Vountesmery Yu.V.

Application of Nonreciprocal Electric Circuits with Passive Components

Р. 7–16.

Fig. 8. Refs.: 27 titles.

This paper describes the method of recording nonreciprocal passive multipoles containing gyrotropic medium with analysis of linear lumped electric circuits. Nonreciprocal passive devices are designed for meter and decameter wave ranges on the basis of nonreciprocal effects of helicon waves propagation in magnetized solid-state plasma. The base element for nonreciprocal passive devices is nonreciprocal transformer containing a helicon resonator. Various schemes of nonreciprocal transformer connection, combined with additional reactive components, are used to design the various nonreciprocal passive devices such as isolator, circulator and gyrator. The resulted dimensions of nonreciprocal passive devices are smaller than the wavelength and must be analyzed using lumped theory of circuits. The paper provides an insight into the methods of calculation of circuit parameters of the nonreciprocal transformer based on helicon resonator and three specific nonreciprocal passive devices based on it. The paper also proposes a method of insertion of nonreciprocal passive devices to the matrix of conduction of the nodal model of lumped circuit. It has been demonstrated that the nonreciprocal passive devices based on gyrotropic medium are exceptions from the reciprocity theorem.

Keywords: nonreciprocal passive devices, helicon resonator, lumped circuit, reciprocity theorem.

Naidenko V.I.

Eigen Waves of Cross-Waveguide

Р. 17–26.

Fig. 6. Refs.: 14 titles.

The purpose of the article is to obtain the algorithms for calculating the characteristics of its own waves in the cross-waveguide cross and demonstrate their abilities. We solve the boundary value problem by the mode matching method. By employing the moment method functional equations arising from the boundary conditions are reduced to systems of homogeneous linear equations (SLE), whose order is equal to 2M+2N+4, where M and N are number of terms in schedules of the fields in subfields  specified below. Using the specific form of SLE, SLE is reduced to lower order, namely – 2M+2. Critical wavelengths of main types of H and E waves in the cross-waveguide are calculated. In addition, we use relatively minor determinant of order – dispersion equation – 4–8. This physical interpretation of the critical wave number changes with the change of boxes size by changing the wave polarization. The obtained results show high convergence of critical wave number with increasing order of the determinant and the number of terms in the sums of its elements. The results can be used in design and synthesis of microwave devices based on cross-waveguide.

Keywords: cross-waveguide, mode matching method, moment method, system of homogeneous linear equations, critical wave number, H and E waves.

Novski V.О., Kurilo I.A., Grudska V.P., Malahatka D.O.

Multifunction Transformer-Valve Converter for the Complex Power Quality Improvement of Three-Phase Systems with Variable and Nonlinear Load

Р. 27–33.

Fig. 3. Tabl. 1. Refs.: 9 titles.

This paper analyzes the design features and functional capabilities of the automatic filter-balancing device (AFBD) developed to ensure electromagnetic compatibility of the important electric energy consumers with the power supply, optimization of low-voltage distributive networks behavior, voltage and energy loss saving, complex power quality improvement. The article presents a detailed description of the schematic solutions realizing the effect of simultaneous voltage system balancing, enhancement of harmonic composition by the odd multiple of 3 harmonics filtering and parametric damping of asymmetrical network voltages fluctuations. Through experiemts conducted we create the pilot sample of AFBD with the highest possible power of 200 kVA. Theoretical and experimental studies reveal that AFBD are appropriate for use in low-voltage distributive networks for complex enhancement of power quality.

Keywords: multifunction converter, booster transformer, key switch, electromagnetic compatibility, power quality, low-voltage network.

Protsenko О.R., Trotsenko Ye.O.

Assessing the Possi­bi­lity of Using Insulating Paper as the Transformer Oil Humidity Sensor Element

Р. 34–38.

Tabl. 4. Refs.: 17 titles.

This paper determines possibilities of using insulating paper as a humidity sensor element for monitoring the humidity level of transformer oil in power transformers. We propose to construct the sensor unit of the humidity sensor as a cylindrical capacitor structure, in which the dielectric is the electrically insulating paper soaked in transformer oil. Moreover, we conduct the investigation of relation between conductivity of insulating paper, transformer oil and moisture; temperature and electric field occurring at measuring their resistance at a constant voltage. Furthermore, we determine the electric field value, at which the resistance of insulating paper soaked in transformer oil can be considered dependent only on the temperature and humidity. We also define the formula describing this dependence. The research results show the possibility of creating the humidity sensor based on the transformation of “moisture-resistance” providing continuous monitoring of moisture in transformer oil during its operation.

