Information and Diagnostics Systems

Theoretical Analysis of the Mean Square Estimator Errors of Basic Frequency

Roman Sliepko1, Oleh Lychak1, Ihor Javorskyj1,2

1. Karpenko Physico-mechanical Institute of NAS of Ukraine
2. University of Science and Technology, Poland

https://doi.org/10.15407/msse2025.01.260

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Keywords

periodically non-stationary random processes, mean square estimator, basic frequency

Abstract

Functional for estimation of the basic frequency for the mean and covariance functions of periodically non-stationary random processes, grounded on the reduced LS functional, analyzed. Such analysis is provided using solutions of the nonlinear equations with appropriate conditions for maximum existence. The solutions are obtained using the small parameter method.

References

  1. Javorskyj I., Yuzefovych R., Dzeryn O., Varyvoda M. Analysis of deterministic components of biperiodically correlated random signals // 10th International Conference on Advanced Computer Information Technologies, ACIT 2020. – P. 65–68.
  2. Javorskyj I., Yuzefovych R., Lychak O., Slyepko R., Semenov P. Detection of distributed and localized faults in rotating machines using periodically non-stationary covariance analysis of vibrations // Meas. Sci. Technol. – 2023. – 34. – № https://doi.org/10.1088/1361-6501/acbc93
  3. Hurd H.L., Gerr N.L. Graphical methods for determining the presence of periodic correlation // J. Time Ser. Anal. – – 12. – P. 337–350. https://doi.org/10.1111/j.1467-9892.1991.tb00088.x
  4. Tyagi S., Panigrahi S.K. An improved envelope detection method using particle swarm optimisation for rolling element bearing fault diagnosis // J. Comput. Des. Eng. – 20174. – P. 305–317. https://doi.org/10.1016/j.jcde.2017.05.002
  5. Liu Y., Qju T., Sheng H. Time-difference-of-arrival estimation algorithms for cyclostationary signals in impulsive noise // Signal Process. – 2012. – 92. – P. 2238–2247. https://doi.org/10.1016/j.sigpro.2012.02.016
  6. Javorskyj I., Yuzefovych R., Matsko I., Zakrzewski Z. The least square estimation of the basic frequency for periodically non-stationary random signals // Digit. Signal Process. – 2022. – 122. – № https://doi.org/10.1016/j.dsp.2021.103333
  7. Javorskyj I., Yuzefovych R., Dzeryn O., Semenov P. Properties of LSM-estimator of correlation function of biperiodically correlated random processes // J. Aut. Inf. Sci. – 2020. – 52. – P. 44–50. https://doi.org/1615/JAutomatInfScien.v52.i6.40