Mathematical Model Of System Research Articles

Interaction of Structural Elements in the Overhead Transmission Power Line

The analysis of the changes of tensile forces in conductors and earth wires is performed during their breakage and impact on the towers of overhead power line with a voltage of 330 kV. Based on the results, a mathematical model of a unified cable-stayed rod system consisting of steel towers, conductors and earth wires and insulating elements has been compiled. The system of equations of the model is solved iteratively using the MS Excel spreadsheet processor for various breakage cases. The dependences of tensile forces in conductors and earth wires during their breakage are presented, as well as the forces which correspond to an acting regime on towers in a linear circuit, taking into account the supporting effect of neighboring towers.

On the well posedness of a mathematical model for a singular nonlinear fractional pseudo-hyperbolic system with nonlocal boundary conditions and frictional damping terms

<abstract><p>This paper is devoted to the study of the well-posedness of a singular nonlinear fractional pseudo-hyperbolic system with frictional damping terms. The fractional derivative is described in Caputo sense. The equations are supplemented by classical and nonlocal boundary conditions. Upon some a priori estimates and density arguments, we establish the existence and uniqueness of the strongly generalized solution for the associated linear fractional system in some Sobolev fractional spaces. On the basis of the obtained results for the linear fractional system, we apply an iterative process in order to establish the well-posedness of the nonlinear fractional system. This mathematical model of pseudo-hyperbolic systems arises mainly in the theory of longitudinal and lateral vibrations of elastic bars (beams), and in some special case it is propounded in unsteady helical flows between two infinite coaxial circular cylinders for some specific boundary conditions.</p></abstract>

System approach to building a mathematical model of a complex organizational-technical system in transport

The current situation in the synthesis of complex organizational and technical systems in transport is characterized by a significant lag in the level of development of special mathematical and software, which significantly reduces the pace of development and efficiency of complex organizational and technical systems. This, in turn, does not allow to fully use the potential opportunities of scientific and technical progress to improve complex organizational and technical systems in transport. The fact of system and circuit synthesis of complex systems, a number of important fundamental tasks of system synthesis of multi-level hierarchical systems, to which complex organizational and technical systems belong. In the literature the objective prerequisites determining the necessity, expediency and possibility of their solution have not been sufficiently considered yet.

Methods of optimization energy consumption in residential and public buildings with the availability of alternative sources of energy supply

The article is devoted to the analysis of the potential for increasing the efficiency of electricity consumption in residential and administrative buildings in the presence of various energy sources and storage systems. This task is relevant in view of the spread of renewable energy sources both in centralized power supply systems and at local facilities and the significant impact of unstable generation on the cost of electricity in the market. In particular, the main consumers of electricity, which can be used as "consumers-regulators", as well as storage systems available for use in buildings, are considered. Taking into account that a significant amount of electricity is used or can be used in building air-conditioning systems, as well as for the needs of hot water supply, the construction of mathematical models of such systems for existing buildings will allow the creation of effective electrical load management systems to optimize energy costs for traditional buildings and ensure autonomy for buildings with close to zero energy consumption. The article describes the priority tasks to be solved to build an energy management system to minimize energy costs and increase the efficiency of the country's energy system and local energy systems of communities. The formulation of the tasks follows from the analysis of information on the actual consumption schedules of residential and public buildings and the analysis of their mutual correlation, which allows using these findings to develop algorithms for monitoring energy consumption and load management on the consumer side. Further stages of the study include additional measurements of actual energy consumption at the facilities with a discreteness of several seconds to an hour, while simultaneously recording potential influencing factors, which will allow creating a digital model of building energy consumption. A preliminary analysis of the research shows that the most promising mathematical apparatus for building such a model is the use of neural networks.