Keywords: transformer oil, moisture insulation, humidity sensor, electrical conductivity, sensor probe, insulating paper.

Shcherba A.A., Makov D.K.

Errors Analysis of Measuring Instruments of Three-phase Voltage Asymmetry

Р. 39–44.

Fig. 2. Refs.: 5 titles.

This article is devoted to the increase of exactness of measuring three-phase indexes of quality of electric power in the systems of three-phase power supply. We analyze transformation equations of three-phase voltage of six-pole is in-process executed with three by an entrance and by three output clamps. We show that four complex coefficients fully characterizing this six-pole can be entered. These are transmitivities for positive-sequence voltage (PSV) as well as of reverse sequence voltage (RSV) of fundamental frequency traditional for an electric signal theory and additional two coefficients of transformation changing PSV and RSV to RSV and PSV of fundamental frequency, accordingly. These coefficients of transformation characterize the variation degree of parameters of six-pole elements. Using this approach, transformation equations of three-phase entry block of digital measuring device of quality indexes of electric power are studied when three-phase voltage is supplied to its entrances and the coefficient of asymmetry on the reverse sequence of fundamental frequency is measured. Each of three chanels of three-phase entry block contains the chart of galvanic upshot, chart of down-scaling, filter of lower frequencies. We analyze additive and multiplicative errors of three-phase entry block is executed, the dominant error of measuring. When this dominant error (that fully feasibly) is corrected, the total error of measuring the asymmetry coefficient will be significantly decreased.

Keywords: indexes of quality of electric power, coefficient of unsymmetry, symmetric systems of voltage of positive, zero, negative sequences.

Bidyuk P.I., Kozhukhivska O.A.

Probabilistic Modeling of Operational Actuarial Risks

Р. 45–58.

Fig. 5. Tabl. 4. Refs.: 25 titles.

Insurance companies are functioning in conditions of uncertainties of various types and nature what results in respective financial risks. All these reasons lead to the problem of timely recognition and development of mechanisms for the risks management. To solve the problem appropriate mathematical models are developed to describe the risks, and methodologies proposed for their practical application. The sources of the insurance fraud are detected and respective risk classification is presented. It is shown that to describe mathematically the risks of this class it is appropriate to apply the models based on the mathematical statistics approach, regression type models, and fuzzy logic. For estimation of the risk of actuarial fraud in auto insurance a model is proposed in the form of Bayesian network. The model structure was estimated using expert and statistical information of insurance company with providing a possibility for detecting hidden interactions between selected variables. An algorithm was also developed for probabilistic inference on the network. The model constructed reflects the causal links between the risk factors and the insurance company losses. It can be applied for analysis of internal states of the company; analysis of external conditions characteristic for the company functioning; for determining probable reasons of company losses due to operational risks as well as for making appropriate managerial decisions.

Keywords: actuarial risks, classification, probabilistic modeling, Bayesian networks, modeling methodology, structure and parameter estimation, practical application.

Kopets M.M.

Integro-Differential Riccati Equation in the Optimal Control Problem by the Process of Heat Conductivity

Р. 59–63.

Refs.: 7 titles.

Riccati equations occur when solving the problems of dynamics of processes in continuous environments, problems of the theory of heat conductivity and diffusion, problems of the theory of optimal control. In case of systems with lumped parameters it is necessary to investigate the usual matrix differential Riccati equations. There are integro-differential Riccati equations for mathematical models of systems with the distributed parameters. In the majority of monographs devoted to the theory of optimum control by systems with distributed parameters, the differential Riccati equations are not considered at all. In the given article the linear-quadratic problem of optimal control is investigated by heat conductivity process. By means of the method of Lagrange multipliers we obtain necessary optimality conditions. The uniqueness of optimal control is proved. Firstly for such problem we use Dirac delta-function and obtain the integro-differential Riccati equations. The formula for calculating the solution of this equation is proposed. By means of the given formula the optimum control is presented in the closed form.

