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  5. VOL 40, NO 2 (2018)
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  7. 2012 год
  8. 34-4

Electronic Modeling

VOL 34, NO 4 (2012)

CONTENTS

Mathematical Methods and Models

  MINAEV Yu.N., FILIMONOVA O.Yu., MINAEVA Yu.I.
Hierarchical Clusterization of Fuzzy Data
3-22
  ATAMANYUK I.P., KONDRATENKO Yu.P.
Algorithm of Optimum Nonlinear Extrapolation of a Random Sequence with Noises
23-40

Accuracy, reliability, diagnostics

  MAKARICHEV A.V.
Fulfilment of Complexes of Complicated Renewable Systems with Time Reserve
41-64

Application of Modelling Methods and Facilities

  VOLOSHKO A.V.
Fulfilment of Harmonic Analysis by Means of the Wavelet-Transformation
65-78
  GAMZAEV Kh.M.
Determination of Nonstationary Field of Pressures under the Elastic Conditions of the Layer by the Data of Point Observations
79-88
  MAMEDOV R.K., MUTALLIMOVA A.S., ALIEV T.Ch.
Analysis of Resolving Ability of the Method of Masks to Smooth Noises on the Binary Images of Objects
89-98 
  GAVRYSH V.I.
Modeling of Temperature Conditions in Heat-Sensitive Microelectronic Devices with Through Foreign Inclusions
99-108 
  DOLGIN V.P.
Procedure of Combinatorial Filtration
109-118 

Short notes

  KOCHKARYOV Yu.A., KUSHCH S.A.
Cognate Realization of Logical Functions on the Basis of Their Representation in Isomorphous Form
119-123

Hierarchical Clusterization of Fuzzy Data

MINAEV Yu. N., FILIMONOVA O.Yu., MINAEVA Yu. l.

ABSTRACT

The questions of clusterization (construction of binary trees-dendrograms) of the data, presented in the form of fuzzy variables, which are in turn simulated by tensors, are considered. A dendrogram encoded by binary alphabet is a 2-adical number, which can be used as the dendrogram characteristic. A comparison of hierarchical clusterizations of fuzzy data and their defuzzifications, performed at the level of 2-adical trees, allows us to draw a conclusion on the presence (absence) of structure nearness of the objects.

KEYWORDS

fuzzy variable, dendrogram, cluster, tensor, 2-adic tree.

