Approximate Calculation Research Articles

Incorporation of the Fermi-Amaldi Term into Direct Energy Kohn-Sham Calculations.

In direct energy Kohn-Sham (DEKS) theory, the density functional theory electronic energy equals the sum of occupied orbital energies, obtained from Kohn-Sham-like orbital equations involving a shifted Hartree exchange-correlation potential, which must be approximated. In the present study, the Fermi-Amaldi term is incorporated into approximate DEKS calculations, introducing the required -1/r contribution to the exchange-correlation component of the shifted potential in asymptotic regions. It also provides a mechanism for eliminating one-electron self-interaction error, and it introduces a nonzero exchange-correlation component of the shift in the potential that is of appropriate magnitude. The resulting electronic energies are very sensitive to the methodologies considered, whereas the highest occupied molecular orbital energies and exchange-correlation potentials are much less sensitive and are similar to those obtained from DEKS calculations using a conventional exchange-correlation functional.

Оптимальне керування режимами розподільних електричних мереж з сонячними електростанціями при несиметричному навантаженні

The article is devoted to improving the system of automatic control of modes of distribution electric networks containing solar power plants in order to achieve a simultaneous reduction of steady-state voltage deviations, voltage asymmetry at the terminals of consumers while maximizing the level of electricity generation by solar power plants. Ensuring normal permissible levels of electricity quality indicators in distribution networks is one of the most pressing issues that arise in the design and operation of modern distribution networks. Deterioration of the quality of electricity in electrical networks leads to the appearance of such negative phenomena, increase in additional losses in the elements of the electrical network, reduce the service life of electrical equipment, reduce the productivity of production equipment and others. The most significant negative impact on the functioning of the elements of electrical distribution networks, including electricity consumers, is observed with increasing levels of steady-state deviation and voltage asymmetry above the normative values. Modern solar inverters allow you to control the level of steady voltage deviation at the point of their connection to the mains. The design features of the construction of inverters of solar power plants allow them to change (within certain limits) not only the level of steady-state voltage deviation, but also to affect the level of voltage asymmetry and the parameters of the reactive power mode. In view of this, the task of improving automatic control systems for the distribution of electric networks with solar power plants, the implementation of which will take into account the multifunctional influence of solar inverters on the parameters of these networks is quite relevant. For the research, a fragment of a typical distribution electrical network with a nominal voltage of 10 kV was used, which contains a solar power plant that connects directly to the 10 kV busbars. The authors of the article set the problem of controlling the parameters of the mode of distribution electric network with solar power plants in the form of the problem of multicriteria optimization. An approach to solving this problem is also proposed, which is based on the method of solving problems of multicriteria optimization by approaching the utopian point in the space of criteria. Approximate calculations are carried out, which confirm the possibility of applying the proposed approach to the construction of systems for automatic control of the parameters of the mode of distribution electrical networks with solar power plants

A redistributed cutting plane bundle-type algorithm for multiobjective nonsmooth optimization

<abstract><p>I construct a new cutting-plane model for approximating nonsmooth nonconvex functions in multiobjective optimization and propose a new bundle-type method with the help of an improvement function. The presented bundle method possesses three features. Firstly, the objective and constraint functions are approximated by a new cutting-plane model, which is a local convexification of the corresponding functions, instead of the entire approximation for the functions, as most bundle methods do. Secondly, the subgradients and values of the objective and constraint functions are computed approximately. In other words, approximate calculation is applied to the method, and the proposed algorithm is doubly approximate to some extent. Thirdly, the introduction of the improvement function eliminates the necessity of employing any scalarization, which is the usual method when dealing with multiobjective optimization. Under reasonable conditions satisfactory convergence results are obtained.</p></abstract>

Підвищення точності визначення місця виникнення короткого замикання в електричних мережах номінальною напругою 110-150 кВ

