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  7. 2017 год
  8. 39-1

Electronic Modeling

Vol 39, No 1 (2017)

https://doi.org/10.15407/emodel.39.01

CONTENTS

Mathematical Modeling and Computation Methods

  KRASILNIKOV A.I.
Class of Non-Gaussian Symmetric Distributions with Zero Coefficient of Kurtosis
3-18
  LISTROVOY S.V., LISTROVAYA E.S., KURTSEV M.S.
Rank Approach to the Solution of Problems of Linear and Nonlinear Boolean Programming for Planning and Management in Distributed Computing Systems
19-38
  GIENGER A., SACHS J., SAWODNY O.
Stochastic Model Predictive Control for Hybrid Energy Systems
39-50

Computational Processes and Systems

  MINAEV Yu.N., FILIMONOVA O.Yu., MINAEVA J.I.
Granular, Fuzzy Set and Tesor-Trace Characteristics of Multidimensional Time Series
51-74
  KALINOVSKY Ya.A.
Efficient Algorithms for Solving Equations of Isomorphic Hypercomplex Digital Systems with the Help of Presented Exponents
75-90

Application of Modeling Methods and Facilities

  MASYUK A.L.
Diff Method for Implementing Undo Stack of the Recent User Actions
91-104
  NIKOLAIEV V.A., KONASHEVYCH O.I.
Not only Structured Query Language Method of Ad Request Processing
105-112
  POZHIVATENKO V.V.
Modelling of Phase Transitions in Calcium–Strontium Superstructures at Low Pressures
113-125

Color figures to the articles are in the insets

CLASS OF NON-GAUSSIAN SYMMETRIC DISTRIBUTIONS WITH ZERO COEFFICIENT OF KURTOSIS

A.I. Krasilnikov

Èlektron. model. 2017, 39(1):03-18
https://doi.org/10.15407/emodel.39.01.003

ABSTRACT

A new class of symmetric non-Gaussian distributions with zero coefficient of kurtosis γ4 has been determined on the basis of a family of two-component mixtures of distribution. Models of three types of this class are constructed, examples of distributions are given. The obtained results allow performing mathematical and computer modeling of non-Gaussian random variables with symmetric distributions and zero coefficients of kurtosis γ4.

KEYWORDS

symmetric distributions, cumulant coefficients, cumulant analysis, coefficient of kurtosis, mixtures of distributions.