REFERENCES

  1. Vorontsov, K.V. “Lectures on clustering algorithms and multidimensional scaling”, available at: www.MachineLearning.ru.
  2. Biryukov, A.S., Rezanov, V.V., and Shmarov, A.S.  (2008), “Solving cluster analysis algorithms teams”,  Zhurnal vychisl. matem. i matem. fiz. , Vol. 48, no.  1, pp. 176-192.
  3. Zhambyu, M. (1988), Iyerarkhicheskiy klaster-analiz i sootvetstviya  [Hierarchical cluster analysis and compliance],  Finansy i statistika, Moscow, Russia.
  4. Mandel, I.D. (1988),  Klasternyy analiz  [Cluster analysis],  Finansy i statistika,  Moscow, Russia.
  5. Tyrtyshnikov, Ye.Ye. (2003), “Tensor approximations of matrices generated by asymptotically smooth functions”, Mat. sbornik, Vol.  194, no.  6, pp. 147-160.
  6. Zak, L. (2002), “Clustering of Vaguely Defined Objects”, Archivum Mathematicum (Brno), Vol.  38, pp. 37-50.
  7. Kofman, A. (1982), Vvedeniye v teoriyu nechetkikh mnozhestv.  Perevod s frants  [Introduction to the theory of fuzzy sets],  Translated from the French, Radio i svyaz,  Moscow, Russia.
  8. Carlsson, G. and M'emoli, F. (2009), “Characterization, Stability and Convergence of Hierarchical Clus­tering Algorithms”, available at: http://jmlr.csail.mit.edu/papers/volumel1/carlsson1Oa/carlsson 10a.pdf
  9. Carlsson, G. and  M'emoli, F. (2010), “Characterization, Stability and Convergence of Hierarchical Clus­tering Methods”, J. of Machine Learning Research, no. 11, pp. 1425-1470.
  10. Burago, D., Burago, Y. and Ivanov, S.A.  (2001), “Course in Metric Geometry”, AMS Graduate Studies in Math. American Mathematical Society, Vol. 33, available at: www.math.psu.edu/petrunin/ papers/alexandrov/bbi.pdf
  11. Guh, Yuh-Yuan,  Yang, Miin-Shen,  Po, Rung-Wei  and  Lee, E.S. (2008),  “Establishing Performance Evalua­tion Structures by Fuzzy Relation-based Cluster Analysis”, Computers and Mathematics with Applications, no. 56, pp. 572-582.
  12. Gol, M.G. and  Yazdi, H.S. (2010),  “A New Hierarchical Clustering Algorithm on Fuzzy Data (FHCA)”, In­tern. J. of Computer and Electrical Engineering, Vol. 2, no.  1, pp. 1793-1816.
  13. Delgado, М.,  Gomez-Skarmeta, A.F. and  Vila, A.  (1996), “Intern. J. of Approximate Reasoning”, no.  14, pp. 237-257.
  14. Minayev, Yu.N and  Filimonova, O.Yu. (2008), “Fuzzy mathematics based on tensor models of uncertainty. Part I. The tensor-variable system of fuzzy sets. Part II. Fuzzy math in the tensor basis”, Elektronnoe modelirovanie , Vol. 30, no. 1, pp. 43-59; no.  2, pp. 4-21.
  15. Colda, Т.G. and Bader, В.W. (2006), “Tensor Decompositions and Applications”, ACM Transactions on Mathematical Software, Vol. 32, no.  4, pp. 635-653.
  16. Kiyoung, Yang and  Cyrus, Shahabi “A PCA-based Similarity Measure for Multivariate Time Se­ries”, available at:  http://infolab.usc.edu/ Docs-De-mos/ mmdb04.pdf
  17. Singhal, D. and Seborg, A. “Clustering of Multivariate Time-series Data”, Proc. of the American Control Conference,  Anchorage, Alaska, USA, May  8-10, 2002,  Vol. 5, pp. 351-358.
  18. Murtagh, F. (2008), “Symmetry in Data Mining and Analysis: A Unifying View based on Hierarchy”, available at: arXiv: 50805. 2744vl [stat.ML] 18 May 2008.
  19. Murtagh, F.,  Downs, G. and  Contreras, P. (2008), “Hierarchical Clustering of Massive, High Dimensional Data Sets by Exploiting Ultrametric Embedding”,  SIAM J. on Scientific Computing, Vol. 30, pp. 707-730.
  20. Gouvea, F.Q. (2003), P-Adic Numbers: An Introduction, Springer.
  21. Schikhof,  W.H. (1984), Ultrametric Calculus. An Itroduction to p-adic Analysis, Cambridge Uni­versity Press. 

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Algorithm of Optimum Nonlinear Extrapolation of a Random Sequence with Noises

ATAMANYUK I.P., KONDRATENKO Yu.P.

ABSTRACT

On the basis of canonical decompositions the algorithm of optimum nonlinear extrapolation of a random sequence is obtained on condition that the measurings are carried out with an error.

KEYWORDS

random sequence, the canonical decomposition, extrapolation.

REFERENCES

  1. Kolmogorov, A.N. (1941), “Interpolation and extrapolation of stationary random sequences”,  Izv. AN SSSR. Seriya  Matematicheskaya,  Vol.  5, no.  1, pp. 3-14.

  2. Viner, N. (1949), Ekstrapolyatsiya, interpolyatsiya i sglazhivaniye statsionarnykh vremennykh posledovatelnostey s inzhenernymi prilozheniyami [Extrapolation, Interpolation and smoothing of stationary time series with engineering applications], J. Wiley, New York, USA.