The article is devoted to the study of improving the efficiency of the electric network with a voltage of 110-150 kV through the use of a developed device FKZ, which uses a radio channel to transmit information. At the present stage of development of electric power industry the question of reliability of work of high-voltage electric networks plays an important role. During the operation of such electrical networks, emergencies inevitably occur, the most dangerous of which are short circuits. Determining the location of damage to the electrical network is the most complex, time-consuming and time-consuming technological operation with significant costs. Therefore, the task of improving the design of devices to determine the location of damage, the use of which will significantly reduce the level of operating costs for electrical networks, is relevant. One of the ways to solve the problem of improving the accuracy of determining the location of a short circuit in the electrical network is the use of special technical means - short circuit clamps. The scheme of the normal regime of the 150 kV electric network of PJSC Kirovogradoblenergo was used for the research. The analysis of the configuration of this network showed that it has a number of substations that receive power from transmission lines, which are deaf branches. Therefore, the installation of short-circuit latches on such lines is necessary. The authors of the article propose the introduction of a radio channel to transmit information about the state of the network and the place of damage to the next personnel of the substation. The most appropriate ways to organize a radio channel are: the use of GSM networks; use of unlicensed frequency transmitters. Approximate calculations have been carried out, which confirm the possibility of creating a radio channel for transmitting information from the short-circuit lock for a distance of up to 20 km, using transceivers of non-licensed frequencies.

Approximate Reachability for Koopman Systems Using Mixed Monotonicity

We present a data-driven method for computing reachable sets for unknown nonlinear dynamical systems using a Koopman operator based approach. We find mixed-monotone decompositions for a class of Koopman lifted dynamics. The mixed-monotone system can be further embedded to a higher-dimensional dynamical model which is propagated in time deterministically. This allows us to find over-approximations of forward reachable sets that do not suffer from the curse of dimensionality. The proposed method can account for unknown nonlinear dynamics and allow a calculation of the conservative approximations of the reachable sets to a prefixed degree of accuracy in a computationally inexpensive manner. We demonstrate the efficacy of the proposed algorithm using an illustrative example with an unknown, nonlinear dynamical model, and compare it to CORA, a well-known existing method.

Robust Design Scheme of C-Type Filter Considering Harmonic Dynamic Characteristics of Traction Power Supply System

The passive filters are widely used in the harmonic control of traction power supply system. However, high-speed trains have many types and frequent working conditions, which result in random dynamic characteristics of the harmonic spectrum of the trains. Moreover, the rapid change in harmonic injection position leads to changes in the harmonic transmission characteristics of the system. So it is difficult for passive filters to fully compensate the harmonics. Meanwhile, the existing method adopts an approximate tuning-frequency calculation formula, which makes it difficult to accurately control its filtering performance. First of all, by deriving an accurate tuning-frequency expression, this study reveals the influence of component parameters on the tuning-frequency and the possibility of tuning-frequency disappearance. Subsequently, based on the impedance-frequency index, which can describe the overall distribution of harmonics, the improved firefly algorithm is used to obtain a robust optimization design of the parameters of the C-type filter. The calculation example analysis shows that the proposed scheme has strong adaptability to harmonic random dynamic characteristics and a better filtering effect than the existing design methods, which is more suitable for a traction power supply system with strong harmonic random dynamic characteristics.

ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ДЕФОРМАЦИЙ В АДДИТИВНОМ ТЕХНОЛОГИЧЕСКОМ ПРОЦЕССЕ ЛАЗЕРНОЙ ПОРОШКОВОЙ НАПЛАВКИ

This article discusses the modeling of the stress-strain state of products during laser powder surfacing using the example of a stepped tubular sample. To calibrate the model, a number of experiments were carried out using an additive powder with a fractional composition of 40–80 μm. During laser powder surfacing of samples, two-point thermometry was carried out, which is necessary for the subsequent calibration of the temperature problem. Powder surfacing was carried out in one layer with pauses between the deposited paths according to the surfacing modes. Helium and argon were used as shielding gases. The creation of an applied tool for the preliminary numerical assessment of warpage and residual stresses in blanks and DSE before carrying out repair technological operations using the powder laser cladding method, which allows for prompt approximate calculations, was the main task of the work. In the model, the element birth/death method was considered, which makes it possible to implement the appearance of hardfacing bodies and is the most convenient in this case. Warping modeling was carried out by dividing the welded part into tracks, which, in turn, are divided into hardfacing bodies. The next stage is the heatingand cooling of each elementary body along the surfacing trajectory, instead of modeling a moving heat source. Command inserts allow you to adjust the surfacing trajectory using automatic numbering of elementary bodies. The proposed technique makes it possible to quickly preprocess the problem and obtain sufficiently accurate calculation results in a short time. The results of modeling and real laser powder surfacing were compared. Verification of the developed model was carried out using the digitized outer surface of the existing experimental samples after surfacing. Calculations show sufficient computational accuracy of the model, however, the use of high-temperature properties of the powder material will reduce the calculation error.

