## 1 Introduction  
With the development of science and technology, the degree of automation and intelligence of mechanical equipment is getting higher and higher. As a key component of mechanical equipment, rolling bearings are widely used in various rotating devices to support rotating objects and transfer torque and power in the transmission system [1]. However, in the actual operating conditions, there are usually complex factors such as non-uniformly distributed load, excessive load, and so on. Bearings are vulnerable to pitting, wear and other damage, resulting in loss of function and even system failure. Once the rolling bearing fails, it will not only affect the operation of machinery and equipment, reducing production efficiency, but also cause huge economic losses and even casualties [2]. Therefore, it is particularly necessary to monitor the working status of bearing parts [3]. Generally speaking, the traditional fault diagnosis is mainly divided into three stages: signal acquisition, feature extraction, and feature classification. In the signal acquisition stage, the sensor can collect the current signal, temperature signal, sound signal, and vibration signal [4]. When rotating machinery fails, the fault part collides with other parts and produces impact characteristics, which shows periodic vibration with the rotation of rotating machinery parts. Therefore, the vibration signal is the most commonly used acquisition signal in the fault diagnosis of rotating machinery [5]. However, the fault signals collected by sensors often contain a lot of interference from background noise. When processing the collected fault signals, the fault features are often submerged by noise, so it is difficult for traditional analysis methods to extract impact features effectively. Therefore, many advanced feature extraction methods are applied to the fault diagnosis of rotating machinery, such as wavelet threshold denoising [6], empirical mode decomposition [7], energy weighting method [8], Fourier transform [9], etc. Since the characteristics of rolling bearing fault signals show periodic sparsity in the whole signal, sparse representation has been gradually applied to the field of mechanical fault diagnosis [10], and good progress has been made. By constructing an over-complete dictionary and using matching pursuit algorithm (MP), the bearing vibration signal is sparsely represented, and the sparse fault impact features are extracted accurately [11]. By using the SVD algorithm in the construction stage of the learning dictionary and feature symbol algorithm in the sparse solution phase, it shows good performance in bearing vibration signal denoising and impact feature extraction [12]. A method combining empirical mode decomposition (EEMD) and k-singular value decomposition (K-SVD) is proposed to extract the periodic impact features of rolling bearing vibration signals in a strong noise environment [13]. The denoising method of sliding window denoising k-singular value decomposition (SWD-KSVD) is adopted to construct a learning dictionary for a section of time-domain signals with impact components by sliding at equal intervals, and the optimal solution with rolling bearing fault impact characteristic information is selected according to the maximum variance principle [14]. In view of the fact that the fault impulse is usually disturbed by background noise, a grouping K-SVD denoising algorithm is proposed to extract bearing fault features, which shows a more effective ability to extract bearing fault features under strong background noise and realizes rolling bearing fault diagnosis under strong background noise [15]. The layered block orthogonal matching algorithm has the advantages of strong sparsity and fast operation speed. Combined with K-SVD algorithm, the important feature extraction of the bearing vibration signal is realized [16].