  3. Shiryaev, A.N. (1980),  Veroyatnost  [Probability], Nauka, Moscow, Russia.

  4. Kalman, R.Е.  (1960), “A New Approach to Linear Filtering and Prediction Problems”, Trans. ASME. Series D. J. Basic Eng., Vol. 82, pp. 35-45.

  5. Spravochnik po prikladnoy statistike. Tom 2 (1990), [Handbook of Applied Statistics. Vol. 2], Finansy i statistika, Moscow, Rusia.

  6. Kudritskiy, V.D. (2001), Filtratsiya, ekstrapolyatsiya i raspoznavaniye realizatsiy sluchaynykh funktsiy [Filtering, extrapolation and recognition of the random functions], FADA, LTD, Kiev, Ukraine.

  7. Pugachev, V.S.  (1962), Teoriya sluchaynykh funktsiy i yeye primeneniye  [Theory of random functions and its application], Fizmatgiz, Moscow, Russia.

  8. Atamanyuk, I.P. (2005), “Extrapolation algorithm non-linear random process on the basis of its canonical decomposition”,  Kibernetika i sistemnyy analiz,  no.  2, pp. 131-138.

  9. Atamanyuk, I.P. (2001),   “Algorithm of implementation nonlinear random sequence based on its canonical decomposition”,  Elektronnoe modelirovanie, Vol.  23, no.  5, pp. 38-46.

  10. Akhiezer,  N.I.  (1961),  Klassicheskaya problema momentov i nekotoryye voprosy analiza, svyazannyye s ney   [The classical moment problem and some questions of analysis related to the problem], Gos. izd-vo fiz.-mat. lit., Moscow, Russia. 

  11. Atamanyuk, I.P. (2011), “Algorithm for determining the optimal parameters of polynomial Wiener filter extrapolator for non-stationary random processes observed with errors”,  Kibernetika i sistemnyy analiz,  no. 2, pp. 154-159.

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Fulfilment of Complexes of Complicated Renewable Systems with Time Reserve

MAKARICHEV A.V.

ABSTRACT

The author has found the asymptotic time distribution of no-failure operation of complexes of complicated renewable systems with time reserve, Markov failure flow of components and individual function of time distribution of maintenance of complicated systems components which quantity increases in inverse proportion to intensity of their failures in such a way that the total load on the maintenance system is bounded from above by the value less than one, with the discipline of demands maintenance in the order of emergence.

KEYWORDS

complexes of complicated renewable systems with time reserve.

REFERENCES

  1. Makarichev, A.V.  (2003), “Asymptotic estimates of the regeneration of complex systems reducible systems for  various disciplines  of service”,   Elektronnoe modelirovanie, Vol.  25, no. 2, pp. 83-97.
  2. Klimov, G.P. (1967), Stokhasticheskiye sistemy obsluzhivaniya  [Stochastic Systems  of service], Nauka,  Moscow, Russia.
  3. Koks, D. and  Smit, V. (1967), Teoriya vosstanovleniya  [Theory of recovery], Sovetskoe radio, Moscow, Russia.
  4. Kozlov, V.V. and  Solovyev,  A.D. (1978), “Optimal service of renewable  systems. 1”, Tekhnicheskaya kibernetika,  no.  3,  pp. 30-38.
  5. Solovyev, A.D.  (1987), Otsenka nadezhnosti vosstanavlivayemykh system [Evaluation of reliability of renewable  systems], Znanie, Moscow, Russia. 

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Fulfilment of Harmonic Analysis by Means of the Wavelet-Transformation

VOLOSHKO A.V.

ABSTRACT

The use of the wavelet-transformation for determining some indices of electric power quality (harmonic groups and interharmonic subgroups) has been considered.

KEYWORDS

wavelet analysis, harmonic analysis, indicators of quality of electric energy.

REFERENCES

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