To solve the fault diagnosis difficulty of bearings with small data samples, a novel multi-information fusion vision transformer (ViT) model based on time–frequency representation (TFR) maps is proposed in this paper. The original vibration signal is decomposed into different scale sub-signals by the discrete wavelet transforms (DWTs), and the continuous wavelet transforms (CWTs) are used to transform these different scale sub-signals into time–frequency representation (TFR) maps, which are concatenated to input to the ViT model to diagnose the bearing fault. Through the multifaceted experiment analysis on the fault diagnosis of bearings with small data samples, the diagnosis results demonstrate that the proposed multi-information fusion ViT model can diagnose the fault of bearings with small data samples, with strong generalization and robustness; its average diagnosis accuracy achieved 99.85%, and it was superior to the other fault diagnosis methods, such as the multi-information fusion CNN, ViT model based on one-dimensional vibration signal, and ViT model based on the TFR of the original vibration signal.

To solve the problem of multi-fault blind source separation (BSS) in the case that the observed signals are under-determined, a novel approach for single channel blind source separation (SCBSS) based on the improved tensor-based singular spectrum analysis (TSSA) is proposed. As the most natural representation of high-dimensional data, tensor can preserve the intrinsic structure of the data to the maximum extent. Thus, TSSA method can be employed to extract the multi-fault features from the measured single-channel vibration signal. However, SCBSS based on TSSA still has some limitations, mainly including unsatisfactory convergence of TSSA in many cases and the number of source signals is hard to accurately estimate. Therefore, the improved TSSA algorithm based on canonical decomposition and parallel factors (CANDECOMP/PARAFAC) weighted optimization, namely CP-WOPT, is proposed in this paper. CP-WOPT algorithm is applied to process the factor matrix using a first-order optimization approach instead of the original least square method in TSSA, so as to improve the convergence of this algorithm. In order to accurately estimate the number of the source signals in BSS, EMD-SVD-BIC (empirical mode decomposition—singular value decomposition—Bayesian information criterion) method, instead of the SVD in the conventional TSSA, is introduced. To validate the proposed method, we applied it to the analysis of the numerical simulation signal and the multi-fault rolling bearing signals.

Fault diagnosis of bearing with small data samples is always a research hotspot in the field of bearing fault diagnosis. To solve the problem, a convolutional block attention module (CBAM)-based attentional feature fusion with an inception module based on a capsule network (Capsnet) is proposed in the paper. Firstly, the original vibration signal is decomposed into multiple intrinsic mode function (IMF) sub-signals by the ensemble empirical mode decomposition (EEMD), and then the original vibration signal and the corresponding former four order IMF sub-signals are input into the inception modules to extract the features. Secondly, these features are concatenated and optimized by the CBAM. Finally, the selected sensitive features are fed into the Capsnet to diagnose the faults. Through the multifaceted experiment analysis on fault diagnosis of bearing with small data samples, the diagnosis results demonstrate that the proposed attentional feature fusion with inception based on Capsnet not only diagnoses the fault of bearing with small data samples, but also is superior to other feature fusion methods, such as feature fusion with inception based on Capsnet and attentional feature fusion with inception based on CNN, etc., and other single diagnosis models such as Capsnet with CBAM and inception, and CNN with CBAM and inception.

In this work, a soft competitive learning fuzzy adaptive resonance theory (SFART) diagnosis model based on multifeature domain selection for the single symptom domain and the single-target model is proposed. In order to solve the problem that the performance of traditional fuzzy ART (FART) is affected by the order of sample input, the similarity criterion of YU norm is introduced into the fuzzy ART network. In the meanwhile, the lateral inhibition theory is introduced to solve the wasteful problem of fuzzy ART mode node. By combining YU norm and lateral inhibition theory with fuzzy ART network, a soft competitive learning ART neural network diagnosis model that allows multiple mode nodes to learn simultaneously is designed. The feature parameters are extracted from the perspectives of time domain, frequency domain, time series model, wavelet analysis, and wavelet packet energy spectrum analysis, respectively. To further improve the diagnostic accuracy, the selective weighted majority voting method is integrated into the diagnosis model. Finally, the selected feature parameters are inputted to the integrated model to complete the fault classification and diagnosis. Finally, the proposed method is verified with a gearbox fault diagnosis test.

Clustering methods have been widely applied to the fault diagnosis of mechanical system, but the characteristic that the number of cluster needs to be determined in advance limits the application range of the method. In this paper, a novel clustering method combining the adaptive resonance theory (ART) with the similarity measure based on the Yu’s norm is presented and applied to the fault diagnosis of rolling element bearings, which can be adaptive to generate the number of cluster by the vigilance parameter test. Time-domain features, frequency-domain features, and time series model parameters are extracted to demonstrate the fault-related information about the bearings, and then considering the irrelevance or redundancy of some features many salient features are selected by an improved distance discriminant technique and input into the proposed clustering method to diagnose the faults of bearings. The experiment results confirmed that the proposed clustering method can diagnose the fault categories accurately and has better diagnosis performance compared with fuzzy ART and Self-Organizing Feature Map (SOFM).