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  8. 43-2

Electronic modeling

Vol 43, No 2 (2021)

 

CONTENTS

Mathematical Modeling and Computation Methods

  PETROV V.V., ANTONOV E.E., SHANOILO S.M.
Simulation Algorithm of MicroprismaticSimulation Algorithm of MicroprismaticLenses for Transformation of Light Beams
3-18
  MATSEVYTYI Yu.M., SAFONOV M.O., HROZA I.V.
Method for Identification of the PowerMethod for Identification of the Powerof a Source of Thermal Energy By Solving the Internal Reverse Problem of Thermal Conductivity
19-28
  GLUKHOV A.D.
Random Permutation Theorem and Some of its Applications
29-36
  PODHURENKO V.S., GETMANETS O.M., TEREKHOV V.E.
The Method of the Estimating Wind Power Plant’s Installed Capacity Utilization Factor

37-50

Informational Technologics

  KATIN P.Y., POKHYLENKO O.A.
Typical "State" Software Patterns for Creating Cortex-M Microcontroller System Software Infrastructure in Real Time Embedded Systems
51-67

Application of Modeling Methods and Facilities

  GURIEIEV V.O., LYSENKO Y.M.
Topological Method for Assessing the Sensitivity to theTopological Method for Assessing the Sensitivity to theDetection of Cybersecurity in Electrical Networks
68-78
  PLESKACH B.M.
Segmentation of the Time Series of Energy Consumption Parameters
79-85
  UZDENOV T.A.
Reduction of Task Queue Execution Time in GRID-systems with Inalienable Reduction
86-96
  PANASENKO A.V.
Improvement of Methods of Calculations of Flood Water Passing Through Medium-Pressure Hydro Units Taking Into Ac-Count the Characteristics of Flood Wave
97-107

SIMULATION ALGORITHM OF MICROPRISMATIC LENSES FOR TRANSFORMATION OF LIGHT BEAMS

V.V. Рetrov, E.E. Antonov, S.M. Shanoilo

Èlektron. model. 2021, 43(2):03-18

ABSTRACT

The traditional Fresnel focusing lens concentrates the light intensity in the center of the formed image. However, sometimes it is necessary to convert a parallel light beam into a light circle; such transforming flat Fresnel lenses are often used in signal processing systems. We propose an algorithm for simulation of Fresnel microprismatic structures that form a uniformly illuminated circle in the focal plane. This method is similar to our simulation algorithm previously proposed for creating focusing microprismatic elements with flat annular focusing facets. The proposed structures with a discrete change of refraction angles for transformation of light beams can be easily fabricated by the method of diamond cutting, which allows obtaining the flat conical working surfaces of high optical quality. The size of such prismatic structures should not be too large to reduce the discreteness of the formed images, so the simulation method involves the creation of refractive zones from several identical small microprisms. A modified algorithm for simulating the parameters of transforming lens is proposed, which takes into account the processes of light concentration by the lens and narrowing of light fluxes by microprisms.

KEYWORDS

Fresnel ring microprisms, light beam concentrator, calculation of refractive zones, simulating microprism parameters, diamond cutting method.