REFERENCES

1. Malakhov, A.N. (1978), Kumuliantnyi analiz sluchainykh negaussovykh protsessov i ikh preobrazovanii [Cumulant analysis of random non-Gaussian processes and their transformations], Sovetskoe radio, Moscow, Russia.
2. Kunchenko, Yu.P. (2001), Polinomialnye otsenki parametrov blizkikh k gaussovskim sluchainyh velichin. Ch. I. Stokhasticheskie polinomy, ikh svoistva i primenenie dlia nakhozhdeniia otsenok parametrov [Parameter polynomial estimators of random variables close to Gaussian. Part I. Stochastic polynomials, their properties and application for finding parameter estimators], ChITI, Cherkassy, Ukraine.
3. Krasilnikov, A.I. (2014), Modeli shumovykh signalov v sistemakh diagnostiki teploenergeticheskogo oborudovaniia [Models of noise signals in the systems of diagnostics of the heat power equipment], Institut tekhnicheskoi teplofiziki NAN Ukrainy, Kyiv, Ukraine.
4. Babak, S.V., Myslovich, M.V. and Sysak, R.M. (2015), Statisticheskaia diagnostika elektrotekhnicheskogo
oborudovaniia [Statistical diagnostics of the electrotechnical equipment], Institut electrodinamiki NAN Ukrainy, Kyiv, Ukraine. 
5. Alexandrou, D., De Moustier, C. and Haralabus, G. (1992), “Evaluation and verification of bottom acoustic reverberation statistics predicted by the point scattering model”, J. Acoust. Soc. Am., Vol. 91, no. 3, pp. 1403-1413.
https://doi.org/10.1121/1.402471
6. Kuznetsov, V.V. (2009), “Use of the moments of the third order in calculations of electric loadings”, Vestnik Samarskogo GTU. Seriia “Tekhnicheskie nauki”, no 2 (24), pp. 166-171.
7. Kuznetsov, B.F., Borodkin, D.K. and Lebedeva, L.V. (2013), “Cumulant models of additional errors”, Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie, no. 1 (37), pp. 134-138.
8. Jondeau, E. and Rockinger, M. (2001), “Gram-Charlier densities”, Journal of Economic Dynamics & Control, Vol. 25, pp. 1457-1483.
https://doi.org/10.1016/S0165-1889(99)00082-2
9. Karpov, I.G. (1999), “Approximate identification of distribution laws of hindrances in adaptive receivers with the use of the method of moments”, Radiotekhnika, no. 7, pp. 11-14.
10. Kendall, M. and Stiuart, A. (1966), Teoriia raspredelenii [Distribution theory], Translated by Sazonov, V.V. and Shiriaev, A.N., Nauka, Moscow, Russia.
11. Krasilnikov, A.I. (2013), “Class of non-Gaussian distributions with zero skewness and kurtosis”, Izvestiia vysshikh uchebnykh zavedenii. Radioelektronika, Vol. 56, no. 6, pp. 56-63.
https://doi.org/10.3103/S0735272713060071
12. Krasilnikov, A.I. (2016), “Models of asymmetrical distributions of random variables with zero asymmetry coefficient”, Elektronnoe modelirovanie, Vol. 38, no. 1, pp. 19-33.
https://doi.org/10.15407/emodel.38.01.019
13. Marchenko, B.G. and Shcherbak, L.N. (1993), “Moment problem and cumulant analysis”, Otbor i obrabotka informatsii, Vol. 9 (85), pp. 12-20.
14. Jondeau, E. and Rockinger, M. (2003), “Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements”, Journal of Economic Dynamics & Control, Vol. 27, pp. 1699-1737.
15. De Carlo, L.T. (1997), “On the meaning and use of kurtosis”, Psychological Methods, Vol. 2, no. 3, pp. 292-307.
https://doi.org/10.1037/1082-989X.2.3.292
16. Krasilnikov, A.I. and Pilipenko, K.P (2007), “Unimodal two-component Gaussian mixture. Excess kurtosis”, Elektronika i sviaz, no. 2 (37), pp. 32-38.
