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.
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