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Signals with multiple components and fast-varying instantaneous frequencies reduce the readability of the time-frequency representations obtained by traditional synchrosqueezing transforms due to time-frequency blurring. We discussed a vertical synchrosqueezing transform, which is a second-order synchrosqueezing transform based on the short-time Fourier transform and compared it to the traditional short-time Fourier transform, synchrosqueezing transform, and another form of the second-order synchrosqueezing transform, the oblique synchrosqueezing transform. The quality of the time-frequency representation and the accuracy of mode reconstruction were compared through simulations and experiments. Results reveal that the second-order frequency estimator of the vertical synchrosqueezing transform could obtain accurate estimates of the instantaneous frequency and achieve highly energy-concentrated time-frequency representations for multicomponent and fast-varying signals. We also explored the application of statistical feature parameters of time-frequency image textures for the early fault diagnosis of roller bearings under fast-varying working conditions, both with and without noise. Experiments showed that there was no direct positive correlation between the resolution of the time-frequency images and the accuracy of fault diagnosis. However, the early fault diagnosis of roller bearings based on statistical texture features of high-resolution images obtained by the vertical synchrosqueezing transform was shown to have high accuracy and strong robustness to noise, thus meeting the demand for intelligent fault diagnosis.

An Enhanced Version of Second-Order Synchrosqueezing Transform Combined with Time-Frequency Image Texture Features to Detect Faults in Bearings