Analysis of Some Approaches to Modeling Nonlinear Dynamical Systems Using Polynomial Operators

The problem of mathematical description of nonlinear dynamical systems remains relevant today, especially given the need to build modern surveillance systems for complex technical objects, such as power plants. The use of polynomial operators obtained with the help of shortened Volterra series to solve this problem, as practice has shown, proved to be promising, because this method allows to display in the mathematical model both nonlinear and dynamic properties of systems. For further development of the method, it is advisable to analyze diffe­rent approaches in order to build effective algorithms for obtaining and applying in the problems of monitoring the functioning of nonlinear systems.

Polarization Models of Radiation in a Solar Energy Concentrator System

The possibility of using renewable energy sources (RES) for the production of hydrogen fuel, in particular solar radiation energy, without using the stage of generating electricity is considered. A mathematical model of a reflector with anisotropy of electrodynamic properties is presented. According to the analysis, using the described model, conclusions were drawn about the possibility of using this effect to ensure the transmission capacity of the energy component of solar radiation with partial or complete retention of polarization. Based on the data obtained, variants of collimating optical systems of energy concentrators are proposed that are potentially capable of realizing the photolysis process.

Synthesis of Fuzzy Logic Mathematical Model for Adaptive Control of the Mig/Mag Surfacing

A functional transformer with fuzzy logic is synthesized, which allows to get the estimations of weld beads height and width at the arbitrary values of entry parameters: wire feed speed and torch transverse oscillations amplitude. The influence of these input parameters on the base metal penetration and beads geometric parameters, welded using MIG/MAG process, were studied. Surfacing was performed by a robotic system with an arc power supply "Fronius TPS- 320i", which operated in the mode of arc process synergetic control. The formation of both individual beads and surfacing layers at different overlap coefficients has been studied. The arc surfacing process was realized in a mixture of protective gases (Ar+18%CO2) using a welding wire Св-08Г2С with a 1.0 mm diameter. Surfacing speed – 4 mm/s, frequency of welding torch oscillations – 1 Hz. The obtained experimental dependences of beads width and height, as well as the length of the welding pool can be used in both: creating of multi-pass MIG/MAG surfacing program for robotic restoration of critical purposes parts surfaces, and in preparing of FEM model of MIG/MAG surfacing.

Analysis of Cumulant Coefficients of Two-Component Mixtures of Shifted Non-Gaussian Distributions

The dependence of the cumulant coefficients of two-component mixtures of shifted non- Gaussian distributions on the weight coefficient is analyzed and conditions are determined under which the cumulant coefficients of any orders are equal to zero. The dependence of the cumulant coefficients of two-component mixtures on the shear parameter is investigated and the parameter values are determined at which the cumulant coefficients of any orders have extrema and zeros. The dependence of the skewness and excess kurtosis of a two-component mixture of shifted Gumbel distributions of type 1 on the weight coefficient and the shear parameter is investigated and their values are obtained at which the skewness and excess kurtosis of the mixture are equal to zero. The features of computer modeling of random variables, the probability density of which is a two-component mixture of shifted distributions, are considered.

The Impact of Environmental Tax Administration on the Cost of Thermal Energy on the Example of Organic and Biofuels Boilers in Ukraine

The article provides an overview of approaches to greenhouse gas emissions taxation and tax rates in European countries. To compare heated boilers with different characteristics, which run on different fuels the average cost of thermal energy for the life cycle LCOH was used. Environmental tax on environmental pollution (as a component of LCOH) is calculated for the three most common types of boilers in Ukrainian boilers with a capacity of 4.65 to 58 MW, burning natural gas, coal, and fuel oil, as well as for low-power boilers (0.5 and 1 MW ), burning fossil fuels and biofuels. The eco-tax for biofuel boilers is calculated under current taxation and subject to the adoption of a European approach to taxation of carbon dioxide emissions. It is established that at the current rates there are almost no economic incentives for the introduction of technologies to reduce the concentration of pollutants in emissions, but increasing the rates of environmental tax may change this situation. However, provided that rates are evenly increased for all types of boilers, the eco-tax for natural gas boilers will remain the lowest, while for biofuel boilers it will increase significantly, which contradicts the stated goal of decarbonizing the economy. It is shown that not only the change of environmental tax rates can be an effective tool for achieving the goals of sustainable development, as the principles of its administration are also important.

