USE OF SOLUTIONS OF THE REVERSE PROBLEM OF LINEAR AUTOREGRESSION PROCESSES FOR SIMULATION OF VIBRATION SIGNALS OF ROTATING NODES OF WIND GENERATORS


  • V. Zvarich Institute of electrodynamics of the National Academy of Sciences of Ukraine 03680, 56 Peremohy av., Kyiv, Ukraine Institute of Renewable Energy of the National Academy of Sciences of Ukraine 02094, 20А Hnata Khotkevycha Str., Kyiv, Ukraine http://orcid.org/0000-0002-1271-4954
Keywords: linear processes of autoregression, characteristic function, kernel of transformation, generative process, infinitely divisible law of dis-tribution, Gamma-distribution, vibrodiagnosis of rolling bearings.

Abstract

Difference methods of power equipment diagnostics are discussed. Comparison of different vibration methods for wind generator diagnostic is represented. Linear autoregressive processes for construction  of wind generator expert systems is considered. Poisson jump spectra's properties are used for the solution of the problem. A method of Gammal AR(2)  generative  process   characteristic function determination is discussed.  The  method is suggested for definition the characteristic function for linear autoregressive AR(2) processes with Gamma distribution of the generative process , namely, autoregressive process AR(2) , , where  are autoregressive parameters;    is a set of integers;   is the random process with discrete time and independent  values having an infinitely divisible distribution, the process is often called the generating process. Sometimes the problem is called inverse problem. It is noted that the logarithm of the one-dimensional   characteristic function of the linear stationary autoregressive process may be determined in Kolmogorov canonical representation  in which the parameter  and spectral functions of jumps  define unequivocally the characteristic function. The logarithm of the characteristic function of the linear stationary autoregressive process may be written down also in the following form  where the parameters and  define the characteristic function of the generative process while  is the kernel of the linear random process.  The parameters  and , and Poisson spectra of jumps    are interrelated as follows    where  is so-called transform kernel, which is invariant with generative process  and uniquely defined by the coefficients . Properties of  are used for the inverse problem solution. Examples the peculiar features of determination of Poisson spectra of jump and characteristic function for the autoregressive AR(2) process are considered. Logarithm of characteristic function for linear AR(2) process with Gamma distribution was calculate.

The method may be used for a solution of the reversible problem for AR processes of others classes. An example of application of vibration signal simulation of wind power generator is considered. Ref. 17, fig. 5.

References

1. Zvaritch V.N., Marchenko B.G. Lineynyye protsessy avtoregressii v zadachakh vibrodiagnostiki uzlov elektricheskikh mashin. [Linear processes of autoregression in problems of vi-brodiagnostics of sections of electric drivers]. Technical Diagnos-tics and Nondestructive Testing. 1996. No. 1. Pp.45–54. [in Rus-sian].

2. Zvarich V.N. Primeneniye metodov avtoregressii dlya postroyeniya sistem vibrodiagnostiki vetroagregatov. [Auto-regression methods application for development of wind genera-tors diagnostic systems]. Vidnovluvana energetika. 2005. No. 1. Pp. 49-54. [in Russian].

3. Zvarich V.N., Marchenko B.G. Metod nakhozhdeniya kharakteristicheskikh funktsiy porozhdayushchikh protsessov dlya lineynykh protsessov avtoregressii. [Method of finding of generating processes characteristic functions of autoregression linear processes]. Radioelectronics and Communication Systems. 1999. v. 42. No. 7. Pp. 64-71. [in Russian].

4. Zvarich V.N. Ispolzovaniye resheniy obratnoy zadachi lineynykh protsessov avtoregressii dlya modelirovaniya vi-bratsionnykh signalov uzlov elektrotekhnicheskogo oborudovani-ya. [Application of invers problem solutions of the linear auto-regressive processes for power equipment vibromonitoring]. Tekhnichna Elektrodynamika. 2016. No. 2. Pp. 83-89. [in Rus-sian].

5. Zarich V.N., Marchenko B.G. Kharakteristicheskaya funktsiya porozhdayushchego protsessa v modeli statsionarnogo lineynogo AR gamma protsessa. [Generating process characteris-tic function in the model of stationary linear AR-gamma process]. University News "Electronics". 2002. v. 45. No. 8. Pp. 12-18. ISSN 0021-3470. [in Russian].

