Abstract
The coherent and the component methods for the estimation of the linear covariance invariants of vectorial periodically correlated random processes (PCRP) are considered. The coherent estimators are calculated by averaging of the samples taken through the non-stationary period. The component estimators are built in the form of trigonometric polynomials, Fourier coefficients of which are calculated by weighted averaging of PCRP realization. The properties of the continuous and the discrete estimators are investigated, the asymptotical unbiasedness and mean square consistency are proved. The formulae for their biases and variances described dependency of these quantities on realization length, time sampling and PCRP covariance components are obtained. The conditions of the absence of the aliasing effects of the first and the second kinds are given. The comparison of the coherent and component estimators is carried out for the case of the amplitude modulated signals. It is shown that the advantage of the component method over coherent grows as a rate of PCRP correlations clumping increases. The example of the using of vectorial statistical processing for diagnosis of rolling bearing are given. The investigation results show that using of the covariance function invariants allow to improve the efficiency of the fault detection and to establish of the defect spatial properties.
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Javors’kyj, I., Matsko, I., Yuzefovych, R., Trokhym, G., Semenov, P. (2020). The Coherent and Component Estimation of Covariance Invariants for Vectorial Periodically Correlated Random Processes and Its Application. In: Chaari, F., Leskow, J., Zimroz, R., Wyłomańska, A., Dudek, A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-030-22529-2_4
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DOI: https://doi.org/10.1007/978-3-030-22529-2_4
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