REFERENCES

  1. Palmer, С.A. and Loewen, E.G. (2014), Diffraction Grating Handbook, 7th edition, Newport Corporation, NY, USA.
  2. Soifer, S.A. (1999), "Computer Optics: Diffractive Optical Elements", Soros Educational Journal, no. 4.
  3. Koronkevich, V.P., Korolkov, V.P. and Poleschuk, A.G. (1998), "Laser Technologies in Diffractive Optics", Optoelectronics, Instrumentation and Data Processing, no. 6, pp. 38-
  4. Poleshchuk, A.G., Nasyrov, R.K. and Asfour, J.M. (2009), "Combined Computer-Genera­ted Hologram for Testing Steep Aspheric Surfaces", Optics Express, Vol. 17, no. 7, pp. 5420-
    https://doi.org/10.1364/OE.17.005420
  5. Liu, X.P., Cai, X.Y., Chang, S.D. and Grover, S.P. (2005), "Bifocal Optical System for Distant Object Tracking", Express, Vol. 13, no. 1, p.136–141.
    https://doi.org/10.1364/OPEX.13.000136
  6. Korolkov, V.P., Nasyrov, R.K. and Shimansky, R.V. (2008), "Zone-Boundary Optimization for Direct Laser Writing of Continious-Relief Diffractive Optical Elements", Applied Optics, 45, no. 1, p. 53-62.
    https://doi.org/10.1364/AO.45.000053
  7. Lenkova, G.A. (2015), "High-Efficiency Diffractive Focusing Deflective Element", Optoelectronics, Instrumentation and Data Processing, Vol.51. pp. 560–567.
    https://doi.org/10.3103/S8756699015060059
  8. Sokolova, E.A. (2004), "Simulation of Mechanically Ruled Concave Diffraction Gratings by Use of an Original Geometric Theory", Applied Optics, 43, no. 1, pp. 20-28.
    https://doi.org/10.1364/AO.43.000020
  9. Volkov, A.V., Kazansky, N.L. and Rybakov, O.E. (1998), "Investigation of Plasma Etching Technology for Obtaining Multi-Level Diffractive Optical Elements", Computer Optics, no. 18, pp. 111-
  10. Antonov, E.E., Kryuchyn, A.A., Fu, M.L., Le, Z.C., Petrov, V.V. and Shanoilo, S.M (2015), Mikropryzmy: optychni parametry ta kontrolʹ [Microprisms: Optical Parameters and Monitoring], Akademperiodyka, Kyiv, Ukraine. ISBN 978-966-360-284-4.
  11. Brinksmeier, E., Gläbe, R. and Schönemann, L. (2012), "Diamond Micro Chiseling of Large-Scale Retroreflective Arrays", Precision Engineering, Vol. 36, pp. 650–657.
    https://doi.org/10.1016/j.precisioneng.2012.06.001
  12. Lapshin, V.V., Zakharevich, E.M. and Grubyi, S.V. (2016), "Machining of Linear Negati­ve Matrices for Fresnel lenses and prisms), Russian Engineering Research, no. 7, pp. 60- URL: http://www.mashin.ru/eshop/iournals/vestnik mashinostroeniya/2016/07/ .
  13. Antonov, E.E. (2012), "Calculation Algorithms for Parameters of Annular Focusing Micro­prismatic Structures", Data Recording, Storage and Processing, Vol. 14, no. 23, pp. 38-47. DOI: 10.35681/1560-9189.2012.14.2.105049.
  14. Petrov, V.V., Antonov, E.E., Kryuchyn, A.A. and Shanoilo, S.M. (2019), Mikropryzmy v oftalʹmolohiyi [Microprisms in Ophthalmology], Naukova Dumka, Kyiv, Ukraine. ISBN 978-9660-00-1639-2.
  15. Born, M. and Wolf, E. (1998), Principle of Optics, 7th ed., Cambridge University Press, Cambridge, UK.
  16. Petrov, V.V., Antonov, E.E., Manko, D.Yu., Zenin, V.N. and Shanoilo, S.M. (2020), "Simulation and Investigation of Parameters for Light Beam Concentrators", Data Recording, Storage and Processing, Vol. 22, no. 3. pp. 3-13. 
    https://doi.org/10.35681/1560-9189.2020.22.3.218803
  17. Petrov, V.V., Antonov, E.E. and Shanoilo, S.M. (2010), "Light Chromatism, Diffraction and Visual Acuity for Fresnel Microprisms", Data Recording, Storage and Processing, Vol. 12, no.1, pp.49-
  18. Sultanova, N., Kasarova, S. and Nikolov, I. (2009), "Dispersion properties of optical polymers", Acta Physica Polonica A, Vol.116, pp.585-587. URL: http://www.refractiveindexes.info.
    https://doi.org/10.12693/APhysPolA.116.585
  19. SOLIDWORKS 2020. URL: http://www.solidworks.com.
  20. Software for design and analysis of illumination and optical systems. URL: https://www.lambdares.com/tracepro/.

