Skip to main content
SpringerLink
Log in

Algorithms for Generating Equivalent Normalized Correlation Matrices of Noisy Random Signals

  • Published:
Cybernetics and Systems Analysis Aims and scope

Abstract

It is shown that signals in control objects are usually various physical quantities such as temperature, pressure, vibration, etc. Therefore, when solving problems of control, diagnostics and identification, it becomes necessary to generate normalized correlation matrices. The difficulties of generating normalized correlation matrices of noisy input-output signals of technical objects are analyzed. Algorithms for determining equivalent readings of the noise and useful signal are proposed and the possibility of their use for generating normalized correlation matrices equivalent to the correlation matrices of useful signals of noisy random processes is shown. It is shown that the procedure of the generating normalized correlation matrices is substantially simplified in this case and the error of their elements significantly decreases.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Aliev, Noise Control of the Beginning and Development Dynamics of Accidents, Springer (2019). https://doi.org/10.1007/978-3-030-12512-7.

  2. T. A. Aliev, Digital Noise Monitoring of Defect Origin, Springer, New York (2007). https://doi.org/10.1007/978-0-387-71754-8.

    Book  MATH  Google Scholar 

  3. T. A. Aliev and N. F. Musaeva, “An algorithm for eliminating microerrors of noise in the solution of statistical dynamics problems,” Autom. and Remote Control, Vol. 59 (2), No. 5, 679–688 (1998).

  4. K. Numpacharoen and A. Atsawarungruangkit, “Generating correlation matrices based on the boundaries of their coefficients,” PLoS ONE, Vol. 7, Issue 11, e48902 (2012). https://doi.org/10.1371/journal.pone.0048902.

  5. J. Hardin, S. R. Garcia, and D. Golan, “A method for generating realistic correlation matrices,” The Annals of Applied Statistics, Vol. 7, No. 3, 1733–1762 (2013). https://doi.org/10.1214/13-AOAS638.

    Article  MathSciNet  MATH  Google Scholar 

  6. G. Khubaev, “Ways to identify errors in large arrays of numerical information,” Voprosy Statistiki, No. 10, 20-24 (2014). https://doi.org/10.34023/2313-6383-2014-0-10-20-24.

  7. Mike K. P. So, Jerry Wong, and Manabu Asai, “Stress testing correlation matrices for risk management,” The North Amer. J. Econ. Finance, Vol. 26, 310–322 (2013). https://doi.org/10.1016/j.najef.2013.02.007.

  8. T. A. Aliev, N. F. Musaeva, and U. E. Sattarova, “Technology of calculating robust normalized correlation matrices,” Cybern. Syst. Analysis, Vol. 47, No. 1, 152–165 (2011). https://doi.org/10.1007/s10559-011-9298-2.

  9. G. D. Bila, “Identification of a nonparametric signal under strongly dependent random noise,” Cybern. Syst. Analysis, Vol. 52, No. 1, 160–172 (2016). https://doi.org/10.1007/s10559-016-9811-8.

    Article  MATH  Google Scholar 

  10. L. S. Stoikova, “Greatest lower bound of system failure probability on a special time interval under incomplete information about the distribution function of the time to failure of the system,” Cybern. Syst. Analysis, Vol. 53, No. 2, 217–224 (2017). https://doi.org/10.1007/s10559-017-9921-y.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. S. Bendat and A. G. Piersol, Engineering Applications of Correlation and Spectral Analysis, Wiley, New York (1993). https://doi.org/10.2514/3.49131.

    Book  MATH  Google Scholar 

  12. D. G Manolakis and V. K. Ingle, “The discrete fourier transform,” in: Applied Digital Signal Processing: Theory and Practice, Cambridge Univ. Press, Cambridge (2011), pp. 353–433. https://doi.org/10.1017/CBO9780511835261.008.

  13. T. A. Aliev, N. F. Musaeva, and M. T. Suleymanova, “Algorithms for indicating the beginning of accidents based on the estimate of the density distribution function of the noise of technological parameters,” Autom. Control and Computer Sci., Vol. 52, Issue 3, 231–242 (2018). https://doi.org/10.3103/S0146411618030021.

    Article  Google Scholar 

  14. V. V. Solodovnikov (ed.), Engineering Cybernetics [in Russian], Book 2, Mashinostroenie, Moscow (1967).

  15. E. S. Ventsel’, Probability Theory [in Russian], Nauka, Moscow (1969).

  16. O. M. Vokhnik, A. M. Zotov, P. V. Korolenko, and Yu. V. Ryzhikova, Modeling and Processing of Stochastic Signals and Structures [in Russian], MGU, Skobeltsyn Institute of Nuclear Physics, Moscow (2012). URL: http://optics.sinp.msu.ru.

Download references

Author information

Authors and Affiliations

  1. Institute of Control Systems, National Academy of Sciences of Azerbaijan, Azerbaijan University of Architecture and Construction, Baku, Azerbaijan

    T. A. Aliev & N. F. Musaeva

  2. Azerbaijan University of Architecture and Construction, Baku, Azerbaijan

    N. E. Rzayeva

Authors
  1. T. A. Aliev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. F. Musaeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. E. Rzayeva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. A. Aliev.

Additional information

Translated from Kibernetyka ta Systemnyi Analiz, No. 4, July–August, 2021, pp. 177–192.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aliev, T.A., Musaeva, N.F. & Rzayeva, N.E. Algorithms for Generating Equivalent Normalized Correlation Matrices of Noisy Random Signals. Cybern Syst Anal 57, 656–668 (2021). https://doi.org/10.1007/s10559-021-00391-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10559-021-00391-5

Keywords

Search

Navigation