Numerical Simulation of Aerodynamics of Simple Geometries Using Approximate Calculation of Flow through the Facet of the Computational Cell Using the AUSM±up2 Method

Numerical Simulation of Aerodynamics of Simple Geometries Using Approximate Calculation of Flow through the Facet of the Computational Cell Using the AUSM±up2 Method

The number sense: a comparison between normal and adapted curriculum pupils in terms of subitization ability, the distance and magnitude effects

Number sense refers to the ability to easily understand, approximate and manipulate numerical quantities. In solving numerical problems, children use exact, respectively approximate calculation strategies. Unfortunately, some persons encounter difficulties in acquiring basic mathematical skills, and this condition represent a specific learning disability called developmental discalculia. The aim of the present study was to compare normal and adapted curriculum pupils in terms of subitization ability and efectiveness of number sense. The presence of magnitude and distance effects was tested in four distinct formats: 3D objects, 2D figures, verbal and visual Arabic numerical representation. The sample consisted of 111 normal and adapted curriculum pupils. Both number of errors and reaction times were registered. Adapted curriculum pupils registered more erroneous answers in the 2D, verbal, and arabic tasks and bigger reaction times in the 3D, tasks with Arabic or verbal numerals. Both normal and adapted curriculum pupils registered the best performances in the visual Arabic numerical representation task. Contrary to the expectations, the magnitude effect was not outlined in terms of reaction times, perhaps due to the calculation strategies which pupils adopted in different tasks.

Sinusoidal buckling behaviour of surface casing with negative friction in thawing permafrost

During the development of oil fields in permafrost regions, once the surface casing buckling occurs under the formation thawing and subsidence, it will cause great economic losses. In this paper, sinusoidal buckling of surface casing under negative friction is studied and preliminarily discussed. Based on the Winkler foundation theory and considering the different distribution forms of negative friction and soil resistance, the elastic stability model of casing is established. Combining dimensionless and Rayleigh-Ritz method, the critical slenderness ratio of sinusoidal buckling is obtained. The influence of boundary conditions, soil resistance and negative friction distribution on casing stability is quantitatively analysed on the basis of sufficient data calculation. It is found that the product of the critical slenderness ratio and the square root of the strain at the lower boundary is a fixed value which only depends on the boundary conditions and the value of soil resistance parameter, and the negative friction of different distribution forms can be superimposed according to the principle of ‘inverse square’ of the critical slenderness ratio. On this basis, the approximate calculation formula of the critical slenderness ratio is obtained by fitting, and the average error is less than 0.4%. The numerical example shows that the increase of soil resistance will weaken the influence of negative friction distribution on the critical slenderness ratio significantly. The ability to resist sinusoidal buckling can be improved by increasing the constraint of the lower casing section and increasing the casing thickness.

Construction of an approximate solution for a dilute magnet based on the solution for a pure magnet on the same lattice

The paper proposes a method for approximate calculation of the magnetization of a dilute Ising magnet on a certain lattice, based on the use of an exact or approximate solution for a pure Ising magnet on the same lattice. Using the proposed method, it is possible to calculate the dependence of magnetization on temperature and concentration of non-magnetic impurities and the Curie temperature as a function of concentration for a diluted magnet. The proposed method is applied in the work to the solution in the mean field approximation, to the solution in the beta approximation, and to the exact solution on a square lattice. Keywords: phase transitions, Ising model, dilute magnet.

Построение приближенного решения для разбавленного магнетика на основе решения для чистого магнетика на той же решетке

The paper proposes a method for approximate calculation of the magnetization of a dilute Ising magnet on a certain lattice, based on the use of an exact or approximate solution for a pure Ising magnet on the same lattice. Using the proposed method, it is possible to calculate the dependence of magnetization on temperature and concentration of non-magnetic impurities and the Curie temperature as a function of concentration for a diluted magnet. The proposed method is applied in the work to the solution in the mean field approximation, to the solution in the beta approximation, and to the exact solution on a square lattice.

Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table

Problem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.

МОДЕЛЬ ЭНЕРГОЭФФЕКТИВНОЙ СОЛНЕЧНОЙ ПАНЕЛИ, РАБОТАЮЩЕЙ ПРИ ПОВЫШЕННЫХ ТЕМПЕРАТУРАХ ОКРУЖАЮЩЕЙ СРЕДЫ

Relevance In conditions of elevated ambient temperatures, a solar battery operating at temperatures above 40 °C reduces the output power by –0.45 % / °C. In the conditions of an isolated hybrid power supply system, this fact can lead to a significant loss of power in the network from heating solar cells and costs, since an additional source of power supply as part of Hybrid Renewable Energy Systems (HRES) is a diesel power plant. Aim of research The main aim of the research to investigate the effect of elevated ambient temperatures and reduced temperature of thermoelectric elements on the solar panel in the MatLAB Simulink environment, to calculate the approximate energy efficiency from the method used as part of hybrid power supply systems based on renewable energy sources (HRES). Research methods As a mathematical model, it is proposed to use the MatLAB Simulink complex, as a device for reducing the temperature of the solar module, it is proposed to use thermoelectric elements. Results Based on mathematical calculations in the MatLAB Simulink environment, with the help of thermoelectric elements, it was possible to increase the maximum power by 0.11 kW, which, according to approximate calculations, will save the equivalent of diesel fuel in the amount of 267,000 rubles in the period from April to September for the village of Kuskurgul with a consumption of 100 kW.

A novel compact broadband and radiation efficient antenna design for medical IoT healthcare system.

This paper investigates and develops a novel compact broadband and radiation efficient antenna design for the medical internet of things (M-IoT) healthcare system. The proposed antenna comprises of an umbrella-shaped metallic ground plane (UsMGP) and an improved radiator. A hybrid approach is employed to obtain the optimal results of antenna. The proposed solution is primarily based on the utilization of etching slots and a loaded stub on the ground plane and rectangular patch. The antenna consists of a simple rectangular patch, a 50 Ƹ microstrip feed line, and a portion of the ground plane printed on a relatively inexpensive flame retardant material (FR4) thick substrate with an overall compact dimension of 22 × 28 × 1.5 mm3. The proposed antenna offers compact, broadband and radiation efficient features. The antenna is carefully designed by employing the approximate calculation formulae extracted from the transmission line model. Besides, the parameters study of important variables involved in the antenna design and its influence on impedance matching performance are analyzed. The antenna shows high performance, including impedance bandwidth of 7.76 GHz with a range of 3.65Ƀ11.41 GHz results in 103% wider relative bandwidth at 10 dB return loss, 82% optimal radiation efficiency in the operating band, reasonable gain performance, stable monopole-shaped radiation patterns and strong current distribution across the antenna lattice. The suggested antenna is manufactured, and simulation experiments evaluate its performance. The findings indicate that the antenna is well suited for medical IoT healthcare systems applications.

Graphoanalytic Method of the Complex Systems Structural Reliability Approximate Calculations

Graphoanalytic Method of the Complex Systems Structural Reliability Approximate Calculations

Investigation on design method of curved compression surface of inlet on scramjet

Suppose that curved compression surface of inlet consists of segments. Two curved surfaces formed by equal compression angles of the micro-element segments and a slight increase in the compression angle of the micro-element segments are designed respectively. The numerical simulation method is used to compare the performance of two curved surfaces with the reference three-wedge compression surface. Select NASA classic test data, in order to determine the turbulence model and calculation method chosen by the numerical simulation Fluent software. The results show: the configuration of the segment compression angle deeply affects compression efficiency of the curved surface compression system. Pressure gradient distribution on the compression surface with constant compression angles segments is nearly constant along the incoming flow direction, and the curved compression surface easily resist the separation of the boundary layer compared to three-wedges compression surface. The approximate calculation method of the bending shock profile is given.