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METHOD FOR IDENTIFICATION OF THE POWER OF A SOURCE OF THERMAL ENERGY BY SOLVING THE INTERNAL REVERSE PROBLEM OF THERMAL CONDUCTIVITY

Yu.M. Matsevytyi, M.O. Safonov, I.V. Hroza

Èlektron. model. 2021, 43(2):19-28

ABSTRACT

An approach to solving the internal inverse problem of heat conduction (OCT) is proposed, using the principle of regularization of A. N. Tikhonov and the method of influence functions. In this work, the power of the energy source is presented as a linear combination of the first-order Schoenberg splines, and the temperature is presented as a linear combination of influence functions. The influence function method makes it possible to use the same vector of unknown coefficients in both representations. The unknown coefficients are found as a result of solving the system of equations, which follows from the necessary condition for the minimum of the functional of A.N. Tikhonov with an effective algorithm for finding the regularization parameter, the use of which makes it possible to obtain a stable solution to the GST. For the regularization of the OST solutions, this functional also uses a stabilizing functional with the regularization parameter as a multiplicative factor. The article presents the numerical results of identifying the power of thermal energy by temperature, measured with an error characterized by a random variable distributed according to the normal law.

KEYWORDS

inverse problem, influence functions, identification, regularization, functional.

REFERENCES

  1. Beck, J.V., Blackwell, B. and St. Clair, C.R., jr. (1985), Inverse heat conduction. Ill-posed problems, J Wiley & Sons, NY, USA. URL: https://doi.org/10.1002/ 19870670331.
  2. Matsevytyi, Yu.M. (2002), Inverse heat conduction problems: in 2 vols. Vol. 1. Metodologiya, Naukova dumka, Kyiv, Ukraine.
  3. Kozdoba, L.A. and Krukovskyi, P.G. (1982), Metody resheniya obratnykh zadach teploperenosa [Methods for solving inverse heat transfer problems], Naukova dumka, Kyiv, Ukraine.
  4. Alifanov, O.M., Artyukhin, Ye.A. and Rumyantsev, S.V. (1988), Ekstremalnyye metody resheniya nekorrektnykh zadach [Extreme methods for solving ill-posed problems], Nauka, Moscow, Russia.
  5. Tikhonov, A.N. and Arsenin, V.Ya. (1979), Metody resheniya nekorrektnykh zadach. [Methods for solving ill-posed problems], Nauka, Moscow, Russia.
  6. Matsevytyi, Yu.M. and Slesarenko, A.P. (2014), Nekorrektnyye mnogoparametricheskiye zadachi teploprovodnosti i regionalno-strukturnaya regulyarizatsiya ikh resheniy [Incorrect Incorrect multi-parameter heat conduction problems and regional structural regularization their solutions], Naukova dumka, Kyiv, Ukraine.
  7. Khamzaev, Kh.M. (2020), “Algorithm for determining the trajectory of the heat source along the heated homogeneous rod”, Elektronnoye modelirovaniye, Vol. 42, no. 1, pp. 25–32.
    https://doi.org/10.15407/emodel.42.01.025
  8. Guseynzade, S.O. (2018), “Pressure recovery at the reservoir boundary based on the solution of the inverse problem”, Elektronnoye modelirovaniye, 40, no. 4, pp. 19–28.
    https://doi.org/10.15407/emodel.40.04.019
  9. Ivanov, V.K., Vasin V.V. and Tanaka V.P. (1978), Teoriya lineynykh nekorrektnykh zadach i yeye prilozhtniya [Theory of linear ill-posed problems and its applications], Nauka, Moscow, Russia.