17. Doane, D.P. and Seward, L.E. (2011), “Measuring skewness: A forgotten statistics?”, Journal of Statistics Education, Vol. 19, no. 2, pp. 1-18, available at: www.amstat.org/publications/jse/v19n2/doane.pdf.
18. Lukach, E. (1979), Kharakteristicheskie funktsii [Characteristic functions], Translated by Zolotarev, V.M., Nauka, Moscow, Russia.
19. Vadzinskii, R.N. (2001), Spravochnik po veroiatnostnym raspredeleniiam [Reference book on probabilistic distributions], Nauka, St. Petersburg, Russia.
20. Krasilnikov, A.I. and Pilipenko, K.P. (2010), “Modeling of discrete mixtures of distributions”, Elektronika i sviaz, no. 2 (55), pp. 57-61.

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RANK APPROACH TO THE SOLUTION OF PROBLEMS OF LINEAR AND NONLINEAR BOOLEAN PROGRAMMING FOR PLANNING AND MANAGEMENT IN DISTRIBUTED COMPUTING SYSTEMS

S.V. Listrovoy, E.S. Listrovaya, M.S. Kurtsev

Èlektron. model. 2017, 39(1):19-38
https://doi.org/10.15407/emodel.39.01.019

ABSTRACT

The efficiency of ranking approach to solving arbitrary Boolean programming tasks has been shown. Procedures are described which allow solving problems of linear and nonlinear programming using algorithms of polynomial complexity with a small error, with arbitrary nonlinearities, both in functionality and limitations. The article also shows the results of experimental investigation of the error of the developed algorithms and their time complexity.

KEYWORDS

discrete programming, ranking approach, planning, distributed computing system.

REFERENCES

1. Papadimitriu, H. and Stayglits, K. (1985), Kombinatornaya optimizatsiya. Algoritmy i slozhnost [Combinatorial optimization. Algorithms and complexity], Mir, Moscow, Russia.
2. Foster, C. and Kesselman, S. (2001), The anatomy of the Grid: Enabling scalable virtual organizations, Intern. J. Supercomputer Applications, Vol. 15, no. 3, available at: http://www.globus.org/alliance/publications/papers/anatomy.pdf.
3. Ponomarenko, V.S., Listrovoy, S.V. and Minukhin, S.V. (2008), Metody i modeli planirovaniya resursov v GRID-sistemakh. Monografiya [Methods and models of scheduling resources in GRID-systems. Monograph], Izdatelskii dom INZhEK, Kharkov, Ukraine.
4. Listrovoy, S.V. and Minukhin, S.V. (2010), “General approach to solutions of optimization problems in distributed computer systems and theory of intelligence systems construction”, Problemy upravleniya i informatika, no. 2, pp. 65-82.
5. Listrovoy, S.V. and Minukhin S.V. (2010), “General approach to solving optimization problems in distributed computing systems and theory of intelligence systems construction”, Journal of automation and information sciences, Vol. 42, no. 3, pp. 30-46.
https://doi.org/10.1615/JAutomatInfScien.v42.i3.30
6. Listrovoy, S.V. , Golubnichiy, D.Yu. and Listrovaya, E.S. (1999), “Solution method on the basis of rank approach for integer linear problems with Boolean variables”, Engineering Simulation, Vol. 16, pp. 707-725.
7. Listrovoy, S.V., Tretjak, V.F. and Listrovaya, A.S. (1999), “Parallel algorithms of calculation process optimization for the Boolean programming problems”, Ibid., Vol. 16, pp. 569-579.
8. Listrovoy, S.V. (1999), “A.Yu. GUL method of minimum covering problem solution on the basis of rank approach”, Engineering Simulation, Vol. 17, pp. 73-89.

