Systems and Means of Informatics

2026, Volume 36, Issue 1, pp 22-44

WAVELET NEURAL NETWORKS BAYES SYNTHESIS OF MULTIDIMENSIONAL NONLINEAR STOCHASTIC SYSTEMS

  • I. N. Sinitsyn
  • V. I. Sinitsyn
  • E. R. Korepanov
  • T. D. Konashenkova

Abstract

New methodological tools of optimal synthesis of multidimensional linear stochastic system (StS) on Bayes criterion (BC) are based on quantitative estimate of output stochastic process (StP). Nonlinear StS is described by Pugachev equation for input and output StP. Input StP contains useful signal and random additive multidimensional normal noise with zero mathematical expectation and known matrix of covariance functions. Random noise does not depend upon vector of random parameters of useful signal. Distribution of random vector parameters is known. After a short survey, the model of BC optimal estimate of output StP is constructed on the basis of wavelet canonical expansion (CE) of random noise and wavelet CE of input StP. To find unknown parameters in optimal output StP, an estimate architecture of multilayer wavelet neural networks (WNN) is developed. The WNN training algorithm for inverse error prevalence by the method of steepest descent is used. Formulae for mathematical expectation, second initial probabilistic moment, and error covariance matrix of BC optimal estimate of output StP are obtained. Numerical experiments with cubic two-dimensional StS illustrate WNN preference with wavelet CE.

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