  10. Vatulyan, A.O. (2007), Obratnye zadachi v mekhanike deformiruemogo tvyordogo tela [Inverse problems in mechanics of deformable solids], Fizmatlit, Moscow, Rusiia.
  11. Sergienko, I.V. and Deyneka, V.S. (2009), Sistemnyi analiz mnogokompanentnykh raspredelyonnykh system [System analysis of multicomponent distributed systems], Naukova dumka, Kyiv, Ukraine.
  12. Denisov, A.M. (1994), Vvedeniye v teoriyu obratnykh zadach [Introduction to the theory of inverse problems], Izdatelstvo MGU, Moscow, Russia.
  13. Romanov, V.G. (1984), Obratnye zadachi matematicheskoi fiziki [Inverse problems of mathematical physics], Nauka, Moscow, Russia.
  14. Kabanikhin, S.I. (2009), Obratnye i nekorrektnye zadachi [Inverse and ill-posed problems], Sibirskoye nauchnoye izdatelstvo, Novosibirsk, Russia.
  15. Vikulov, A.G. and Nenarokomov, A.V. (2019), “Identification of mathematical models of heat transfer in spacecraft”, Inzhenerno-fizicheskiy zhurnal, 92, no. 1, pp. 32–44.
  16. Golovin, D.Yu., Divin, A.G., Samodurov, A.A., Turin, A.I. and Golovin, Yu.I. (2020), “New express method for determining the thermal diffusivity of materials and finished products”, Inzhenerno-fizicheskiy zhurnal, 93, no. 1, pp. 240–247.
    https://doi.org/10.1007/s10891-020-02113-8
  17. Nenarokomov, A.V., Chebakov, E.V., Krainova, I.V., Morzhukhina, A.V., Reviznikov, D.L. and Titov, D.M. (2019), “Geometric inverse problems of radiation heat transfer as applied to the development of backup attitude control systems for spacecraft”, Inzhenerno-fizicheskiy zhurnal, 92, no. 4, pp. 979–987.
    https://doi.org/10.1007/s10891-019-02008-3
  18. Machanyek, A.A., Goranov, V.A. and Dedyu, V.A. (2019), “Determination of the thickness of the protein layer on the surface of polydisperse nanoparticles from the distribution of their concentration along the measuring channel”, Inzhenerno-fizicheskiy zhurnal, 92, no. 1, pp. 21–32.
    https://doi.org/10.1007/s10891-019-01903-z
  19. Ahlberg, J.H., Nilson, E.N. and Walsh, J.L. (1967), The theory of splines and their applications, Academic Press. URL: https://doi.org/10.1002/19700500646.
  20. Matsevytyi, Yu.M. and Hanchin, V.V. (2020), “Multiparametric identification of several thermophysical characteristics by solving the internal inverse heat conduction problem”, Problemy mashinostroeniya, 23, no 2, pp. 14–20.
    https://doi.org/10.15407/pmach2020.02.014
  21. Matsevytyi, Yu.M. and Lushpenko, S.F. (1990), Identificatsiya teplofizicheskikh cvoystv tverdykh materialov [Identification of thermophysical properties of solid materials], Naukova dumka, Kyiv, Ukraine.
  22. Matsevytyi, Yu.M., Safonov, N.A. and Hanchin, V.V. (2016), “On the solution of nonlinear inverse boundary problem of heat conduction”, Problemy mashinostroeniya, 19, no. 1, pp. 28–36.
    https://doi.org/10.15407/pmach2016.01
  23. Matsevytyi, Yu.M., Sirenko, V.N., Kostikov, A.O., Safonov, N.A. and Hanchin, V.V. (2020), “Method for identification of non-stationary thermal processes in multilayer structures”, Kosmicheskaya nauka i nechnologiya, Vol. 26, no. 1(122), pp. 79–89.
    https://doi.org/10.15407/knit2020.01.079
  24. Matsevytyi, Yu.M., Kostikov, A.O., Safonov, N.A. and Hanchin, V.V. (2017), “To the solution of nonstationary nonlinear boundary value problems of heat conduction”, Problemy mashinostroeniya, Vol. 20, no. 1–2, pp. 34–45. URL: https://doi.org/10.15407/ pmach2017.02. 022.