Comparative Analysis of Nonlinear Dynamics of an Angular Velocity System of 2-DOF Aerial Manipulator with Different Physical Parameters

The two-degree-of-freedom (2-DOF) aerial manipulator is composed of a quadrotor aircraft and a 2-DOF manipulator, which significantly expands the scope of grabbing and transporting objects. After the manipulator is installed on the quadrotor, the manipulator and the load will cause serious interference to the quadrotor, resulting in difficulty of system control and even instability. This paper presents a mathematical model of the angular velocity system of the 2-DOF aerial manipulator. The model considers the influence of the manipulator and the load on the quadrotor. Based on this model, the nonlinear dynamics of the angular velocity system of the 2-DOF aerial manipulator are analyzed by solving the equilibrium points, calculating the Lyapunov exponents, analyzing the dynamic bifurcation diagram, and drawing the dynamic region distribution map. It is found that angular velocity can produce the dynamic behaviors of sink, period-doubling, and chaos under certain circumstances. By analyzing the nonlinear dynamic behaviors of the angular velocity system under different manipulator postures, different manipulator configurations, different load masses, and different load resistances, the stability of the angular velocity system is analyzed to guide the use of the aerial manipulator more safely and efficiently.

Research on the Calculation Methods of the Mathematical Model of Null-Flux Coil Electrodynamic Suspension System and Experimental Verification

Research on the Calculation Methods of the Mathematical Model of Null-Flux Coil Electrodynamic Suspension System and Experimental Verification

Математические модели обменных процессов для идентификации и управления электромеханическими объектами

The issues of constructing mathematical models for systems that, in addition to the object, include a power converter, a measuring system and an on-board computer are considered. The last three elements are united by a single concept – «device». It is shown that the newly obtained «device–object» system, under certain conditions, should be considered and described as a single whole when solving problems of identification and control. Using a heuristic method, mathematical models of the «device–object» system are constructed and justified, in particular, the system of exchange equations, the exchange function and the Green’s function in the coordinate-time and pulse-energy representation.

The car paintwork defects contactless control system mathematical model

The car paintwork defects contactless control system mathematical model

The Study on the Theoretical Perspectives of Soliton and Its Applications

Abstract: A soliton is a strongly stable, nonlinear, self-reinforcing, localised wave packet that propagates freely at a constant speed and keeps its shape even after colliding with other similar localised wave packets. Its exceptional stability arises from the balanced cancellation of nonlinear and dispersive effects in the medium. In engineering, a soliton wave is a self-reinforcing solitary wave packet that keeps its shape as it travels at a steady speed. It results from the medium's non-linear and dispersive effects cancelling each other out. Many systems exhibit dispersive effects, in which the wave frequency controls the wave's speed of propagation. It was then demonstrated that soliton solutions provide stable solutions for a wide class of dispersive partial differential equations that are weakly nonlinear and describe physical systems. Solitons are preferred for high-speed, longdistance transmissions because of their self-restoring characteristics. Given that transmission speeds over longer distances are now close to 40 Gbit per second, the strain on networks is rapidly approaching a critical threshold. Solitons may provide interesting alternatives in the future. Non-linear wave equations that describe how waves propagate in specific physical systems are solved to get soliton solutions. These waves appear as solutions in mathematical models of various systems, such as optical wave-guides, crystal lattice vibrations, and water waves.

Digital Transformation of Optimal Decision-making in Economic and Engineering Systems Based on the Theory and Methods of Vector Optimization

Objective: The purpose of the work is to analyze, study the processes of digital transformation and make optimal decisions in economic and engineering systems based on the theories and methods of vector optimization. Methods: Methods for studying the processes of digital transformation of economic and engineering systems are based on the author's theory of vector optimization, which is represented by: axiomatics and optimality principles that show how one solution is better than another. On the basis of the principles of optimality, constructive methods for solving vector problems have been built, firstly, with equivalent criteria, and, secondly, with a given priority of the criterion: https://rdcu.be/bhZ8i (Springer Nature's "Vector optimization with equivalent and priority criteria" is distributed free of charge.) The paper presents that the problem of accepting the optimal process is carried out as a result of the digital transformation of the initial (statistical, experimental) data into vector problems in optimization, which represents a mathematical model of economic and engineering systems. Depending on the number and type of criteria, we solve problems with a vector of criteria, each component of which is directed to the maximum, and with a vector of criteria, each component of which is aimed at a minimum, in aggregate. Results: The result of the study is the practical orientation of digital transformation, which is shown in the computer-aided design of economic and engineering systems based on vector optimization. For this purpose, software for solving vector problems of linear and nonlinear programming has been developed. Linear vector problems are used in economic systems (forecasting, planning). Software for solving vector problems of nonlinear programming are used digital transformation of optimal decision-making in engineering problems. Conclusion: In conclusion, numerical examples in the field of economic systems are presented by the digital transformation of optimal decision-making in the development of the company. When making optimal decisions in engineering systems, the following has been developed: the construction of initial data (technical task) for modeling; transformation of a mathematical model under uncertainty into a model under conditions of certainty; making an optimal decision with equivalent criteria; making the optimal decision with a given priority criterion

