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.

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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

Author 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.

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