Fast time-frequency manifold learning and its reconstruction for transient feature extraction in rotating machinery fault diagnosis

The transient features caused by local fault are of vital importance for rotating machinery fault diagnosis, while they are always submerged and distorted by a large amount of noise interference and macro-structural vibrations. Time-frequency manifold (TFM) has been developed to extract these transient features in time-frequency domain, and the corresponding TFM-based data denoising has been further used to recover the time-domain transient signal. However, due to its time-frequency analysis and nonlinear manifold learning properties, there will be not only high computational cost for TFM learning but also a challenge for reliable transient feature recovery, which has further limited this technique to application in practical and on-line rotating machinery fault diagnosis. To overcome these problems, an improved fast TFM (FTFM) method is first developed to effectively but efficiently extract the transient characteristics. In the process of FTFM learning, a new time-frequency analysis technique called short-frequency Fourier transform (SFFT) is introduced to efficiently describe time-frequency distribution as a time-frequency image (TFI), and two-dimensional discrete wavelet transform (2-D DWT) is used to further compress the inherent time-frequency structure for nonlinear manifold learning. Subsequently, different from the conventional model-based sparse expression, by means of sparse latent components of FTFM basis, the corresponding signal reconstruction is later proposed in a series of inverse transformations, including the inverse SFFT developed and inverse 2-D DWT employed in this paper. The proposed FTFM-based reconstruction method indicates attractive prospects in the following two aspects: effective but efficient TFM learning for practical and on-line application, sound and adaptive signal reconstruction with the data-driven FTFM basis. Theoretical analysis and experimental verification using simulation and testing data indicated the computational efficiency and effectiveness of the proposed FTFM-based method for rotating machinery fault diagnosis. (C) 2019 Elsevier Ltd. All rights reserved.