Nonlinear mathematical model of pressure measurement systems in gas-liquid media

The primary element of the instrumentation for measuring the pressure of a gas-liquid medium is a sensor that supplies data on the pressure of the working medium. It determines the proper functioning of machines, mechanisms, and systems. Increasing the service life, reducing development time, and reducing the cost of sensors is one of the important tasks. Mathematical modeling of pressure measurement systems’ functioning plays an important role at the design stage of such systems. This article examines a nonlinear one-dimensional model of a mechanical system “pipeline – pressure sensor” designed to measure and control the pressure of the working gas-liquid medium in the combustion chambers of engines. In such a system, the sensor is connected to the engine via a pipeline and is located at some distance from it to reduce the impact of vibration accelerations and high temperatures. The purpose of the work is to study the dynamics and stability of joint oscillations of the elastic sensitive element in the pressure sensor and of the working medium in the pipeline for a given law of pressure change in the combustion chamber. The study is provided under the assumption that the working medium is ideal and compressible. To describe the movement of the working medium (gas or liquid), a nonlinear model of fluid and gas mechanics is used. Mathematical description of the process of interest includes an initial boundary value problem, whose formulation contains a nonlinear partial differential equation. To solve it, numerical-analytical method of solution based on the Galerkin method is proposed, which makes it possible to reduce the study of the problem to solving a system of ordinary differential equations. A numerical experiment is carried out and examples of calculating the dynamics of the sensor's sensitive element are presented. The proposed mathematical model makes it possible to determine the law of change in the deviation of the sensor's sensitive element depending on the law of change in pressure in the combustion chamber. The research results are intended for use at the design stage of pressure measurement systems.

Dynamics of Automatic Firing System Type Gas-Operated Weapon

The paper presents a new approach to establish a mathematical model of an automatic firing system of gas-operated weapons, which is based on the Lagrange's theory. In contrast to previous studies, a dynamic model is supplemented with dynamic link between a basic mechanism and a receiver assembly with longitudinal clearance without taking into account horizontal clearance. The automatic firing system of the PKMS machine gun has been selected for calculation of a theoretical model and a verification test. Through comparison between theoretical and experimental results, the mathematical model is proven to be accurate and reliable. The results obtained from the paper are the basis for evaluating the automatic firing system ability to work. This is also a reliable source of reference for designers in the process of optimising the structure of the automatic firing system.

Aircraft Firefighting Capabilities Using Suspended Containers

In the world, the fight against forest and industrial fires is carried out by both ground based equipment and aircraft – airplanes and helicopters. Each of these has its specific advantages and disadvantages. The use of aviation containers for extinguishing fires is an alternative to existing methods at the moment. They are particularly effective in the initial outbreaks of fires in hard-to-reach areas and fires caused by toxic substance, as well as in limiting the growth of their spread. The advantage is that they can be targeted at a specific place and, depending on the type of fire, can be filled with the corresponding fire-fighting substance. These containers can be hung on airplanes and helicopters depending on their load capacity. They are used in the following way, after their targeted drop from the aircraft at a specific effective height, the container is destroyed and a fire-fighting substance is poured onto the burning surface. The moment of release of the aviation fire-fighting container is determined depending on the flight conditions and the targeting system of the aircraft used. For this purpose, mathematical modelling of the process of using the aviation container was carried out, mathematical models for the movement of the aircraft and the aviation fire-fighting container were compiled, and a mathematical model of the targeting system was created.