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Stochastic Model Predictive Control for Hybrid Energy Systems

A. Gienger, PhD student, J. Sachs, PhD,
O. Sawodny, Professor
Institute for System Dynamics, University of Stuttgart
(Waldburgstr. 17/19, 70563 Stuttgart, Germany)
Tel.: +49 71168565934, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.,
e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.
Tel.: +49 71168566302, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Èlektron. model. 2017, 39(1):39-50
https://doi.org/10.15407/emodel.39.01.039

ABSTRACT

Microgrids are a promising approach for the integration of renewable energy sources in existing networks and the energy supply of rural areas. A cost effective option for a microgrid is given by a hybrid energy system, which combines e.g. diesel generators, photovoltaic panels and batteries as considered in this paper. However, the interaction of the components and uncertainties in the load demand and photovoltaic power make the controller design challenging. This paper discusses a Stochastic Model Predictive Control approach which yields promising results regarding effectiveness and reliability as shown in a simulation study.

KEYWORDS

microgrid, hybrid energy system, optimal energy dispatch, Stochastic Model Predictive Control.

REFERENCES

1. Kuznetsova, E., Li, Y.-F., Ruiz, C. and Zio, E. (2014), “An integrated framework of agent-based modelling and robust optimization for microgrid energy management”, Applied Energy, vol. 129, pp. 70-88.
https://doi.org/10.1016/j.apenergy.2014.04.024
2. Dong, C., Huang, G., Cai, Y. and Liu, Y. (2013),“ Robust planning of energy management systems with environmental and constraint-conservative considerations under multiple uncertainties”, Energy Conversion and Management, Vol. 65, pp. 471-486.
https://doi.org/10.1016/j.enconman.2012.09.001
3. Zakariazadeh, A., Jadid, S. and Siano, P. (2014), “Stochastic multi-objective operational planning of smart distribution systems considering demand response programs”, Electric Power Systems Research, Vol. 111, pp. 156-168.
https://doi.org/10.1016/j.epsr.2014.02.021
4. Alharbi, W. and Raahemifar, K. (2015), “Probabilistic coordination of micro-grid energy resources operation considering uncertainties”, Electric Power Systems Research, Vol. 128, pp. 1-10.
5. Baziar, A. and Kavousi-Fard, A. (2013), “Considering uncertainty in the optimal energy management of renewable mi-crogrids including storage devices”, Renewable Energy, Vol. 59, pp. 158-166.
6. Hooshmand, A., Poursaeidi, M., Mohammadpour, J., Malki, H. and Grigoriads, K. (2012), “Stochastic model predictive control method for microgrid management”, 2012 IEEE PES Innovative Smart Grid Technologies, Washington, 2012.
7. Gulin, M., Matusko, J. and Vasak, M. (2015), “Stochastic model predictive control for optimal economic operation of a residential DC microgrid”, 2015 IEEE International Conference on Industrial Technology, Seville, 2015.
8. Olivares, D. et al. (2015), “Stochastic-predictive energy management system for isolated microgrids”, IEEE Transactions on Smart Grid, Vol. 6, no. 6, pp. 2681-2693.
https://doi.org/10.1109/TSG.2015.2469631
9. Parisio, A. and Glielmo, L. (2013), “Stochastic Model Predictive Control for economic/environmental operation management of microgrids”, 2013 European Control Conference, Zurich,
2013.
10. Parisio, A., Rikos, E. and Glielmo, L. (2016), “Stochastic model predictive control for economic/environmental operation management of microgrids: An experimental case study”, Journal of Process Control, Vol. 43, pp. 24-37.
https://doi.org/10.1016/j.jprocont.2016.04.008
11. Zhu, D. and Hug, G. (2014), “Decomposed stochastic model predictive control for optimal dispatch of storage and gen-eration”, IEEE Transactions on Smart Grid 5.4, pp. 2044-2053.
https://doi.org/10.1109/TSG.2014.2321762
12. Sachs, J., Gienger, A. and Sawodny, O. (2016), “Combined Probabilistic and Set-Based Uncertainties for a Stochastic Model Predictive Control of Island Energy Systems”, 2016 American Control Conference, Boston, 2016.
13. Sachs, J. and Sawodny, O. (2016), “A Two-Stage Model Predictive Control Strategy for Economic Diesel-PV-Battery Island Microgrid Operation in Rural Areas”, IEEE Transactions on Sustainable Energy, Vol. 7, no. 3, pp. 903-913.
https://doi.org/10.1109/TSTE.2015.2509031
14. De Soto, W., Klein, S. and Beckman, W. (2006), “Improvement and validation of a model for photovoltaic array perfor-mance”, Solar Energy, Vol. 80, no. 1, pp. 78-88.
https://doi.org/10.1016/j.solener.2005.06.010
15. Shepherd, C. (1965), “Design of primary and secondary cells II. An equation describing battery discharge”, Journal of the Electrochemical Society, Vol. 112, no. 7, pp. 657-664.
https://doi.org/10.1149/1.2423659
16. Sachs, J., Sonntag, M. and Sawodny, O. (2015), “Two layer model predictive control for a cost efficient operation of island energy systems”, 2015 American Control Conference, Chicago, 2015.
17. Lee, C.-M. and Ko, C.-N. (2011), “Short-term load forecasting using lifting scheme and arima models”, Expert Systems with Applications, Vol. 38, no. 5, pp. 5902-5911.
https://doi.org/10.1016/j.eswa.2010.11.033
18. Bellman, R. (1956), “Dynamic programming and Lagrange multipliers”, Proceedings of the National Academy of Sciences, pp. 767-769.
https://doi.org/10.1073/pnas.42.10.767

