Bearing fault diagnosis under constant operational condition has been widely investigated. Monitoring the bearing vibration signal in the frequency domain is an effective approach to diagnose a bearing fault since each fault type has a specific Fault Characteristic Frequency (FCF). However, in real applications, bearings are often running under time-varying speed conditions which makes the signal non-stationary and the FCF time-varying. Order tracking is a commonly used method to resample the non-stationary signal to a stationary signal. However, the accuracy of order tracking is affected by many factors such as the precision of the measured shaft rotating speed and the interpolation methods used. Therefore, resampling-free methods are of interest for bearing fault diagnosis under time-varying speed conditions. With the development of Time-Frequency Representation (TFR) techniques, such as the Short-Time Fourier Transform (STFT) and wavelet transform, bearing fault characteristics can be shown in the time-frequency domain. However, for bearing fault diagnosis, instantaneous time-frequency characteristics, i.e. Time-Frequency (T-F) curves, have to be extracted from the TFR. In this paper, an algorithm for multiple T-F curve extraction is proposed based on a path-optimization approach to extract T-F curves from the TFR of the bearing vibration signal. The bearing fault can be diagnosed by matching the curves to the Instantaneous Fault Characteristic Frequency (IFCF) and its harmonics. The effectiveness of the proposed algorithm is validated by experimental data collected from a faulty bearing with an outer race fault and a faulty bearing with an inner race fault, respectively.

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