MODEL OF TRANSPORT SAFETY ASSESSMENT IN MULTIMODAL TRANSPORTATION SYSTEMS

In this paper methods, criteria and models of safety assessment of multimodal transportation systems are investigated. Today, new types of transportation systems are formed – multimodal transportation systems, which may be defined as the result of the synthesis of several transport systems, where different modes of transport are effectively interact. The need for such systems was formed due to the peculiarities of each mode of transport, its technological and technical characteristics, which restrain the ability to compete and promote transport interaction. In this context, the problem of transport safety assess of multimodal freight transportations becomes highly important. An analysis of modern scientific researches on topic of transport safety is conducted. Unfortunately, the considered approaches to transport safety have a set of disadvantages if the complex systems are considered in form of, for example, combined, multimodal or intermodal transportations: the problem of local optimum; the problem of safety management in case of transport company is not the actual infrastructure owner; the problem of unifying estimates for several modes of transport, and so on. The system’s safety depends on its integrity and sustainable development, which is directly dependent on the objective conditions of its formation, development and operation. At the same time, the state of safety is directly dependent on subjective factors, the purpose of which is to ensure security, i.e., to preserve the integrity and maintain sustainable development and optimal functioning of the system. Thus, there is a conditional field of protection of transport system objects, which provides counteraction to a set of existing or perceived threats. In this context, modelling the transport safety assessment of multimodal freight is relevant and requires appropriate scientific developments. In the research, methods of mathematical modelling of transport systems were used in order to develop methodological approach that could be potentially used in improving the multimodal freight transportation safety. A methodical approach to safety assessment on the example of multimodal transportation, which takes into account the drawbacks of existing studies, is proposed. The practical application of developed model was demonstrated on the existing system of multimodal transportation. The developed safety assessment method may be potentially used both to assess the transportation route safety level and as key factor in optimal transportation route designing.

PONDERING THE CHOICE OF PCM AND MATHEMATICAL MODEL IN AUTOMOTIVE LHTS

Phase change materials are latent heat storage materials. As the source temperature rises, the chemical bonds within the PCM break up as the material changes phase. Upon storing heat in the storage material, the material begins to melt when the phase change temperature is reached. The temperature then stays constant until the melting process is finished. The heat stored during the phase change process of the material is called latent heat. Ideally, automotive engine cooling is undesirable from the thermodynamic point of view. If the heat transfer rates from the gas to metal could be reduced, then more power could be produced at a particular fuel flow rate, i.e. the thermal efficiency of the engine would increase. Also the heat removed out via radiator could be reduced and hence smaller radiator size. That is why powertrain thermal management is extremely necessary for good engine reliability and durability with a compromise of the thermal efficiency. One of the most technically and commercially available options for this is the use of latent heat thermal energy storage system. Despite the fact that there are numerous works and reviews covering this topic, the author hopes to draw attention to some aspects of the choice of material and mathematical model for such systems. Keywords: phase-change materials, latent heat, energy storage systems, thermal conductivity, thermo-physical properties, kinetic properties.

Man-Power-Amplifying Exoskeleton with Pneumatic Actuator

This study describes the activity of developing a force amplifier exoskeleton with one degree of freedom. The system was developed as a research prototype to conduct control system studies. The device consists of an arm with a pneumatic cylinder actuator controlled by a pressure regulator. As for the human–machine interface, the system has a force sensor. The idea is to verify the possibility of developing a simple system from the sensor system’s point of view and the control system’s architecture while simultaneously obtaining an effective, economical, and reliable device. The idea developed in this project is to use the user’s available ability to control movements in unknown environments. The user constitutes the central part of the entire control system: he defines the references for the speeds and forces to be applied to the environment and observes the rates of the controlled robotic system through his own sight and proprioceptive system. On the other hand, the machine produces and controls the forces applied to the environment by the actuator. In this way, the device shows an increased admittance. A mathematical system model was created to verify the idea’s feasibility. Following the results of the simulations, a prototype was built on which experimental tests were carried out. As stated above, it was possible to obtain the described behavior with the use of a force sensor, one-axis type, interposed between the machine and the user, to constitute the human–machine interface; using a pressure regulator, it was possible to avoid the sensors for the force feedback by the environment. The result is a simple architecture for the sensors and the control algorithm. Specific test protocols were proposed to test the performance of the human–machine “system”, and a test bench was developed that allows the tracking of variable signals represented on a monitor, which the user must follow. The system is intuitive to use, with a rapid learning curve, and the user can handle high loads according to the different signals to be followed with good precision, even at high speeds.