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GRANULAR, FUZZY SET AND TESOR-TRACE CHARACTERISTICS OF MULTIDIMENSIONAL TIME SERIES

Yu.N. Minaev, O.Yu. Filimonova, J.I. Minaeva

Èlektron. model. 2017, 39(1):51-74
https://doi.org/10.15407/emodel.39.01.051

ABSTRACT

The questions of representation of multidimensional (multicomponent) time series (TS) as a 3D tensor model; its following tensor decomposition with the use of procedures of PARAFAC-decomposition and higher-order singular decomposition (HOSVD) allows us to represent the entire TS (or its components — window, a fragment, a segment) in the form of a certain granule — a subset of ordered triples with properties similar to those of the second type FS called the second type psevdoFS.
The analogy is shown between the properties of the existing traces, singular values and F-norm of standard singular decomposition (2D matrix) and HOSVD used for 2D matrix. Examples showing the representation of multidimensional TS by granules — subsets of ordered triples.

KEYWORDS

singular decomposition, fuzzy multiple granule, higher-order singular decomposition, trace of a matrix, F-norm, time series.

REFERENCES

1. Esbensen, K. (2005), Analiz mnogomernyh dannyh. Izbrannye glavy [Analysis of multidimensional data. Selected chapters], Transl. from Engl. S.V. Kucheryavskiy; Ed O.E. Rodionova, Izdatelstvo IPHV RAN, Chernogolovka, Russia.
2. Dobos, L. and Abonyi, J. (2012), “On-line detection of homogeneous operation ranges by dynamic principal component analysis based time-series segmentation”, Chemical engineering science, Vol. 75, pp. 96-105.
https://doi.org/10.1016/j.ces.2012.02.022
3. Ringberg, H., Soule, Au., Rexford, J. and Diot, Ch. (2007), “Sensitivity of PCA for traffic anomaly detection”, SIGMETRICS’07, June 12-16, 2007, San Diego, California, USA. Copyright 2007 ACM 978-1-59593-639-4/07/0006
4. Skillicorn, D. (2007), Data mining and knowledge discovery series. Understanding complex datasets. Data mining with matrix decompositions, Chapman & Hall/CRC.
5. Minaev, Ju.N., Filimonova, O.Ju. and Minaeva, Ju.I. (2015), “Structured granules of fuzzy set in the problems of granular computing”, Elektronnoe modelirovanie, Vol. 37, no. 1, pp.77-95.
6. Minaev, Ju.N., Filimonova, O.Ju. and Minaeva, Ju.I. (2014), “Kronecker (tenzor) models of fuzzi-set granules”, Kibernetika i sistemnyj analiz, Vol. 50, no. 4, pp. 42-52.
7. Minaev, Ju.N., Filimonova, O.Ju. and Minaeva, Ju.I. (2013), “Tenzor models of NM-granules and their use for solving problems of fuzzy arithmetic”, Iskusstvennyj intellect, no. 2, pp. 22-31.
8. Minaev, Ju.N., Filimonova, O.Ju. andMinaeva, Ju.I. (2016), “Nonfuzzy multiple characteristics of unidimensional time series (TS)”, Elektronnoe modelirovanie, Vol. 38, no. 6, pp. 45-66.
https://doi.org/10.15407/emodel.38.06.045
9. Van Loan, Ch. (2000), “The ubiquitous Kronecker product”, Journal of computational and applied mathematics, Vol. 123, pp. 85-100.
https://doi.org/10.1016/S0377-0427(00)00393-9
10. Shen, H. and Huang, J.Z. (2008), “Sparse principal component analysis via regularized low rank matrix approximation”, Journal of multivariate analysis, Vol. 99, pp. 1015-1034.
https://doi.org/10.1016/j.jmva.2007.06.007
11. Bader, B.W. and Kolda, T.G. (2006), Tensor decompositions, the MATLAB tensor toolbox, and applications to data analysis. Tensor decompositions multilinear operators for higher-order decompositions. Technical Report SAND2006-2081, Sandia National Laboratories, April 2006. Albuquerque, New Mexico 87185 and Livermore, California 94550, available at: - http://csmr.ca.sandia. gov/~tgkolda/
12. De Silva, V. and Lim, L. Tensor rank and the ill-posedness of the best low-rank approximation problem, Institute for Computational and Mathematical Engineering, Stanford University, Stanford. CA 94305-9025, available at: arxiv.org/pdf/math/0607647.
13. Voevodin, V.V. and Voevodin, Vl.V. (2006), Entsiklopedia lineynoi algebry. Elektronnaya sistema LINEAL [Encyclopedia of linear algebra. Electron system LINEAL], BHV-Peterburg, St-Petersburg, Russia.
14. Kibangou, Al.Y. (2009), Tensor decompositions and applications. An overview and some contributions, GIPSA-N_CS. March 17, 2009, available at: www.sandia.gov/~tgkolda/.../TensorReview.pdf
15. Kofman, A. (1982), Vvedenie v teoriyu nechetkikh mnozhestv [Introduction in the theory of fuzzy sets], Transl. from French, Radio i svyaz, Moscow, Russia.
16. Van Loan, C.F. and Pitsianis, C.F. (1993), Approximation with Kronecker products, Eds M.S. Moonen et al., Linear algebra for large scale and real-time applications, Kluver Publishers, Dordrecht, the Netherlands.
17. De Lathauwer, L., De Moor, B. and Vandewalle, J. (2000), “On the best rank-1 and rank-(R1,R2, ..., RN) approximation of higher-order tensors”, SIAM J. MATRIX ANAL. APPL. Society for Industrial and Applied Mathematics, Vol. 21, no. 4, pp. 1324-1342.
https://doi.org/10.1137/S0895479898346995
18. Costantini, R., Sbaiz, L. and S u sstrunk, S. (2008), “Higher order SVD analysis for dynamic texture synthesis”, IEEE Transactions on Image Processing, Vol. 17, no. 1, pp. 42-52.
https://doi.org/10.1109/TIP.2007.910956
19. Papalexakis, E., Faloutsos, Ch., Sidiropoulos, N. and Harpale, A. (2013), “Large scale tensor decompositions: Algorithmic developments and applications”, Bulletin of the IEEE Computer Society Technical Committee on Data Engineering, pp. 59-67.
20. Kamalja, K.K. and Khangar, N.V. (2013), “Singular value decomposition for multidimensional matrices. Researh article”, Int. Journal of engineering research and applications, Vol. 3, Iss. 6, pp. 123-129.
21. Sidiropoulos, D., Giannakis, G.B. and Bro R. (2000), “Blind PARAFAC. Receivers for DS-CDMA Systems”, IEEE Transactions on Signal Processing, Vol. 48, no. 3, pp. 810-823. 
https://doi.org/10.1109/78.824675
22. Cheng, D., Qi, H. and Xue, A.A. (2007), “Survey on semi-tensor product of matrices”, J. syst. sci. and complexity, Vol. 20, pp. 304-322.
https://doi.org/10.1007/s11424-007-9027-0

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