Sparse Signal Reconstruction Based on Time–Frequency Manifold for Rolling Element Bearing Fault Signature Enhancement

Denoising based on signal reconstruction has been one of the most important tasks in signal processing for rolling element bearing fault diagnosis. This paper proposes a sparse signal reconstruction method combining time-frequency manifold (TFM) and sparse reconstruction for fault signature enhancement of rolling element bearings. TFM has good denoising performance for analyzing the defective bearing vibration signals. However, the amplitude information will be influenced by its nonlinear processing. This paper proposes employment of the sparse decomposition method to overcome this problem. The sparse decomposition is first conducted to process the TFM-based result on a designed overcomplete dictionary. Furthermore, the coefficients of the achieved sparse atoms are obtained by projecting the raw signal on the atoms to realize reconstruction of the bearing fault signature. The TFM-based sparse signal reconstruction method takes advantage of both TFM in denoising and the atomic decomposition in sparse reconstruction. The proposed method has a valuable theoretical contribution on explicit expression of nonlinear signal processing results. The results verified by experimental analysis indicate the value in fault signature enhancement of rolling element bearings and other mechanical movements.