Adaptive High-Order Synchroextracting Transform With Time-Varying Parameter and Its Application in Gearbox Fault Diagnosis

To address the limitations of existing time-frequency analysis (TFA) techniques, including low time-frequency resolution and fixed window parameters when analyzing strongly time-varying signals, this study proposes an adaptive higher order synchroextracting transform adaptive high order synchroextracting transform (AHSET) with time-varying parameters. The method reduces the approximation error of instantaneous frequency (IF) estimation through performing higher-order Taylor expansion of the signal phase and amplitude. The aggregation quality in the time-frequency representation (TFR) is quantified through minimizing Rényi entropy, thereby enabling the adaptive selection of optimal window parameters for each frequency band. Building on this framework, an adaptive high-order synchroextracting operator (AHSEO) is constructed that achieves both precise IF estimation and TFR throughout the entire period. Simulation analyses show that compared with the traditional TFA method, AHSET offers superior time-frequency resolution and IF estimation accuracy when processing strong frequency modulation signals, while also demonstrating enhanced noise robustness across various signal-to-noise ratios (SNRs). In addition, the angular domain IF fluctuation analysis is proposed for gearbox fault diagnosis based on the estimated current IF by AHSET. This method relates the periodic IF fluctuation of motor current with the meshing period of faulty tooth, and improves the reliability of fault diagnosis. The experimental analysis confirm that the proposed method can accurately extract the fault features under time-varying operating conditions and successfully diagnose the faults of the RV gearbox.