Skip to main content
Log in

Solution of the Nonparametric Identification Equation in a Dynamic System Based on the Hyperdelta Approximation

  • AUTOMATION AND CONTROL IN ENGINEERING
  • Published:
Journal of Machinery Manufacture and Reliability Aims and scope Submit manuscript

Abstract

This paper is devoted to the method for defining the weight function in a dynamic system based on the hyperdelta approximation of autocorrelation and cross-correlation functions of random input and output signals with arbitrary distributions, as well as on the Laplace transform. The results can be used to perform nonparametric identification of the dynamic systems within the constraints on the computing resources and to measure the input and output signals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.

Similar content being viewed by others

REFERENCES

  1. Dzhinchvelashvili, G.A., Mkrtychev, O.V., Koval’chuk, O.A., Kolesnikov, A.V., and Sosnin, A.V., Identifikatsiya raschetnykh modelei pri dinamicheskikh vozdeistviyakh (Identification of Calculation Models at Dynamic Excitations), Moscow: ASV, 2018.  https://doi.org/10.22337/9785432302045

  2. Omorov, T.T. and Osmonova, R.Ch., The short review of methods of identification of the operated dynamic systems, Izv. Razzakov Kyrgyz. Gos. Tekh. Univ., 2018, no. 1, pp. 46–58.

  3. Sokolov, S.V., Kovalev, S.M., Kucherenko, P.A., and Smirnov, Yu.A., Metody identifikatsii nechetkikh i stokhasticheskikh system (Identification Methods for Stochastic Systems), Moscow: Fiziko-Matematicheskaya Literatura, 2018.

  4. Granichin, O.N., Stochastic approximation search algorithms with randomization at the input, Autom. Remote Control, 2015, vol. 76, no. 5, pp. 762–775.  https://doi.org/10.1134/S0005117915050033

    Article  MathSciNet  MATH  Google Scholar 

  5. Grinkevich, V.A., The identification of a device based on a Peltier element by the least squares method, Dokl. Akad. Nauk Vyssh. Shkoly Ross. Fed., 2020, nos. 1–2, pp. 17–27.  https://doi.org/10.17212/1727-2769-2020-1-2-17-27

  6. Kulakov, B.B., Kulakov, D.B., and Lun, T., Gradient identification of parameters of the mathematical model for a electrohydraulic servo drive, Gidravlika, 2020, no. 10, p. 64.

  7. Sandler, E.A. and Sandler, I.L., Recurrent algorithm for parameter identification of asynchronous electric motors at the presence of self-correlated measurement errors by the method of stochastic approximation, Vestn. Transp. Povolzh’ya, 2018, no. 4, pp. 84–90.

  8. Antonova, T.V., Methods of identifying a parameter in the kernel of the equation of the first kind of the convolution type on the class of function with discontinuities, Numer. Anal. Appl., 2015, vol. 8, no. 2, pp. 89–100.  https://doi.org/10.1134/S1995423915020019

    Article  MathSciNet  Google Scholar 

  9. Voskoboinikov, Yu.E. and Krysov, D.A., Nonparametric identification of a dynamical system at nonprecise input signal, Avtom. Program. Inzh., 2017, no. 4, pp. 86–93.

  10. Gar’kina, I.A., Danilov, A.M., and Tyukalov, D.E., Complex systems: Identification of dynamic characteristics, of disturbances and interference, Sovrem. Probl. Nauki Obraz., 2015, no. 1-1, p. 88.

  11. Korneeva, A.A., Chernova, S.S., and Shishkina, A.V., Non-parametric algorithms of reconstruction of mutually ambiguous functions from observations, Sib. J. Sci. Technol., 2017, vol. 18, no. 3, pp. 510–519.

    Google Scholar 

  12. Shatov, D.V., Identification of delay of one-dimensional linear objects by finite-frequency method, Probl. Upr., 2015, no. 4, pp. 2–8.

  13. Yareshchenko, D.I., About non-parametric identification of partial-parametred discrete-continuous process, Sib. J. Sci. Technol., 2020, vol. 21, no. 1, pp. 47–53.  https://doi.org/10.31772/2587-6066-2020-21-1-47-53

    Article  Google Scholar 

  14. Smagin, V.A. and Filimonikhin, G.V., On modeling random processes on the basis of hyper-delta distribution, Avtom. Vychisl. Tekh. (Riga), 1990, no. 1, p. 25.

  15. Smagin, V.A., Nemarkovskie zadachi teorii nadezhnosti (Non-Markovian Problems of the Reliability Theory), Leningrad: Ministr. Oborony SSSR, 1982.

Download references

Funding

This study was conducted within the framework of a research project on assessing the future evolution of robotic systems and technologies. It was initiated by the Federal State Autonomous Institution, Military Innovation Technopolis ERA.

I thank the Main Directorate of Scientific Studies and Engineering Support of Advanced Technologies (Innovative Research) of the Russian Ministry of Defense for support in carrying out these studies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ya. N. Gusenitsa.

Ethics declarations

The author declares that he has no conflicts of interest.

Additional information

Translated by N. Bogacheva

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gusenitsa, Y.N. Solution of the Nonparametric Identification Equation in a Dynamic System Based on the Hyperdelta Approximation. J. Mach. Manuf. Reliab. 51, 80–85 (2022). https://doi.org/10.3103/S1052618821060091

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1052618821060091

Keywords:

Navigation