Adaptive window rotated second-order synchroextracting transform and its application in fault diagnosis of wind turbine gearbox

Time frequency (TF) analysis (TFA) based on vibration signals is a vital method for the health monitoring of wind turbine gearboxes. Based on classical synchrosqueezing transform and short-time Fourier transform (STFT), synchroextracting transform (SET) abstractly retains primary TF energy around the interested frequency components by reassigning the TF transformation coefficient. However, as the fixed window of these traditional TFA methods, they have poor matching effects on multi-component signals with fast-varying frequencies. To address this problem, this paper first optimizes the width of the short-term window based on STFT, and then proposes adaptive short-time Fourier transform (ASTFT). That is, the direction of the window function in the STFT is changed by automatically matching a series of rotation operators. Then, based on ASTFT and SET, the second-order partial derivatives of time and frequency are used to modify the formula of instantaneous frequency estimation. Therefore, adaptive window rotated second-order synchroextracting transform (AWRSSET) is put forward to obtain and sharpen TF representations of multi-component vibration signals of wind turbines in this paper. In order to accurately diagnose faults in wind turbines, this paper extracts the rotation speed curve from the TF plane, which is generated through AWRSSET, and then makes subsequent order-frequency analyses without a tachometer. AWRSSET can be applied to diagnosing faulty wind turbine gearboxes and gears with broken teeth under time-varying speed, both of which testify to the advantages of this method.