing and setting up Verkhnyaya Amga, a photovoltaic system in the Republic of Yakutia. The results showed that it is best to use lead–carbon batteries with a total capacity of 144 kW·h.

This study considers the issue of extending the existing methods of indicator-based analysis of the current energy security (ES) performance to a comprehensive assessment of options for the development of energy systems. The relevance of the above issue is due to the increasing uncertainty of the future, including the beginning of the transition to a low-carbon strategy. The study proposes a mix of metrics that varies depending on the time frame covered and takes into account the economic and environmental aspects of ES. An approach to assessing the significance of individual metrics in the formation of comprehensive overall metrics of the ES performance is outlined. The results of optimization calculations to assess changes in such metrics for two options for power supply of the European Russia and the Ural are presented. These options differ in the cost of fuel for power plants (in the second option, gas is 25% more expensive and coal 5% more expensive than in the first option). The rising cost of fuel affects the mix of capacity additions in different regions, increasing the share of carbon-free plants and reducing CO2 emissions. However, this increases the cost of generating electricity and risks for potential investors. The overall metric of ES takes into account this multidirectional influence. Its growth indicates that the first option is more preferable from the standpoint of ES. It is concluded that it is possible and expedient to use this kind of metrics as an additional performance criterion when comparing options for the development of the energy sector and the regional system of energy supply. As the projection time frame increases, the number of the metrics used should decrease, and the importance of the economic and environmental aspects of ES will grow.

A sustainable trend of recent decades is the search for and implementation of efficient, rational and renewable sources of thermal energy to reduce environmental pollution. Pellets from biomass (waste wood and agriculture) can be used as biofuels, which is an efficient method for obtaining biofuels with the same characteristics as wood. The article presents the results of experiments on obtaining pellets with the inclusion of animal waste and a mathematical model of the biofuel combustion process is proposed, confirming that the addition of animal waste in certain proportions to the biomass of raw materials is an environmentally friendly, resource-saving and efficient alternative to the production of traditional fuel.

Khanty-Mansi Autonomous Okrug-Yugra has a large area of forest territories (more than 90% of the total area of the district). And forest vegetation naturally dies sooner or later, as a result of which carbon dioxide is released into the atmosphere from organic matter and global warming increases.

In order to prevent an increase in global temperature, it is necessary to estimate the carbon stock in the form of the amount of vegetation biomass.

One of the ways to assess vegetation biomass is to create carbon maps using of the Earth remote sensing methods. The use of satellite images obtained with remote sensing methods and methods of their processing will make it possible to obtain a map of the district with full coverage of the entire territory, and the use of machine learning models will make it possible to develop a model with which it will be possible to obtain a carbon map of the district with a given accuracy.

This paper provides an overview of the decisions of foreign scientists over the past 5 years in the field of remote sensing aimed at creating carbon maps. Based on this review, a research program has been proposed that will allow us to develop an approach that allows us to obtain a digital carbon map of the KhMAO with the necessary accuracy.

The paper is devoted to the need to integrate studies of energy and socio-ecological systems, due to their mutual influence. To support interdisciplinary research in these areas involving the integration of energy, environmental and social components, it is proposed to use an ontological approach to identifying, describing and structuring the relationships between these complex systems. The interrelations reflecting both negative and positive influence of functioning of power facilities on the corresponding socio-ecological system are considered. The indicators of sustainable development of socio-ecological systems are considered. In order to compare the positive and negative impact of the functioning of energy facilities on the population, quality of life indicators are considered as a way to assess this impact. Ontologies structuring the basic concepts of the subject area of research on the anthropogenic impact of energy facilities, quality of life and reflecting their integration are presented.

The work discusses of ontological modeling of such a subject area as vehicles of dynamic air cushion. The connection of ontologies with various tasks of this subject area is shown. The optimization of the shape of a wing of finite span moving at ultra-small distances from the ground surface is discusses too. In context of ontologies, the features of the formulation of optimal design problems of low-flying wings are highlighted. It is noted that the corresponding ontologies can be used to classify and systematize various tasks in this subject areas. They allow to explicitly formulate the ideas and concepts underlying the corresponding solutions.

The article develops mathematical models of a three-wheeled mobile robot based on the apparatus of state variables and in operator form, on the basis of which the synthesis of its adaptive control system is carried out using the method of constructing modal PID controllers and the method of inverse problems of dynamics. The mathematical model allows, without hardware implementation of a mobile robot, to analyze the work of the created control system and, if necessary, make the necessary corrections. The mathematical model of a mobile robot consists of kinematic and dynamic models. The kinematic model is the simplest description of the behavior of a mobile robot and allows the study of its properties. The dynamic model is a more detailed description of the mobile robot and takes into account the force and moment effects produced by the actuators. In order to mathe-matically describe the mobile robot, a number of conditions are introduced, formulated as the following assump-tions: 1) the mobile robot is considered under the condition that its mechanism is rigidly connected; 2) the wheels are non-deformable and are in point contact with the surface; 3) the movement of the robot is carried out without slipping; 4) the platform is considered as a solid body on which the wheel system is fixed. The paper presents the following results of the study: developed mathematical models of a mobile robot in the state space and in operator form; the robot motion control algorithm was synthesized based on the method of inverse prob-lems of dynamics; a Simulink model of a controlled mobile robot was developed based on the modal PID control technique. The stability of the control system is ensured by introducing an external negative feedback on the an-gular velocity of the robot platform. The simulation results show that, compared with an accurate continuous mathematical model of robot control, the errors in coordinates, angular and linear velocities and moments are 5-7%, which allows us to draw a conclusion on the acceptability of the developed digital robot model, its accurate continuous analogue.

The article presents a client-server library for the interaction of the Kuka LBR iiwa collaborative robot (on the KUKA Sunrise.OS operating system) with a remote PC. An intuitive high-level library implemented in the Matlab software package. Includes a server for the Kuka iiwa controller, as well as a client based on the MathWorks Matlab environment. The library's tool set includes more than 30 functions covering such operations as calculating forward and inverse kinematics, controlling the robot in Cartesian space and using sets of axis bends, path planning, graphical display and feedback. The developed software runs on a remote computer con-nected to the robot controller via the TCP/IP protocol. The article presents the developed methods and possible examples of robot control from the library.