МОДЕЛИ И ФУНКЦИИ ИНТЕЛЛЕКТУАЛЬНОЙ СИСТЕМЫ ПОДДЕРЖКИ ПРИНЯТИЯ УПРАВЛЕНЧЕСКИХ РЕШЕНИЙ В ЭНЕРГОСИСТЕМАХ

The aim of the work is to study models and intelligent systems for supporting management decisions in energy systems. The article is devoted to solving the problem of adequate description of systems for supporting management decision-making in energy systems, as well as analysing models and functions of intelligent system models for supporting management decision-making in energy systems. As part of the research, methods of generalization and systematization of models, functions of an intelligent management decision support system, as well as systemic, evolutionary, categorical and modelling methods are used to form a conceptual model of the Transnistrian Moldavian Republic power systems which is necessary to further develop a mathematical model of intelligent system for supporting management decisions in energy systems. The novelty of the research lies in the fact that a conceptual model of a decision information system for the power supply control in the power systems of the Pridnestrovian Moldavian Republic is developed. The results of the study include analysing the subject area and developing a conceptual database model and the information support structure in the energy systems of the Transnistrian Moldavian Republic. Findings state that to develop an information system project, a system analysis of the energy industry, in particular information processes in the power supply is performed. The main aims and objectives of the project are determined, which become the basis for constructing an objective tree.

A mathematical model for tumor-immune competitive system with multiple time delays

A mathematical model is proposed to study the complicated dynamics of tumor-immune interactions with three discrete time delays. The proposed model consists of nine coupled ordinary differential equations (ODEs) whose components are tumor cells, tumor-specific CD8+T cells, dendritic cells, macrophages, regulatory T-cells (Tregs), interleukin-10 (IL-10), IL-12, transforming growth factor-β (TGF-β) and interferon-γ (IFN-γ). By utilizing the quasi-steady-state approximation for cytokine concentrations, we obtain a system of four coupled ODEs. We introduce three discrete time delays into our deterministic system to better understand the tumor-immune dynamics. Basic properties of the system, including existence, uniqueness, positivity, boundedness, and uniform persistence are discussed. Stability analysis of both the delayed and non-delayed system has been performed and the conditions for stability and direction of Hopf bifurcation have been determined. Furthermore, we assess the length of time delay required to maintain the stability of period-1 limit cycle. Parameter estimation techniques are discussed and numerical simulations are provided to support our theoretical analysis. Notably, we observe that time delays do not significantly influence the system behavior for the existing set of parameters value.

ОЦЕНКА ДИФФЕРЕНЦИАЦИИ РЕГИОНОВ АРКТИЧЕСКОЙ ЗОНЫ РФ НА ОСНОВЕ ИНФОРМАЦИОННО-АНАЛИТИЧЕСКИХ ТЕХНОЛОГИЙ

The formation of a single economic space in the Arctic zone of the Russian Federation is considered as the main task, which is the basis for realizing the development goals of the regions of the Russian Arctic. One of the solutions to the problem of creating a common spatially localized territory of the Russian Arctic megaregion, taking into account the significant differentiation of regions according to socio-economic indicators, is to identify tools for smoothing regional disparities. The use of the tested by the authors IRES RAS methodology “Information and analytical technologies for complex verification of the information base of economic and mathematical modeling of spatial economic systems” is proposed as a tool for constructing data sets suitable for full-fledged mathematical research compiled on the basis of collections of the Federal State Statistics Service.

Mathematical modeling of the ion extraction system of a radio-frequency ion source

In order to ensure space debris removal from the near-Earth space, the world scientific community is developing various technical means potentially capable of transporting the spent spacecraft to disposal orbits. The so-called Ion Beam Shepherd is among them. According to this method, in order to transfer momentum efficiently from an ion beam generated by a radio-frequency ion source mounted on board a service spacecraft, it is necessary to ensure the generation of an ion beam with the minimum divergence angle. In order to provide generation of a highly collimated ion beam for a system of contactless removal of technogenic space debris, an ion extraction system was modeled with the aim to study the influence of its geometric parameters on the angle of ion beam divergence at the ion source exit plane. Based on the preliminary study, a model of 28 full factorial experiment was developed for two types of electrodes in an ion extraction system. The regression coefficients have been defined that allow, without performing a large array of numerical studies, to assess the influence of various geometric parameters on the ion beam divergence angle.