I.N. Sinitsyn1, V.I. Sinitsyn2, E.R. Korepanov3, T.D. Konashenkova4

1−4 FRC «Informatics and Computer Science» of RAS (Moscow, Russia)
 

Article is devoted to methodological support and software tools of stochastic systems with high availability (SHA) at nonstationary disturbances. The methodology is based on Haar wavelet expansions and wavelet canonical expansions and Bayes Criteria (BC) for linear nonstationary SHA. Basic results:

general algorithms of BS organization of linear for nonstationary SHA for special case, when structural function does not belong to functional space ;

1) partial algorithms for parameters with normal distributions;

2) specific algorithms for 3 typical BC;

3) software tools for BC synthesis of linear nonstationary SHA in special case;

4) example confirming high accuracy of BC in special case.

Sinitsyn I.N., Sinitsyn V.I., Korepanov E.R., Konashenkova T.D. Software tools for analysis and synthesis of stochastic systems with high availability (XVII). Highly Available Systems. 2023. V. 19. № 2. P. 5−24. DOI: https://doi.org/ 10.18127/j20729472-202302-01 (in Russian)

1. Dobeshi I. Desyat' lekcij po vejvletam. Moskva–Izhevsk: NIC «Regulyarnaya i haoticheskaya dinamika», 2004 (in Russian).
2. Proskurin A.V., Sagalakov A.M. Wavelet Approximation and Boundary Eigenvalue Problems in Mathematical Physics. Izvestiya of Altai State University. 2014. № 1. DOI: 10.14258/izvasu(2014)1.1-52; https://www.researchgate.net/publication/270526718.
3. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (IV). Sistemy vysokoj dostupnosti. 2017. T. 13. № 3. S. 55–59 (in Russian).
4. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (V). Sistemy vysokoj dostupnosti. 2018. T. 14. № 1. S. 59–70 (in Russian).
5. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Stohasticheskie kanonicheskie vejvlet razlozheniya v zadachah modelirovaniya vibroudaronadezhnosti komp'yuternogo oborudovaniya. XVIII mezhdunarodnaya nauchnaya konferenciya «Sistemy komp'yuternoj matematiki i ih prilozheniya» (SKMP – 2017), g. Smolensk, 19–21 maya 2017 goda. Smolensk: Izd-vo SmolGu, 2017.
   S. 123–124 (in Russian).
6. Sinicyn I.N., Sergeev I.V., Korepanov E.R., Konashenkova T.D. Ekspress modelirovanie stohasticheskih sistem vysokoj dostupnosti na osnove vejvlet kanonicheskih razlozhenij. Sistemy komp'yuternoj matematiki i ih prilozheniya: materialy HIH mezhdunarodnoj nauchnoj konferencii, posvyashchennoj 100-letiyu fiziko-matematicheskogo fakul'teta SmolGU. Smolensk: Izd-vo SmolGU, 2018. Vyp. 19. S. 213–220 (in Russian).
7. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Optimizaciya stohasticheskih sistem na osnove vejvlet kanonicheskih razlozhenij. Avtomatika i telemekhanika. 2020. № 11. S. 138–156 (in Russian).
8. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XI). Sistemy vysokoj dostupnosti. 2021. T. 17. № 1. S. 25–40. DOI: https://doi.org/10.18127/j20729472-202101-03 (in Russian).
9. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XII). Sistemy vysokoj dostupnosti. 2021. T. 17. № 2. S. 26–44. DOI: https://doi.org/10.18127/j20729472-202102-03 (in Russian).
10. Sinicyn I.N., Zhukov D.V., Korepanov E.R., Konashenkova T.D. Metod linejnoj optimal'noj obrabotki informacii posredstvom vejvlet razlozhenij. Sistemy komp'yuternoj matematiki i ih prilozheniya: Materialy XXI Mezhdunarodnoj nauchnoj konferencii. Smolensk: Izd-vo SmolGU, 2020. – Vyp. 21. S.213–221. http://fizmat.smolgu.ru/images/stories/SKMP/skmp_2020.pdf (in Russian).
11. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XIII). Sistemy vysokoj dostupnosti. 2021. T. 17. № 3. S. 39–58. DOI: https://doi.org/10.18127/j20729472-202103-03 (in Russian).
12. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie vejvlet optimal'nogo sinteza nestacionarnyh sistem po slozhno-statisticheskomu kriteriyu. Sistemy komp'yuternoj matematiki i ih prilozheniya (SKMP-2021): materialy XXII Mezhdunarodnoj nauchnoj konferencii. Smolensk: Izd-vo SmolGU. 2021. Vyp. 22. S. 166–175 (in Russian).
13. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XV). Sistemy vysokoj dostupnosti. 2022. T. 18. № 1. S. 47−61. DOI: https://doi.org/ 10.18127/j20729472-202201-05 (in Russian).
14. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie analiza i sinteza stohasticheskih sistem vysokoj dostupnosti (XVI). Sistemy vysokoj dostupnosti. 2022. T. 18. № 2. S. 58−77. DOI: https://doi.org/ 10.18127/j20729472-202202-04 (in Russian).
15. Sinicyn I.N., Sinicyn V.I., Korepanov E.R., Konashenkova T.D. Instrumental'noe programmnoe obespechenie sinteza optimal'noj sistemy po bejesovomu kriteriyu metodom vejvlet kanonicheskih razlozhenij. Sistemy komp'yuternoj matematiki i ih prilozheniya (SKMP-2022): materialy XXIII Mezhdunarodnoj nauchnoj konferencii. Smolensk: Izd-vo SmolGU, 2022. Vyp. 23. S. 161–178 (in Russian).
16. Sinitsyn I., Sinitsyn V., Korepanov E., Konashenkova T. Bayes Synthesis of Linear Nonstationary Stochastic Systems by Wavelet Canonical Expansions. Mathematics 2022. V. 10. Is. 9. 1517. https://doi.org/10.3390/math10091517.
17. Pugachev V.S., Sinicyn I.N. Teoriya stohasticheskih sistem. M.: Logos, 2000, 2004. [Angl. per. Stochastic Systems Theory and Applications. Singapore. World Scientific, 2001] (in Russian).
18. Sinicyn I.N. Kanonicheskie predstavleniya sluchajnyh funkcij i ih primenenie v zadachah komp'yuternoj podderzhki nauchnyh issledovanij. M.: TORUS-PRESS. 2009 (in Russian).
19. Boldyrev Yu.Ya. Variacionnoe ischislenie i metody optimizacii: uchebnoe posobie dlya vuzov. M.: Yurajt. 2019 (in Russian).