Keywords: Dirac delta-function, integro-differential Riccati equation, linear-quadratic problem, optimal control, Lagrange multiplier method, necessary conditions of an optimality, heat conductivity process.

Kryvoboka G.I., Silvestrov A.M., Skrynnyk O.M.

Ap­plication of Filters Theory for Analytical Description of Logical-Analytical Dependences

Р. 64–69.

Fig. 8. Tabl. 6. Refs.: 5 titles.

In this paper, we develop the approach combining local mathematical models into one comprehensive analytical mathematical model with its significant complications. Partial models are described using as simple analytical dependences as possible. The partial models obtained should be combined in one analytical model through multiplying them with the analytical ones in the whole range of weight functions of the object variables – equivalents of frequency filters. The single uniform analytical dependence is constructed by adding private models weighed by weight functions. The analyticity of the single model for the whole range remains at such statement. In this paper, we present the results confirming the possibility of developing the sufficiently simple analytical model by using the proposed method. Its accuracy of approximation meets modern methods and object-oriented modeling. The models developed by employing this method can be used for analytical calculations of optimum operating modes of non-stationary stochastic objects, diagnostics of their condition, interpolation and extrapolation of variables of object and for other purposes by identifying local mathematical models and their combining into full analytical model without essential complication both of mathematical model and natural experiment.

Keywords: nonlinear model, object identification, approximation, analytical model, weight function.

Maltsev A.Yu.

The Cauchy Problem for Evolutionary Essentially Infinite-Dimensional Differential Equation

Р. 70–75.

Refs.: 5 titles.

This paper presents the theoretical study of the infinite-dimensional analysis field. It is inspired by Paul Levy’s scientific works and grabbed the attention of many mathematicians. The Laplace–Levy operator has many very interesting properties and many applications for stochastic analysis. The essentially infinite-dimensional operator is a generalization of well-known Levy–Laplace operator. Specifically, the operator of the formally second order satisfies the Leibniz property. This paper deals with studying non-stationary parabolic differential equations of the second order for functions defined for infinite dimensional equations in the Hilbert space. Differential operators of the second order related to these equations have no finite-differential analogs. We construct a solution to the Cauchy problem for any other non-stationary differential equation with essentially infinite-dimensional operator. In addition, we prove that this problem is equally correct.

Keywords: Laplace-Levy operator, essentially infinite-dimensional operator, evolutionary family, parabolic equation.

Maslianko P.P., Rudenko P.А.

Component Model of the Automated Testing System with the Open form of the Test Task Presentation

Р. 76–84.

Fig. 3. Tabl. 1. Refs.: 11 titles.

In this paper we present state of the art for the automated testing systems that use an open form for the test task presentation. We have developed a numerical criterion for the comparison of the existing automated testing systems with the open form of the test task presentation. In the paper we also present a strategy for improving the efficiency of the automated testing systems with the open form of the test task presentation. This strategy is based on the answer presentation model, a semantic search algorithm allowing to compare the answers with the given template, an answer evaluation model, and an interactive means for the automated testing. In the paper we have compared the efficiency of the developed testing system with the existing systems based on the proposed numerical criterion, and shown that our system has advantages. The results analysis given by the automated testing system and their comparison with the results given by a teacher-expert shows that these results converge.

Keywords: the automated testing, fuzzy inference, open form, degree of accordance, degree of importance, human language.

Trehub V.G., Klymenko О.М.

Control of Periodic Ac­tion Apparatus

Р. 85–89.

Fig. 6. Refs.: 7 titles.

The article analyzes and studies features of constructing systems of dynamic control (SDC) of periodic action apparatus (PAA). Programming control and control with constraints are employed for PAA dynamic control. Technological requirements as well as solving the problem of dynamic optimization or heuristic method can be used to develop the program of transition functions from the initial to PAA final state. The choice of the control system depends on technological requirements, specificity of functioning and completeness of information on these objects. MatLab software environment is used to implement and to evaluate the regulation quality of one of the block diagram variants of the multiplanimetric programming control system (PCS) with an additional connection for changing tasks and logical functional units as compared with single PCS. The most effective SDC is a system with the additional connection for changing tasks and logical functional unit. If the transition function is not determined by technological requirements and control system with prognostic physical model can be used as the driving force of the process imposed by critical constraints to construct SDC.