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RANDOM PERMUTATION THEOREM AND SOME OF ITS APPLICATIONS

А.D. Glukhov

Èlektron. model. 2021, 43(2):29-36

ABSTRACT

In the study of the structural properties of complex discrete systems, graph theory is widely used. Thus, to assess the ability of a system to retain certain structural properties when breaking the relationships between its elements, it is important to study different types of connectivity of the graph and their generalizations. Of particular interest is the question of how likely it is that a given graph will remain connected or have a sufficiently large connected component when a certain number of its edges are removed? In this paper, the theorem on random permutations is proved and a number of its applications in graph theory are considered. The operation of "permutation gluing of graphs" is introduced. It is shown how with the help of such gluing of two given graphs of a rather simple structure it is possible to construct graphs which with sufficient probability have the necessary connected properties. In particular, the constructions are described, which with a given probability allow to build expanders as well as graphs of greater connectivity. This approach allows you to synthesize graphs with certain properties as a result of some stochastic process followed by selection.

KEYWORDS

complex discrete system, graph, permutation group.

REFERENCES

  1. Glukhov, (2016), “Quasi-Random Graphs and Structural Stability of Complex Discrete Systems”, Elektronnoe modelirovaniye, Vol. 38, no. 5, pp. 35-41.
    https://doi.org/10.15407/emodel.38.05.035
  2. Glukhov, O. and Korostil, Ju. (2004), “Structural safety of complex discrete systems with random failures”, Modelirovanie ta informaziyni tehnologii, Vol. 27, pp. 91-95.
  3. Diestel, R. (2000), Graph Theory, Springer-Verlag, NY, USA.
  4. Erdős, P. and Rényi, A. (1959), “On Random Graphs I”, Publicationes Mathematicae Debrecen, Vol. 6, pp. 290-297.
  5. Glukhov, O. (2008), “On the application of permutation groups in some combinatorial problems”, Ukrayinskyy matematychnyy zhurnal, Vol. 60, no. 11, pp.1568-1571.
    https://doi.org/10.1007/s11253-009-0173-5
  6. Kartesi, F. (1980), Vvedenie v konechnye geometrii [Introduction to finite geometries], Nauka, Moscow, Russia.
  7. Hoory, S., Linial, N. and Wigderson, A. (2006), “Expander graphs and their applications”, Bulletin of the American Mathematical Society, Vol. 43, no. 4. pp. 439-561.
    https://doi.org/10.1090/S0273-0979-06-01126-8
  8. Diniz, E.A, Karzanov, A.V. and Lomonosov, M.V. (1976), “About a structure of a system of minimum cut sets of the graph”, Issledovaniya po diskretnoy optimizatsii, pp. 290-306.
  9. Sachkov, V. (1978), Veroyatnostnye metody v kombinatornom analise [Probabilistic methods in combinatorial analysis], Nauka, Moscow, Russia.

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THE METHOD OF THE ESTIMATING WIND POWER PLANT’S INSTALLED CAPACITY UTILIZATION FACTOR

V.S. Podhurenko, О.M. Getmanets, V.E. Terekhov

Èlektron. model. 2021, 43(2):37-50

ABSTRACT

The purpose of this work is to find a simple analytical dependence for the utilization factor of the installed capacity of a wind power plant on the parameters of its power characteristics and the parameters of the wind cadastre at the proposed location of the wind power plant at a given height of the axis of its wind wheel. Based on the study of the power characteristics of 50’s wind power plants of various manufacturers with a capacity of 2.0 MW to 3.6 MW, it has been shown that these characteristics are well described by the Weibull – Gnedenko two-parameter integral distribution. A simple asymptotic expression for the installed power utilization factor depending on two parameters of the Weibull – Gnedenko differential distribution for the wind speed and two parameters of the Weibull – Gnedenko integral distribution for the power characteristic of a wind power plant has been obtained. It has been shown that the predictions of the asymptotic expression differ by no more than 2% from the results of numerical calculations of the installed capacity utilization factor and, therefore, can be used to select or design a specific wind power plant on the proposed area at a given height of the wind wheel axis.

KEYWORDS

wind energy, wind wheel, wind cadastre zones, power curve, Weibull-Gnedenko distribution, tabulated function.

