ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 10. Vol. 30. 2024

DOI: 10.17587/it.30.499-503

D. I. Liksonova, Cand. of Tech. Sc., Assistant Professor, A. V. Chubarov, Cand. of Tech. Sc., Assistant Professor, Siberian Federal University, Krasnoyarsk, Russian Federation,
O. V. Chubarova, Cand. of Tech. Sc., Assistant Professor,
Siberian State University of Science and Technology named after M. F. Reshetnyova, Krasnoyarsk, Russian Federation

Nonparametric Modeling of Mutually Ambiguous Mappings

This paper considers the problem of approximating a function from observations in the case when the object under study contains mutually ambiguous characteristics in its description. This formulation is essential in identifying and controlling systems of the Wiener and Hammerstein class, in which nonlinear processes can be represented as a sequential connection of linear dynamic and nonlinear inertia-free blocks. Often elements such as hysteresis loop, backlash and others are used as nonlinear blocks. These elements are mutually ambiguous mappings. In connection with the transition to automated digital production, which is controlled in real time by intelligent systems rather than humans, nonlinear dynamic processes are found everywhere. The complexity of solving the problem lies in the lack of sufficient a priori information about the parametric structure of the model of the process under study. The paper proposes some modifications of the nonparametric estimation of the regression function, allowing for the modeling of mutually ambiguous mappings. Some fragments of numerical studies are presented that show acceptable results in terms of reconstruction accuracy.
Keywords: nonparametric algorithms, mutually ambiguous mappings, mathematical modeling, multidimensional system

P. 499-503

References

1. Medvedev A. V. Fundamentals of the theory of nonparametric systems, Krasnoyarsk, Sibirskij gosudarstvennyj aerokosmi-cheskij universitet, 2018, 727 p. (in Russian).
2. Ilyushin I. A., Evdokimov I. V. Software for identifying economic nonlinear dynamic systems in the class of block-oriented models, Sovremennye informacionnye tekhnologii, 2016, no. 23 (23), pp. 21—24 (in Russian).
3. Bolkvadze G. R. Computer control of fuel and energy facilities in the class of block-oriented models, Upravlenie razvitiem krupnomasshtabnyh sistem (MLSD'2011), 2011, pp. 351—354 (in Russian).
4. Zavadskaya T. V. Block-oriented model of a multi-connected air distribution control system in a mine ventilation network, Nauchnye trudy Doneckogo nacional'nogo tekhnicheskogo universiteta, 2008, no. 7 (150), pp. 104—115.
5. 5. Timonin D. V. Parametric identification of nonlinear systems of the Hammerstein class in the presence of autocorrelated noise in the output signals, Samara, Samarskij gosudarstvennyj universitet putej soobshcheniya, 2013, 178 p. (in Russian).
6. Chernova S. S., Shishkina A. V. On nonparametric estimation of mutually ambiguous functions from observations, Molodoj uchenyj, 2017, no. 25 (159), pp. 13—20 (in Russian).
7. Korneeva A. A., Chernova S. S., Shishkina A. V. Non-parametric algorithms of reconstruction of mutually ambiguous functions from observations, Siberian Journal of Science and Technology, 2017, vol. 18, no. 3, pp. 510—519.
8. Agafonov E. D., Shesterneva O. V. Mathematical modeling of linear dynamic systems, Krasnoyarsk, Sibirskij federal'nyj universitet, 2011, 92 p. (in Russian).
9. Nadaraya E. A. Nonparametric probability density and regression curve estimation, Tbilisi, Izdatel'stvo Tbilisskogo universiteta, 1983, 194 p.
10. Vasiliev V. A., Dobrovidov A. V., Koshkin G. M. Nonpara-metric estimation of functionals from distributions of stationary sequences, Moscow, Nauka, 2004, 508 p. (in Russian).
11. Karavanov A. V., Kirichenko V. N., Liksonova D. I. Study of the influence of the type of kernel function and the kernel blur coefficient on the accuracy of nonparametric estimation of the regression function, Nauchno-tekhnicheskij vestnik Povolzh'ya, 2022, no. 5, pp. 93—96 (in Russian).
12. Krasnoselsky M. A., Pokrovsky A. V. Systems with hyste­resis, Moscow, Nauka, 1983. 272 p. (in Russian).

To the contents