Journal Highly available systems №2 for 2018 г.
Article in number:
Software tools for analysis and synthesis of stochastic systems with high availability (VI)
Type of article: scientific article
UDC: 621
Keywords: analytical modeling canonical expansion (CE) covariance matrix linear nonstationary StS matrix of covariance functions stochastic process (StP) stochastic systems (StS) vector of mathematical expectations wavelet CE
Authors:

.N. Sinitsyn – Dr.Sc.(Eng.), Professor, Main Research Scientist, FRC «Computer Science and Control» RAS (Moscow) E-mail: sinitsin@dol.ru

I.V. Sergeev – Ph.D.(Eng.), Deputy Director, FRC «Computer Science and Control» RAS (Moscow) E-mail: isergeev@ipiran.ru

E.R. Korepanov – Ph.D.(Eng.), Leading Research Scientist, FRC «Computer Science and Control» RAS (Moscow) E-mail: ekorepanov@ipiran.ru

T.D. Konashenkova – Leading Programmer, FRC «Computer Science and Control» RAS (Moscow) E-mail: tkonzshenkova@ipiran.ru

Abstract:

The article proceeds the thematic cycle dedicated to analytical modeling of linear nonstationary stochastic systems (StS) based on wavelet and wavelet canonical expansions. Section 2 contains elements of spectral and correlation theory. Section 3 is devoted to canonical expansions (CE) of stochastic processes. In Sections 4−6 wavelet algorithms for analytical modeling of mathematical expectation, covariance matrix and matrix of covariance functions are described. Sections 7 and 8 is dedicated to applications of wavelet CE for spectral and correlation analytical express modeling algorithms. Test examples (Appendices 1 and 2) and generalizations are given.

Pages: 40-56
References
  1. Siniczy’n I.N., Sergeev I.V., Korepanov E’.R., Konashenkova T.D. Instrumental’noe programmnoe obespechenie analiza i sinteza stoxasticheskix sistem vy’sokoj dostupnosti (IV) // Sistemy’ vy’sokoj dostupnosti. 2017. T. 13. № 3. S. 55−69.
  2. Siniczy’n I.N., Siniczy’n V.I., Korepanov E’.R., Belousov V.V., Konashenkova T.D., Sergeev I.V., Semendyaev N.N., Basilashvili D.A. Instrumental’noe programmnoe obespechenie analiza i sinteza sistem vy’sokoj dostupnosti (V) // Sistemy’ vy’sokoj dostupnosti. 2018. T. 14. № 1. S. 59−70.
  3. Pugachev V.S., Siniczy’n I.N. Stochastic Systems Theory and Applications. Singapore: World Scientific. 2001. 908 p.
  4. Siniczy’n I.N., Siniczy’n V.I. Lekczii po normal’noj i e’llipsoidal’noj approksimaczii v stoxasticheskix sistemax. M.: Torus Press. 2013. 488 s.
  5. Siniczy’n I.N. Kanonicheskie predstavleniya sluchajny’x funkczij i ix primeneniya v zadachax komp’yuternoj podderzhki nauchny’x issledovanij. M.: Torus Press. 2009.
  6. Siniczy’n I.N., Sergeev I.V., Korepanov E’.R., Konashenkova T.D. Stoxasticheskie kanonicheskie vejvlet razlozheniya v zadachax modelirovaniya vibroudaronadezhnosti komp’yuternogo oborudovaniya // XVIII Mezhdunar. nauchn. konf. «Sistemy’ komp’yuternoj matematiki i ix prilozheniya» (SKMP-2017). Smolensk. 19−21 maya 2017 g. Smolensk: Izd-vo SmolGu. S. 123−124.
  7. Siniczy’n I.N., Sergeev I.V., Agafonov E.S. Primenenie kanonicheskix predstavlenij sluchajny’x funkczij v zadachax rascheta vibrozashhitny’x sistem dlya komp’yuternogo oborudovaniya // Materialy’ XI Mezhdunar. nauchn. konf. «Sistemy’ komp’yuternoj matematiki i ix prilozheniya», posvyashhennoj 70-letiyu professora V.P. D’yakonova. Smolensk: Izd-vo SmolGu. 2010. № 11. S. 239−241.
  8. Siniczy’n I.N., Sergeev I.V. Metodicheskoe obespechenie izmereniya, kontrolya i ispy’tanij vy’chislitel’nogo oborudovaniya v usloviyax udarny’x vozdejstvij // Trudy’ konf. «Texnicheskie i programmny’e sredstva sistem upravleniya, kontrolya i izmereniya» (UKI-2010). M.: IPU RAN. 2010. S. 47−56.
  9. Dobeshi I. Desyat’ lekczij po vejvletam. Moskva–Izhevsk: NICz «Regulyarnaya i xaoticheskaya dinamika». 2004. 464 s.
  10. Xu J. and Shann W. Galerkin-wavelet methods for two point value problems // Numer. Math. 1992. № 63. P. 123−144.
  11. Gagnon L. and Lina J.M. Symmetric Daubechies' wavelets and numerical solutions of NLS2 equations // J. Phys. A: Math. Gen. 1994. № 27. P. 8207−8230.
  12. Lepik U. Numeral solution of evolution equations by the Haar wavelet metods // Appl. Math. Comput. 2007. № 185. P. 695−704.
  13. Lepik U. Application of the Haar wavelet transform to solving integral and differential equations // Proc. Estonian Acad. Sci. Phys. Math. 2007. № 56. P. 28−46.
  14. Pissaneczki S. Texnologiya razrezhenny’x matricz. M.: Mir. 1988. 412 s.
Date of receipt: 8 мая 2018 г.