REFERENCES

  1. Statistical review of world energy, 69th edition (2020), BP p.l.c., URL: https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/statistical- review/bp-stats-review-2020-full-report.pdf (accessed: January 01, 2021).
  2. GWEC global wind report (2019), URL: https://gwec.net/global-wind-report-2019/ (accessed: January 01, 2021).
  3. Installed capacity of the IPS of Ukraine values as of 12/2020, NPC «Ukrenergo», URL: https://ua.energy/installed-capacity-of-the-ips-of-ukraine/ (accessed: January 01, 2021).
  4. Manwell, J.F., McGowan, J. and Rogers, A. (2008), Wind energy explained: theory, design, and application, 2nd, Chichester: John Wiley&Sons, London, England.
    https://doi.org/10.1002/9781119994367
  5. Weibull, W. (1951), “A statistical distribution functions of wide applicability”, Journal of Applied Mechanics, Vol. 18, no. 3, pp. 293–297.
    https://doi.org/10.1115/1.4010337
  6. Gnedenko, B.V. (1944), “Limit laws for sums of independent random variables”, Uspekhi matematicheskikh nauk, Vol. 10, pp. 115–165.
  7. Lydia, M., Kumar, S.S., Selvakumar, A.I. et al. (2014), “Comprehensive review on wind turbine power curve modeling techniques”, Renewable and Sustainable Energy Reviews, Vol. 30, pp. 452–460.
    https://doi.org/10.1016/j.rser.2013.10.030
  8. Sohoni, V., Gupta, S.C. and Nema, R.K. (2016), “A Critical Review on Wind Turbine Power Curve Modeling Techniques and Their Applications in Wind Based Energy Systems”, Journal of Energy, Vol. 1, pp. 1-18.
    https://doi.org/10.1155/2016/8519785
  9. IEC (2005), Wind Turbines, Part 12-1: Power Performance Measurements of Electricity Producing Wind Turbines; IEC61400-12-1; International Electrotechnical Commission: Geneva, Switzerland.
  10. Romanuke, V. (2018), Wind Turbine Power Curve Exponential Model with Differentiable Cut-in and Cut-out Parts. Research Bulletin of the National Technical University of Ukraine Kyiv Polytechnic Institute.
    https://doi.org/10.20535/1810-0546.2018.2.121504
  11. Albadi, M. and El-Saadany, E. (2009), “Wind Turbines Capacity Factor Modeling”, A Novel Approach. Power Systems, IEEE Transactions, Vol. 24, no. 3, pp. 1637- 
    https://doi.org/10.1109/TPWRS.2009.2023274
  12. Al-Shamma'a, A., Addoweesh, K. and Eltamaly, A. (2015), “Optimum Wind Turbine Site Matching for Three Locations in Saudi Arabia”, Advanced Materials Research, pp. 347-353. 
    https://doi.org/10.4028/www.scientific.net/AMR.347-353.2130
  13. Diyoke, C. (2019), “A new approximate capacity factor method for matching wind turbines to a site: case study of Humber region, UK”, International Journal of Energy and Environmental Engineering, Vol. 10, no. 4, pp. 451-462. 
    https://doi.org/10.1007/s40095-019-00320-5
  14. Sagias, N.C. and Karagiannidis, G.K. (2005), “Gaussian class multivariate Weibull distributions theory and applications in fading channels”, IEEE Transactions on Information Theory, Vol. 51, no. 10, p. 3608–3619.
    https://doi.org/10.1109/TIT.2005.855598
  15. Prudnikov, A.V., Brychkov, A.V. and Marychev, O.I. (1981), Integraly i ryady [Integrals and series], Nauka, Moscow, Russia.
  16. Podgurenko, V.S., Terekhov, V.Ye., Getmanets, O.M. et al. (2019), Patent No. 135302, MPK F03D 1/00 G01P 5/00 “The method of estimation the wind power plant production”, u2019 00597; application date January 21, 2019; Bulletin no. 12.

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