Rolling bearings are important components of rotating machines. For their preventive maintenance, it is not enough to know whether there is any fault or the fault type. For an effective maintenance, a fault severity monitoring needs to be conducted. Currently, the bearing fault diagnosis method based on time–frequency image (TFI) recognition is attracting increasing attention. This paper contributes to the ongoing investigation by proposing a new approach for the fault severity monitoring of rolling bearings based on the texture feature extraction of sparse TFIs. The first and main step is to obtain accurate TFIs from the vibration signals of rolling bearings. Traditional time–frequency analysis methods have disadvantages such as low resolution and cross-term interference. Therefore, the TFIs obtained cannot satisfactorily express the time–frequency characteristics of bearing vibration signals. To solve this problem, a sparse time–frequency analysis method based on the first-order primal-dual algorithm (STFA-PD) was developed in this paper. Unlike traditional time–frequency analysis methods, the time–frequency analysis model of the STFA-PD method is based on the theory of sparse representation, and is solved using the first-order primal-dual algorithm. For employing the sparse constraint in the frequency domain, the STFA-PD obtains a higher time–frequency resolution and is free from cross-term interference, as the model is based on a linear time–frequency analysis method. The gray level co-occurrence matrix is then employed to extract texture features from the sparse TFIs as input features for classifiers. Vibration signals of rolling bearings with different fault severity degrees are used to validate the proposed approach. The experimental results show that the developed STFA-PD outperforms traditional time–frequency analysis methods in terms of the accuracy and effectiveness for the fault severity monitoring of rolling bearings.
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.
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