Tacholess Order Analysis of Gearbox Vibration for Planetary-Gear Fault Diagnosis in Variable-Speed Offshore Wind Turbines

Offshore wind-turbine gearboxes operate under continuously varying speeds, while incipient planetary-gear fault signatures are weak, modulated, and difficult to recover without a tachometer. This study presents a tachometer-free framework that separates low- and high-oscillation components using adaptive oscillatory behavior signal decomposition, with its Q-factor and sparsity parameters selected by a convergence index and multi-scale periodic-modulation-intensity double loop. The integrated workflow uses existing gearbox vibration channels for phase estimation and order analysis when a tachometer signal is unavailable. Its contribution is the coupling of adaptive component selection, compact high-order time–frequency analysis and ridge-based resampling. A downsampled fourth-order synchrosqueezing transform (DSST4) produces a compact, concentrated time–frequency representation. Penalized global-path ridge extraction then estimates shaft speed, and segmented integral-approximation resampling converts the signal to the angle domain. For a simulated amplitude- and frequency-modulated signal at −5 dB, DSST4 reduces Rényi entropy from 7.35 to 5.65 and computation time from 4.959 s to 0.002 s, relative to the full-sampling fourth-order transform. In the University of Ottawa variable-speed bearing dataset, speed-estimation error is 18.67 rpm. For a 2 MW offshore wind turbine, order spectra identify a ring-gear component near order 0.714 in March, and an additional planet-gear component near 0.456 with modulation sidebands in April. Teardown confirmed spalling on both gears.