Fault-tolerant Structures of Digital Devices Based on Boolean Complement with the Calculations Checking by Sum Codes

The article considers the construction of fault-tolerant digital devices and computing systems that does not use the principles of introducing modular redundancy. To correct the signals, a special distorted signal fixation unit, concurrent error-detection by the pre-selected redundant code circuit, as well as a signal correction block are used. The distorted signal fixation unit is implemented by the Boolean complement method, which makes it possible to design a large number of such blocks with different indicators of technical implementation complexity. When synthesizing a fault-tolerant device according to the proposed method, it is possible to organize a concurrent error-detection circuit for both the source device and the Boolean complement block in the structure of the distorted signal fixation unit. This makes it possible to choose among the variety of ways to implement fault-tolerant devices according to the proposed method, one that gives a device with the least structural redundancy. Various redundant codes can be used to organize concurrent error-detection circuits, including classical and modified sum codes. The author provides algorithms for the synthesis of distorted signal fixation unit and the Boolean complement block. The results of experimental researches with combinational benchmarks devices from the well-known LG’91 and MCNC Benchmarks sets are highlighted. The article presents the possibilities of the considered method for the organization of faulttolerant digital devices and computing systems.

Mathematical Models of Main Units and Units of Automated Stabilization Instrument Complex

This work presents the developed mathematical models of the main components and units that are part of the stabilizer: control panel, gyrotachometer GT46, position sensor, control unit, etc. Mathematical models of the armament unit and turret with gearbox and motor are obtained. A mathematical model of analog and digital control path of the horizontal guidance channel is obtained; vertical guidance channel; results of mathematical modeling of control modes: for vertical channel, for horizontal channel. Mathematical models have been developed, which are used in modeling the stabilizer control modes, as well as in the study of changes in the circuit-technical solution of the weapon stabilizer in order to increase its accuracy. The reliability of the obtained results was confirmed by the results of experimental testing.

Risk Management and Assessment in Software Development Projects

The article defines the concept of threat model. Described a list of current security guidelines for the development and administration of web systems. Formed the list of cybersecurity threats, the consequences of their implementation are determined. Described the process of forming a model of cybersecurity threats of web systems. Defined the list of threats based on the recommendations and experience of authoritative organizations in the world and Ukraine. Defined the concepts of risk, risk index and risk status for the security of web systems. Defined the main principles of risk management in software development projects.

Spatial and Frequency Correlation Parametric Methods for Determining the Coordinates of Leaks in Underground Pipelines

Two parametric methods for determining the coordinates of leaks in underground pipelines are presented. The methods are a development of the well-known correlation method for determining the coordinates of leaks in the direction of taking into account complications that introduce a multiplicity of types of waves and damage in conjunction with extraneous interference. Both methods use secondary data processing, namely the processing of correlation functions to determine their quality parameters, which are then maximized. According to the first method, maximization occurs using the spatial displacement of the sensors at the points of access to the pipeline, according to the second method, by choosing the frequency range of signals. For this, the correlation function is provided in the form of a frequency dependence of its quality parameters - power, signal-to-noise ratio, with the display of the corresponding coordinate. Also, the concepts of "coordinate shelf" and its length, which are convenient for analysis, are used. The methods have been practically tested. Both methods are explained with examples.

Mathematical Model of Determination and Analysis of Heat Exchange in Elements of Digital Technology Devices

A mathematical model of heat exchange analysis between an isotropic two-layer plate heated by a point heat source concentrated on the conjugation surfaces of layers and the environment has been developed. To do this, using the theory of generalized functions, the coefficient of thermal conductivity of the materials of the plate layers is shown as a whole for the whole system. Given this, instead of two equations of thermal conductivity for each of the plate layers and the conditions of ideal thermal contact, one equation of thermal conductivity in generalized derivatives with singular coefficients is obtained between them. To solve the boundary value problem of thermal conductivity containing this equation and boundary conditions on the boundary surfaces of the plate, the integral Fourier transform was used and as a result an analytical solution of the problem in images was obtained. An inverse integral Fourier transform was applied to this solution, which made it possible to obtain the final analytical solution of the original problem. The obtained analytical solution is presented in the form of an improper convergent integral. According to Simpson's method, numerical values of this integral are obtained with a certain accuracy for given values of layer thickness, spatial coordinates, specific power of a point heat source, thermal conductivity of structural materials of the plate and heat transfer coefficient from the boundary surfaces of the plate. The material of the first layer of the plate is copper, and the second is aluminum. Computational programs have been developed to determine the numerical values of temperature in the given structure, as well as to analyze the heat exchange between the plate and the environment due to different temperature regimes due to heating the plate by a point heat source concentrated on the conjugation surfaces. Using these programs, graphs are shown that show the behavior of curves constructed using numerical values of the temperature distribution depending on the spatial coordinates. The obtained numerical values of temperature indicate the correspondence of the developed mathematical model of heat exchange analysis between a two-layer plate with a point heat source focused on the conjugation surfaces of the layersand the environment, the real physical process.