Synchronous decomposition match-reassigning transform and its application in planetary gearbox fault diagnosis

Abstract Under time-varying operating conditions, the instantaneous frequency (IF) of the vibration signal of the planetary gearbox exhibits non-stationary time-varying closely spaced characteristics as well as non-proportional and non-synchronous characteristics. This in turn leads to challenges for traditional time-frequency analysis (TFA) methods to accurately identify its fault features and obtain accurate time-frequency representations (TFR). To address this challenge, in this study, a TFA method is proposed based on Synchronous Decomposition Match-Reassigning Transform (SDMRT). First, the successive variational mode decomposition (SVMD) is used to adaptively separate non-synchronous frequency components in the original vibration signal. Second, the chirp rate (CR) describing the signal harmonic structure is used to synchronously match each frequency component, obtaining the TFR corresponding to each component. Third, all TFRs are merged to obtain a complete TFA result. Finally, the energy spread is re-aggregated to the ridge of the IF using the reassignment principle, resulting in a new frequency estimation operator termed the Synchronous Decomposition Match-Reassigning Operator (SDMRO). SDMRT can adaptively separate non-proportional and non-synchronous IFs and realize precise matching of time-varying closely spaced IFs, thereby completing the TFR of the vibration signal generated by the planetary gearbox. By analyzing simulated signals and measured vibration signals from planetary gearboxes, Rényi entropy and IF estimation errors of SDMRT correspond to 12.14% and 0.59%, respectively. The energy concentration degree and IF estimation results are significantly better than other TFA methods, which proves the effectiveness and superiority of SDMRT.