Keywords: system of dynamic control, logical functional unit, prognostic model.

Kazarin D.A., Volkotrub M.P., Pryutsky M.I.

Obtaining Ferrotitanium by Aluminothermic Method with 40–43 % of Titanium Content without Adding Titanic Waste

Р. 90–93.

Fig. 1. Tabl. 7. Refs.: 7 titles.

This paper seeks to enhance the aluminothermic technology by selecting and calculating charge materials so that this technology provides obtaining ferrotitanium from the ilmenite concentrate without adding titanic waste with 40–43 mas. % of titanium content. To conduct the experiments we use the ilmenite concentrate of the Illich Metallurgy Plant with ТіО2 63 % content as main raw materials. The concentrate previously subjected to oxidizing annealing at a temperature of 1100–1150 °С that allows increasing the titanium output and lowering aluminum consumption. Melting is carried out in the crucible (H – 200 mm, Æ 160 mm) lining with a mix of magnesite powder (95 %), liquid glass (0,7 %) and refractory clay (4,3 %). The thickness of lining is 25–30 mm. Microstructure and phase structure of the obtained samples are studied on a raster electronic microscope of REM 106і and the x-ray RIGAKU diffractometer, respectively. Through experiments conducted, ferrotitanium of the following chemical composition is obtained (%): 41,7 Ті; 37,2 Fe; 10,1 Аl; 7,2 Si; 1,46 Mn; 0,87 Ca; 1,25 Cr; 0,1 P. Such chemical composition corresponds to FeTi40Al10 brand ferrotitanium on ДСТУ 4761-91. Thus, the conducted experiments confirm that the aluminothermic way allows obtaining FeTi with maintenance of titanium of 40–43 mas. % from the concentrate without using titanic waste leading to cost reduction.

Keywords: ferrotitanium, ilmenite, aluminothermic method, microstructure, titanic waste.

Kyrychok T.Yu., Melnychenko A.A., Nesterenko V.M.

Ana­lysis of Ukrainian Hryvnia Banknotes Wearing Qua­lities in a Real Circulation

Р. 94–104.

Fig. 7. Tabl. 7. Refs.: 14 titles.

The algorithm of accuracy increasing is developed for orientation system – strapdown Attitude and Heading Reference System (AHRS) at its installation on ships or other carrier objects with known distance from swaying center. The proposed algorithm allows to compensate AHRS errors caused by accelerations at object swaying, in autonomous mode where AHRS sensors (accelerometers and rate sensors) are used only. Accuracy of these errors compensation is evaluated. At this the proportional-integral variant of rate sensors correction from accelerometers is considered. Formulas for estimation of residual error of AHRS with proposed algorithm depending on AHRS sensors performance, parameters of AHRS correction circuit, swaying parameters, accuracy of AHRS position determination relative to the swaying center are derived. Experimental test results are shown that confirm essential decreasing of AHRS errors at swaying (in 4 times) when proposed algorithm is applied. Calculated estimates of AHRS errors coincide with the test results.

Keywords: sorting banknotes, banknote deterioration, soiling, local stains, violation of banknotes structure and form.

Roik T.А, Glushrova D.B., Tarabanova V.P., Rak L.М.

The Connection between Structural State and Wear-Resistance of Steels for the Detail’s Scraper Conveyer’s

Р. 105–109.

Fig. 6. Refs.: 6 titles.

The paper is devoted to establishing of connection between of hardness, wear-resistance and the nature of structure. It is used structural analysis, measuring of microhardness and wearing tests. It is conducted the comparison of wear-resistances speed, microhardness of three steels 30Г, 25ХГСР, А335/А335М grade P22 (ASTM) for the details of scraper conveyer, which subjected to wear during the exploitation. It is established on the frequency curve of hardness distribution, that most of grains in the steel 25ХГСР was great hardness. That is one out of factors, which explains the very small wear-resistance’s speed for 6 and 36 hours in this steel in the comparison with others steels. Such particular properties of steel 25ХГСР are connected with its structure, which is troostite with small quantity of dispersed carbides, arranged uniformly. The investigations, which are executed with using the method of electron microscope, allowed to establish, that the carbides of alloy elements in the steel 25ХГСР are enough dispersed, have spherical form and are disposed uniformly in the structure. It is positive fact for the wear-resistance, which promotes slowing – down and braking of process of intensive wearing details.

