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