Multiple Wave Shape Mode Decomposition for Bearing Fault Diagnosis

Due to the complex vibration transmission path and rotating time-varying speed, fault components separation from nonstationary vibration signals of rolling bearing is still a challenging task. Time–frequency representation (TFR) can reveal time-varying features and provide the required prior knowledge for signal decomposition, thus the high-resolution TFR and accurate instantaneous frequency (IF) estimation are also important for fault diagnosis. In this article, a multiple wave shape mode decomposition (MWMD) based on enhanced TFR (ETFR) is proposed to iteratively separate fault feature components from time-varying vibration signals. Based on the periodic relationship of IFs and phase functions in nonstationary bearing vibration signals, the time-varying wave shape function is simplified and MWMD is proposed to decompose nonstationary vibration signals. The IFs of fault components need to be estimated for the solution of the optimization problem in MWMD. Thus, ETFR is developed by combining two short-time Fourier transform (STFT) representations (i.e., Gaussian window and the first derivative of Gaussian window) to acquire the high-resolution TFR. Finally, the harmonic ridges extraction (HRE) is proposed to extract IFs by incorporating an integer-multiple deviation constraint to path optimization problem. The effectiveness of MWMD is verified by simulation signal and bearing vibration signal under speed-up condition. Moreover, the comparison with time–frequency postprocessing methods and other decomposition method verifies the superiority of MWMD in extracting fault features of bearing vibration signals.