I.N. Sinitsyn – Dr.Sc.(Eng.), Professor, Main Research Scientist, 

FRC «Computer Science and Control» of RAS (Moscow)

E-mail: sinitsin@dol.ru

D.V. Zhukov – Head of Department, 

FRC «Computer Science and Control» of RAS (Moscow)

E-mail: dzhukov@ipiran.ru

E.R. Korepanov – Ph.D.(Eng.), Leading Research Scientist, 

FRC «Computer Science and Control» of RAS (Moscow)

E-mail: ekorepanov@ipiran.ru

T.D. Konashenkova – Leading Programmer, 

FRC «Computer Science and Control» of RAS (Moscow) E-mail: tkonzshenkova@ipiran.ru

The article proceeds the thematic cycle dedicated to software tools for analytical modeling of linear with parametric noises (Gaussian and nongaussian) stochastic systems with high availability based on nonlinear correlation theory (normal approximation method and canonical expansions method). Nowadays such complex stochastic systems describes organizations-technical-economical systems (OTES) functioning in presence of internal and external noises and stochastic factors. Special survey concerning methodological and instrumental software tools for stochastic systems with high availability based on wavelet canonical expansions (WLCE) is given. Survey of stochastic structural theory of OTES based on WLCE, linear and nonlinear correlation theory and correspond algorithms is given. We use: 1) orthogonal expansions of elements of covariance matrix by two dimensional Daubechi wavelet with compact carrier; 2) Galerkin–Petrov wavelet methods; 3) algorithms and software tools «StIT-CE.WL.2». Elements of stochastic systems with parametric noises theory (linear stochastic equations, correlational equations, nonlinear correlational equations and linear equations with parametric noises) are given. For solving corresponding deterministic equations by Daubechi wavelet numerical methods of MATLAB are used. Wavelet algorithms for analytical modeling of mathematical expectation (Section 1 – Linear stochastic systems with parametric noises), covariance matrix (Section 2 – Wavelet analytical modeling mathematical expectation) and matrix of covariance function (Section 3 – Wavelet analytical modeling of covariance matrix) are developed. Special attention is paid to application of algorithms based on WLCE of random wide and narrow band. Formulae for number of members in WLCE of variable in state equations for estimation are suggested (Section 4 – Wavelet analytical modeling covariance function) processes. Wavelet algorithms for express analytical modeling are considered in Section 5 – Implementation for express modeling. Principles of substitution of parametric nongaussian noises by equivalent additive Gaussian noises are discussed. Test example and some generalizations are given in Sections 6 and Conclusion. Results of computer experiments for OTES are presented.

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