The health condition of rolling bearings has a direct impact on the safe operation of rotating machinery. And their working environment is harsh and the working condition is complex, which brings challenges to fault diagnosis. With the development of computer technology, deep learning has been applied in the field of fault diagnosis and has rapidly developed. Among them, convolutional neural network (CNN) has received great attention from researchers due to its powerful data mining ability and feature adaptive learning ability. Based on recent research hotspots, the development history and trend of CNN is summarized and analyzed. Firstly, the basic structure of CNN is introduced and the important progress of classical CNN models for rolling bearing fault diagnosis in recent years is studied. The problems with the classic CNN algorithm have been pointed out. Secondly, to solve the above problems, combined with recent research achievements, various methods and principles for optimizing CNN are introduced and compared from the perspectives of deep feature extraction, hyperparameter optimization, network structure optimization. Although significant progress has been made in the research of fault diagnosis of rolling bearings based on CNN, there is still room for improvement and development in addressing issues such as low accuracy of imbalanced data, weak model generalization, and poor network interpretability. Therefore, the future development trend of CNN networks is discussed finally. And transfer learning models are introduced to improve the generalization ability of CNN and interpretable CNN is used to increase the interpretability of CNN networks.

The working condition of high-speed train wheelset bearings is complex and bad, which makes its vibration signal contain strong noise. To obtain more information of samples, Signals are constructed into graphs and fitted by graph convolution network (GCN). The existing GCN-based models still have some problems, such as insufficient theoretical basis of graph and the unstable and overfitting during training of models, which significantly limits the diagnosis accuracy. To address these issues, firstly, a weighted ε-recurrence network is proposed to construct the recurrence graph (RG). The recurrence relationship between samples is analyzed by the recursive nature of vibration signals. MMD is used to obtain the regenerated Hilbert spatial distribution distance between two samples to reduce the weight gap between different recursive pairs. And the proposed method has better ex-ante interpretability. Secondly, a vertex mean normalization (MN) layer is proposed to normalize individual vertex features to introduce some spatial perturbations and reduce the variance of vertex features, which can improve training stability and reduce overfitting. In addition, multi-channel MN-GCN is proposed to fit multi-scale graph features. Analyze recurrence nature of samples at different scales through RGs with varying densities of connection to improve the anti-noise ability. Experimental results show that the proposed model can obtain spatial topology information accurately and improve the wheelset bearing system fault diagnosis performance.

Most fault diagnosis methods require that the source and target machines fault classes should overlap and the number of samples should be comparable. However, such assumptions are unrealistic in the wheelset bearing fault diagnosis. The high reliability of wheelset bearings and the difficulty of collecting fault signals make the datasets insufficient. However, the datasets obtained by laboratories can be rich in the number of samples, types of faults, and working conditions, which contain a wealth of fault information. Therefore, a graph attention based multi-channel transfer learning network (GAMTLN) is proposed. Fault features of multiple working conditions aretransferred by combining a recurrence graph attention residual network (ResGANet) with multiple distribution adaptations and a multi-channel diagnosis decision strategy. The former enriches the prior knowledge under small samples and improves the transfer effect through margin disparity discrepancy (MDD). The latter can jointly train multiple channels by a multi-channel loss compensation strategy. The non-shared fault class filtering is combind to obtain useful information in non-shared fault class samples and avoid the negative effects of large domain differences. Two cases verify that GAMTLN can enhance the wheelset bearings fault diagnosis accuracy and fully use the existing fault samples as to the traditional methods.

The time-frequency energy distribution processed by a short-time Fourier transform can be compressed to the real instantaneous frequency by the synchrosqueezing transformation (SST), which improves the time-frequency energy concentration of the signal. However, there is a large error in the instantaneous frequency estimation of a multicomponent nonpure harmonic signal by the SST. Therefore, a method for determining the instantaneous frequency (IF) of a rolling bearing based on a fractional synchrosqueezing transformation (FRSST) is proposed. First, the theoretical derivation of the FRSST algorithm as a signal processing technique is given and the steps of the IF estimation are presented. Second, the main advantages of the proposed FRSST algorithm are proved. In the comparison of simulation signals, it is verified that the FRSST algorithm has a high time-frequency concentration, is non-fragile to the frequency modulation rate, has noise robustness and has nonsensitivity to the cross-frequency signal. Finally, the FRSST algorithm is applied to the IF estimation of a rolling bearing under rising speed and fluctuated speed, and is compared with the SST based on variational mode decomposition (VMD-SST), the generalized parametric SST (PSST) and polynomial chirplet transform (PCT). The test results show that the estimation error of IF based on the FRSST method is the least for a rolling bearing with the four fault types under rising speed. On average, the estimation error is 2.2180 Hz less than the corresponding error of the VMD-SST and 1.1862 Hz less than the corresponding error of the PSST method.

Wheelset bearings are a core component of high-speed trains, and their fault diagnosis is the key to smooth operation. Deep learning is widely used in fault diagnosis due to its powerful classification ability. To explicitly fit the features of vibration signals and further explore the relationship between the signals, the graph attention network (GAT) is becoming a focus of research. Unlike traditional graph neural networks, GATs can focus on edges with stronger correlations with vertices, making the model more powerful when fitting graph samples in non-Euclidean space. However, existing GATs have two limitations. Firstly, most graph construction methods do not consider the characteristics of vibration signals, so the graph interpretation is not good. Secondly, the existing methods of graph attention coefficient cannot effectively reflect the importance of edges. To address these issues, a recursive multi-head graph attention residual network (RMHGARN) is proposed. In RMHGARN, vibration signals are transformed into recurrence graphs due to the recursive nature of nonlinear time series. A multi-kernel Gaussian symmetric graph attention mechanism is proposed to obtain the Hilbert spatial distribution between neighboring vertices. In addition, a graph encoding module is proposed to improve the feature representation of input samples. The effectiveness and superiority of RMHGARN under strong noise samples are verified using three wheelset bearing datasets.