6. Krasilnikov A.I. Modeli shumovykh signalov v siste-makh diagnostiki teploenergeticheskogo oborudovaniya. [Models of noise type signals at the diagnostic systems of heat power engi-neering equipment]. Kiev. Polygraph-service. 2014. 112 p. [in Russian].

7. Marchenko B.G., Myslovich M.V. Vibrodiagnostika podshipnikovykh uzlov elektricheskikh mashin. [Vibration Diag-nosis of rolling bearings of electric driver parts]. M. Kiev. Nauko-va dumka. 1992. 196 p. [in Russian].

8. Marchenko B.G., Zvarich V.N., Bedny N.S. Lineinye sluchainye protsessy v nekotorykh zadachakh modelirovaniya informatsionnykh signalov. [Linear random processes in the some problems of information signals simulation]. Electronic modeling. [Elektronnoe modelirovanie]. 2001. v. 23. No. 1. Pp. 62-69. [in Russian].

9. 13. Alliot P. Some theoretical results on Markov-switching autoregressive models with gamma innovations. C.R. Acad. Sci. Paris. 2006. Ser. I 343. Pp. 271-274. [in English].

10. Bayar T. Putting Wind to the Test. Power Engineering International. 2015. No. 12. Pp. 16-18. [in English].

11. 9. Hoelf D. When Virtual meets Reality. Power Engi-neering International. 2016. No. 9. Pp. 26-27. [in English].

12. 12. Lawrance A.J. The Innovation Distributions for Gamma Distributed Autoregressive Process.Scandinavian Journal of Statistics. Theory and Applications. 1982. Vol. 9. Pp. 234-236. [in English].

13. Manning L. Bearing up to turbine testing. Power Engi-neering International. – 2014. - No 2. pp. 32-34. [in English].

14. 12. McKenzie Ed. Innovation Distributions for Gamma and Negative Binomial Autoregressions. Scandinavian Journal of Statistics. Theory and Applications. 1987. Vol. 14. Pp. 79-85. [in English].

15. 8. Torres G.L., Garia A., Blas M.D., Francisco A.D. Forecast of hourly average wind speed with ARMA models in Navarre (Spain). Solar energy. Vol.79. 2005. Pp. 65-77. [in Eng-lish].

16. Zvaritch V., Glazkova E. Application of Linear AR and ARMA Processes for Simulation of Power Equipment Diagnostic System Information Signals. Proceedings 2015 16 th Internation-al Conference on Computational problems of Electrical Engineer-ing (CPEE). Lviv. Ukraine. 2015. Pp. 259-261. [in English].

17. Zvaritch V., Glazkova E. Some Singularities of Kernels of Linear AR and ARMA Processes and Their Applications to Simulation of Information Signals. Computational Problems of Electrical Engineering. 2015. Vol. 5. No. 1. Pp. 71-74. [in Eng-lish].

Author Biography

V. Zvarich, Institute of electrodynamics of the National Academy of Sciences of Ukraine 03680, 56 Peremohy av., Kyiv, Ukraine Institute of Renewable Energy of the National Academy of Sciences of Ukraine 02094, 20А Hnata Khotkevycha Str., Kyiv, Ukraine

Zvarich.pngAuthor information: doctor of technical science, senior researcher of Renewable Energy Institute of NAS of Ukraine, leading researcher of Institute of electrodynamics of the NAS of Ukraine.
Education: National Technical University of Ukraine “Kyiv Polytechnic Institute” Radioengineering Faculty by specialty “Radioengineering”.
Reasearch area: renewable energy, signal processing, expert systems.
Publications: 100 including 1 patent.


Abstract views: 14
PDF Downloads: 11
Published
2019-09-25
How to Cite
Zvarich, V. (2019). USE OF SOLUTIONS OF THE REVERSE PROBLEM OF LINEAR AUTOREGRESSION PROCESSES FOR SIMULATION OF VIBRATION SIGNALS OF ROTATING NODES OF WIND GENERATORS. Vidnovluvana Energetika, (3(58), 48-57. https://doi.org/https://doi.org/10.36296/1819-8058.2019.3(58).48-57