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Bi-periodically correlated random processes as a model for gear pair vibration

The model of gear pair vibration in the form of bi-periodically correlated random processes (BPCRP) that describes its stochastic recurrence with two periods is proposed. Particular cases of this model are considered. It is shown that BPCRP model allows one to analyses unequally the mean and the covariance function of the additive and multiplicative components. There are considered technologies for the estimation of the Fourier coefficients of the mean and the covariance functions.