Using Unbiased Autocorrelation to Enhance Kurtogram and Envelope Analysis Results for Rolling Element Bearing Diagnostics

Envelope analysis is one of the most advantageous methods for rolling element bearing diagnostics but finding the suitable frequency band for demodulation has been a substantial challenge for a long time. Introduction of spectral kurtosis (SK) mostly solved this problem but in situations where signal to noise ratio is very low or in presence of non-Gaussian noise this method will fail. This major drawback may noticeably decrease the effectiveness of the SK and goal of this paper is to overcome this problem. Vibration signals from rolling element bearings exhibit high levels of 2nd order cyclostationarity, especially in the presence of localised faults. A second-order cyclostationary signal is one whose autocovariance function is a periodic function of time: the proposed method, named Autogram by the authors, takes advantage of this property to enhance the conventional spectral kurtosis. First, a maximal overlap discrete wavelet packet transform (MODWPT) is adopted to split a signal in different frequency bands and central frequencies. Second, unbiased autocorrelation of the squared envelope is calculated to reduce the level of uncorrelated random noise. Third, kurtosis of the autocorrelation is computed and a two dimensional colormap, named Autogram, is presented in order to locate the optimal frequency band for demodulation. The purpose is to increase the detection and characterization of transients in the temporal signal, which contains the bearing defect frequencies as well as appropriate frequency at which the fault impulses are modulated. Finally, the Fourier transform is used to obtain a frequency domain representation of the envelope signal so to identify the defect frequencies of the bearing. The proposed method has been tested on experimental data and compared with literature results so to assess its performances in rolling element bearing diagnostics. The results are very positive, and bearing characteristic frequencies from signals masked by Gaussian and non-Gaussian background noise can be extracted.