Keywords: structure, steels for details of scraper conveyer, hardness, wear-resistance, form of carbides.

Rudakov K.M., Jakovlev A.I.

Large Strains Modeling. Report 4. Physical Equations of Thermoplasticity and Creep Using Logarithmic Measure of Hencky’s Strains

Р. 110–118.

Refs.: 11 titles.

The paper considers the general relation of the theory of thermo-plasticity and creep. We apply multiplicative decomposition and Hencky’s logarithmic strain for modeling the process of deformation with simultaneous presence of deformations of different type: temperature, elastic, plastic and creep. To this end, we use the second law of thermodynamics, multiplicative decomposition of a gradient of deformations, the exact branch of a temperature component of deformations gradient, experimentally established fact of incompressible metal at irreversible deformations, parity between components of Piola–Kirchhoff’s second tensor with Euler–Cauchy’s tensor components, asymmetrical Mandel stress tensor. In addition, we consider the specific capacity of internal forces and collect Lagrange’s functional. Finally, we determine that associated laws of incremental plasticity and creep theories operate in the main axes of elastic deformations. They are analogous to those applied at infinitesimal deformations. However, we can represent the laws concerning the proposed speeds of plastic deformations and creep deformations by using Noll’s stress.

Keywords: large strains, multiplicate decomposition, thermoelastic, plastic, creep, logarithmic strain.

Chvertko Ie.P.

Prediction of the Quality of Welded Joints in Flash-Butt Welding

Р. 119–123.

Fig. 1. Tabl. 2. Refs.: 7 titles.

Statistical methods of analysis are currently widely used to develop control and monitoring systems for different welding processes. These methods allow to obtain information on the process including the effect of all factors on its results, which is often difficult to evaluate due to the process complexity. The paper reveals development of the study based on neural networks for classifying flash-butt welding processes by continuously applied disturbances. The author has proposed the alternative method of preliminary data processing which can be applied to network training and evaluation of processes. The developed method is based on the simplified algorithm with standard deviation of the voltage in the welding circuit used as an informative parameter. The calculation step was also reduced. The results of effectiveness check for neural networks developed with application of the new data processing method are presented. The principal possibility of application of the developed method of data processing in the real-time systems of automated process control is shown.

Keywords: flash-butt welding, neural network, quality monitoring, data processing.

Chernega D.F., Neshcadim V.N., Kud P.D., Ivanchenko D.V.

Investigation of Iron Ore Pellets Sintering with High-Content of Solid Fuels

Р. 124–128.

Fig. 3. Refs.: 14 titles.

This paper experimentally confirmed the possibility to obtain fluxed pellets with sufficient strength and high degree of metallization and cost-effective for it use in the blast furnace process. Specifically, we study the influence of the mineral composition of pellets by their strength and establish that the pellets strength with high basicity is somewhat reduced in the temperature range 1473–1493 K due to the significant amount of more brittle slag frame and decrease of the oxidation of pellets, which consequently reduces the amount of hematite, but meets GOST requirements. We investigate the effect of increasing fuel content in the pellets on their metallization efficiency. In this case, the maximum degree of metallization (31,5 %) is achieved with pellet content of about 12 % of pulverized coke fractions 0,08–0,8 mm. Increased pellets metallization occurs because the process of the liquid phase formation is extensively developing in the temperature range 1553–1593 K with the increase of their basicity. Moreover, the more lime is in the pellets, the greater the amount of the liquid phase, in which FeO oxide prevails. The combination of sintering and metallization allows transferring the recovery process from the blast furnace at the stage of preparing metallurgical materials.

Keywords: ore pellets, metallization, strength, charge, blast furnace process, yield of pellets.

Kolobrodov V.G., Pivtorak D.О.

An Algorithm for Image Coding of Photographing Object Having a Large Range of Brightness

Р. 129–132.

Fig. 1. Refs.: 12 titles.