Fuzzy system F-CalcRank for calculating functions of fuzzy arguments and ranking of fuzzy numbers

Assessing functions of fuzzy arguments and ranking of fuzzy quantities are two key steps in fuzzy modeling and Fuzzy Multicriteria Decision Analysis (FMCDA). Approximate calculations along with the use of centroid index as a defuzzification based ranking methods are a generally accepted approach to applications in the fuzzy environment. This paper presents a novel fuzzy system, F-CalcRank, which is integration of two coupled fuzzy systems: F-Calc (Fuzzy Calculator) and F-Ranking (Fuzzy Ranking). F-Calc allows assessing functions of fuzzy numbers with the use of different approaches: approximate calculations, standard fuzzy arithmetic, and transformation methods. The input values to F-Calc are fuzzy numbers with the following membership functions: triangular and trapezoidal, Gaussian, bell shape, sigmoid, and piece-wise linear continuous or upper semicontinuous membership functions of any complexity, as well as fuzzy linguistic terms of a given term set. F-Ranking system is intended for ranking of a given set of fuzzy numbers, including those, which are inputs and/or outputs of the F-Calc system. F-Ranking includes six ranking methods: three defuzzification based and three pairwise comparison ones. The structure of F-CalcRank as well as input and output information and the user interfaces of both F-Calc and F-Ranking systems, which can also be used independently, are presented. Examples of computing functions of fuzzy arguments and ranking of fuzzy numbers using implemented methods as well as exploring a real case study in agro-ecology with the use of a math model in fuzzy environment are considered. These examples stress the features and novelty of F-CalcRank system as well as presented applied research. The computer modules created within F-CalcRank are a basis for different FMCDA models developed by the authors. F-CalcRank system is intended for university education, research and various applications in engineering and technology.

Dynamics of an oscillator with a quadratic nonlinearity in the expression of the elastic force loaded with a step pulse

The unsteady oscillations of an oscillator with a quadratic nonlinearity in the expression of the elastic force under the action of an instantaneously applied constant force are described. The analytical solution of a second-order nonlinear differential equation is expressed in terms of periodic Jacobi elliptic functions. It is shown that the dynamic coefficient of a nonlinear system depends on the value of the instantaneously applied force and the direction of its action, since the elasticity characteristic of the system is asymmetric. If the force is directed towards positive displacements, then the characteristic of the system is "rigid" and the dynamic coefficient is in the interval , that is, it is smaller than that of a linear system. In the case when the force is directed towards negative displacements, the elasticity characteristic of the system is «soft» and the dynamic coefficient falls into the gap (2, 3), that is, it is larger than in the linear system. In the second case of deformation, there are static and dynamic critical values of the force, the excess of which leads to a loss of stability of the system. The dynamic critical force value is less than the static one. Since the displacement of the oscillator is expressed in terms of the Jacobi functions, the proposed formula for their approximate calculation using the table of the full elliptic integral of the first kind. The results of calculations are given, which illustrate the possibilities of the stated theory. For comparison, in parallel with the use of analytical solutions, numerical computer integration of the differential equation of motion was carried out. The convergence of the calculation results in two ways confirmed the adequacy of the derived formulas, which are also suitable for analyzing the motion of a quadratically nonlinear oscillator with a symmetric elastic characteristic. Thus, the considered nonlinear problem has an analytical solution in elliptic functions, and the process of motion depends on the direction in which the external force acts. In addition, when a force is applied towards a lower rigidity, a loss of system stability is possible.
 Keywords: nonlinear oscillator, quadratic nonlinearity, stepwise force impulse, Jacobi elliptic functions.

Estimation of the value of leaks through a through defect of the pipeline when using in-pipe repair elements

The loss of hydrocarbons when using in-pipe repair elements is determined by the nature of the fluid flow in the gap between the pipe and the repair sleeve. An accurate analytical calculation of the flow parameters for a real sleeve, taking into account its length, the asymmetry of the defect and other design features, is very difficult. In this article, the problem of accurate calculation of the radial flow of a viscous incompressible fluid in a thin layer between two annular plates simulating a circular region with a center coincide with a pipeline defect is solved. The area consists of two circles formed by the pipeline wall with a through defect and the surface of the internal repair element. The results obtained will allow us for accurate calculations in the area adjacent to the defect of the pipe and approximate calculations for the whole repair element.