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Keywords = wavelet canonical expansion

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18 pages, 2757 KiB  
Article
Synthesis of Nonlinear Nonstationary Stochastic Systems by Wavelet Canonical Expansions
by Igor Sinitsyn, Vladimir Sinitsyn, Eduard Korepanov and Tatyana Konashenkova
Mathematics 2023, 11(9), 2059; https://doi.org/10.3390/math11092059 - 26 Apr 2023
Cited by 1 | Viewed by 1074
Abstract
The article is devoted to Bayes optimization problems of nonlinear observable stochastic systems (NLOStSs) based on wavelet canonical expansions (WLCEs). Input stochastic processes (StPs) and output StPs of considered nonlinearly StSs depend on random parameters and additive independent Gaussian noises. For stochastic synthesis [...] Read more.
The article is devoted to Bayes optimization problems of nonlinear observable stochastic systems (NLOStSs) based on wavelet canonical expansions (WLCEs). Input stochastic processes (StPs) and output StPs of considered nonlinearly StSs depend on random parameters and additive independent Gaussian noises. For stochastic synthesis we use a Bayes approach with the given loss function and minimum risk condition. WLCEs are formed by covariance function expansion coefficients of two-dimensional orthonormal basis of wavelet with a compact carrier. New results: (i) a common Bayes’ criteria synthesis algorithm for NLOStSs by WLCE is presented; (ii) partial synthesis algorithms for three of Bayes’ criteria (minimum mean square error, damage accumulation and probability of error exit outside the limits) are given; (iii) an approximate algorithm based on statistical linearization; (iv) three test examples. Applications: wavelet optimization and parameter calibration in complex measurement and control systems. Some generalizations are formulated. Full article
(This article belongs to the Special Issue Mathematical Modeling, Optimization and Machine Learning)
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14 pages, 619 KiB  
Article
Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions
by Igor Sinitsyn, Vladimir Sinitsyn, Eduard Korepanov and Tatyana Konashenkova
Mathematics 2022, 10(9), 1517; https://doi.org/10.3390/math10091517 - 2 May 2022
Cited by 3 | Viewed by 1509
Abstract
This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems [...] Read more.
This article is devoted to analysis and optimization problems of stochastic systems based on wavelet canonical expansions. Basic new results: (i) for general Bayes criteria, a method of synthesized methodological support and a software tool for nonstationary normal (Gaussian) linear observable stochastic systems by Haar wavelet canonical expansions are presented; (ii) a method of synthesis of a linear optimal observable system for criterion of the maximal probability that a signal will not exceed a particular value in absolute magnitude is given. Applications: wavelet model building of essentially nonstationary stochastic processes and parameters calibration. Full article
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