Methods of Hidden Periodicity Discovering for Gearbox Fault Detection

It is shown that the models of gear pair vibration, proposed in literature, are particular cases of the bi-periodically correlated random processes (BPCRPs), which describe its stochastic recurrence with two periods. The possibility of vibration and analysis within the framework of BPCRP approximation, in the form of periodically correlated random processes (PCRPs), is grounded and the implementation of vibration processing procedures using PCRP techniques, which are worked out by the authors, is given. Searching for hidden periodicities of the first and the second orders was considered as the main issue of this approach. The estimation of the non-stationary period (basic frequency) allowed us to carry out a detailed analysis of the deterministic part, the covariance structure of the stochastic part, and to form, using their parameters, the sensitive indicators for fault detection. The results of the processing of the wind turbine gearbox vibration signals are presented. The amplitude spectra of the deterministic oscillations and the time changes of the stochastic part power for different fault stages are analyzed. The most efficient indicators, which are formed using the amplitude spectra for practical applications, are proposed. The presented approach was compared with known in literature cyclostationary analysis and envelope techniques, and its advantages are shown.

Approximate spectral models of random processes with periodic properties

We consider approaches to simulation of periodically correlated random processes based on the nonstandard spectral representation of the process with parameters periodically varying in time and also on spectral representations using the vector stationary Gaussian processes.

Discrete estimators of covariance components of vectorial periodically nonstationary random processes

The properties of estimators for invariants of covariance tensor-function of vectorial periodically correlated random processes, calculated on the base of discrete data, are analyzed. It is shown that aliasing effect of the first kind leads to incorrect estimation of the mean function Fourier coefficients and the second kind leads to decreasing a convergence of covariance components estimator. The conditions of avoidance of the aliasing effect of the first and the second kinds are obtained. Formulas for the estimator variance and bias, which allow comparing efficiency of the discrete and the continuous estimators, are derived. The consistency of estimators is proved. Dependences of the estimators variances and biases on realization length and signal parameters are found.