###### Abstract  
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. rolling bearing; vibration signal; fault severity monitoring; sparse time-frequency analysis; gray level co-occurrence matrix; texture feature +
Footnote †: journal: Applied Softimportant practical significance. As bearing failure is a dynamic process, it is insufficient to know whether there is any fault or the fault type for the preventive maintenance of bearings in engineering applications. Determining the failure evolution process and accurately monitoring the fault severity are paramount for an effective bearing maintenance [4; 5; 6]. Consequently, the fault severity monitoring of rolling bearings is becoming increasingly important [7; 8]. It would be instructive and practical to describe overall modes of bearing failure first. Bearing failure is not always due to vibration. There are many reasons for bearing failure. In fact, in most cases, the initiating source of failure is lubrication. The lack of a lubricant film between the rolling element and races will result in increased friction and wear. These conditions lead to generated heat, and thus, surface scoring and scuffing and even bearing dimensional instability. Of course, these can lead to vibration; however, by the time this occurs, the bearing is really in a failed state and needs to be replaced. There are three sources of failure for which the timely monitoring of vibrations is effective for prevention. The first one is poor assembly or loss of preload or interference fit, which leads to out-of-balance rotation and gradually excessive cage responses [9]. The second one is the variable compliance vibration which is inherent to ball and rolling element bearings [10; 11]. Any amplitude increase at this frequency can lead to premature resonance and occurs with loss of preload or radial interference fit. The last one is increased contact loads, which cause fatigue spalling as the result of sub-surface stresses [12], leading to pits, cracks, etc. on the rolling surfaces. In this study, we focus on monitoring the fault severity of rolling bearings caused by the latter source of failure using vibration signals.