This paper proposes an algorithm for image coding of photographing object having a large range of brightness. It allows to achieve a high quality image of the photographing object by constructing it of the most informative images' elements of the object obtained under the same environmental conditions and different exposures. We also propose an algorithm for resulting HDR (High Dynamic Range) image coding from a series of LDR (Low Dynamic Range) images obtained by exposure bracketing or sensitivity bracketing of the optical receiver. Patterning of digital HDR image is based on calculation and recording of actual values ​​of brightness of the object’s photographed portions corresponding to each pixel in the image. The calculation of the real brightness of the object’s photographed portions is photographed by averaging the data obtained from a series of LDR images. When averaging the data the most informative elements of each image are taken with a maximum weighting factor determining the quality of the resulting image.

Nesterenko O.I., Ignatovych O.V.

Errors Comppensation of Attitude and Heading Reference System at Object Swaying

Р. 133–139.

Fig. 1. Refs.: 8 titles.

The algorithm of accuracy increasing is developed for orientation system – strapdown Attitude and Heading Reference System (AHRS) at its installation on ships or other carrier objects with known distance from swaying center. The proposed algorithm allows to compensate AHRS errors caused by accelerations at object swaying, in autonomous mode where AHRS sensors (accelerometers and rate sensors) are used only. Accuracy of these errors compensation is evaluated. At this the proportional-integral variant of rate sensors correction from accelerometers is considered. Formulas for estimation of residual error of AHRS with proposed algorithm depending on AHRS sensors performance, parameters of AHRS correction circuit, swaying parameters, accuracy of AHRS position determination relative to the swaying center are derived. Experimental test results are shown that confirm essential decreasing of AHRS errors at swaying (in 4 times) when proposed algorithm is applied. Calculated estimates of AHRS errors coincide with the test results.

Keywords: AHRS, strapdown system, orientation, swaying compensation.

Chizh I.G., Golembovskiy O.O.

Technique and Device for Measuring the Human Eye’s Depth of Focus

Р. 140–146.

Fig. 8. Refs.: 15 titles.

In this paper, we demonstrate that the depth of focus (DOF) of the eye’s optical system during implantation of intraocular lenses and aberration correction of presbyopian eyes should be identified and measured. The known methods and devices are described to determine the pseudo-accommodation volume of presbyopic eyes by subjective and objective methods. Their advantages and disadvantages are analyzed. We show that the main disadvantage of subjective methods is the impossibility to separate a pseudo-accommodation component caused by the eye’s optics from its total volume. The disadvantage of the objective method based on results of eye aberrometry is an extremely complicated and cumbersome mathematical procedure of evaluating the DOF. The method and device are proposed for objective measurement of geometric parameters of the DOF deprived of the above-mentioned deficiencies. This method is based on the image analysis of the luminous point on the retina in the reverse light. A scheme was shown for the device that allows to scan the "air" image in a short period of time.

Keywords: Depth of the focus, pseudo-accommodation volume.

Barbash V.A., Danilenko A.A., Nagorna Ju.M.

Investigation of Various Stages Process for Producing Microcrystalline Pulp from Hemp for its Quality Indicators

Р. 147–151.

Tabl. 4. Refs.: 8 titles.

A comparative analysis of the chemical composition of the hemp fibers and stalks with cotton and representatives of hardwood and softwood was performed. The possibility of obtaining microcrystalline cellulose from hemp fibers by alkaline sulfite-alcohol delignification with preliminary acid and alkaline hydrolysis was investigated. It was found that carrying out an acid and an alkali pre-hydrolysis reduces the mineral content and partly of residual lignin in the plant material. The various bleaching schemes of organosolvent pulp with using environmentally friendly reagent – hydrogen peroxide were analyzed. It is recommended to perform the process of bleaching organosolvent hemp pulp by scheme Q–P1–P2–A with the total consumption of hydrogen peroxide up to 12 % by weight of the cellulose with the addition of NaOH solution instead of conventional Na2SiO3, NaOH and MgSO4. It is shown that the performing of the acid pre-hydrolysis of bleached organosolvent hemp pulp by 2,5 N hydrochloric acid allows reducing the degree of polymerization and to obtains microcrystalline cellulose with quality indexes that meet the requirements of the standard.

Keywords: hemp fiber, bleaching, microcrystalline cellulose.