Dependence analysis of planetary gearbox vibration marginals

Time-frequency distribution (TFD) methods have been widely used for planetary gearbox fault detection. The aim of TFD is to represent a signal by a joint energy distribution in the time-frequency domain. Positivity is one of the most important properties for TFDs. Copula-based positive TFD construction methods utilize the time marginal, the frequency marginal and the dependence structure between the marginals. In this study, the dependence between the time marginal and the frequency marginal is studied explicitly by numerical and graphical rank-based statistics. Rank-based statistics are invariant with monotone transformations of the marginal distributions. This study demonstrates that the dependence does exist between the time marginal and the frequency marginal. The findings build one theoretical foundation for further study on copula-based TFD construction for one planetary gearbox vibration. Moreover, the results show that with the increase of the gearbox degradation, the Kendall's Tau's absolute value increases as well. This indicates that the more severe the fault is, the stronger the dependence would be.