Renyi entropy-based generalized statistical moments for early fatigue defect detection of rolling-element bearing

Statistical moments have been widely used for condition monitoring and diagnosis of rolling-element bearings. However, lower moments are less sensitive to incipient faults, whereas higher moments are over-sensitive to spurious vibrations and noise. Hence, the statistical moments used in practice are limited to kurtosis and third normalized moment of rectified data, i.e. Honarvar third moment S-r. In order to overcome the drawbacks of kurtosis and S-r a class of new diagnostic indices have been derived from the viewpoint of Renyi entropy, to characterize the vibration signature. These new indices can be treated as a generalization of the traditional statistical moments, of which kurtosis and S-r are just two special cases. Numerical simulations and experiments have been conducted. The results show that these new indices are as effective as kurtosis and S-r in detecting the defect of a bearing, and that some of the new indices could provide a better compromise performance than kurtosis and S-r with respect to the sensitivity and the robustness.