Bearing fault diagnosis plays a pivotal role in the safe and reliable operation of modern mechanical systems. However, the existing fault diagnosis methods rarely deal with the problem of category imbalance and various speeds concurrently, which cannot work effectively in practical scenarios. Considering the underlying similarities of data in frequency domain, data mining under various speeds can help to reduce the deviation of domain distribution. Therefore, a novel fault diagnosis method based on spectrum alignment (SA) and deep transfer convolution neural network (DTCNN) is proposed, where the SA and data augmentation module are designed to extract SA features from the unbalanced bearing data. The DTCNN model based on joint distribution adaptation is built to facilitate learning reliable domain-invariant features. Different from the existing studies, a more general transfer task with time-varying speed is considered, even with complex faults. For 14 transfer tasks in two unbalanced fault diagnosis cases under variable speed, the average accuracy, F1-score, and area under curve of the proposed method can reach more than 97.76%, 97.57%, and 98.75%, respectively. The results show that this method has superior diagnostic effect and better generalization ability than various state-of-the-art methods.

The data-driven intelligent fault diagnosis method of rolling bearings has strict requirements regarding the number and balance of fault samples. However, in practical engineering application scenarios, mechanical equipment is usually in a normal state, and small and imbalanced (S & I) fault samples are common, which seriously reduces the accuracy and stability of the fault diagnosis model. To solve this problem, an auxiliary classifier generative adversarial network with spectral normalization (ACGAN-SN) is proposed in this paper. First, a generation module based on a deconvolution layer is built to generate false data from Gaussian noise. Second, to enhance the training stability of the model, the data label information is used to make label constraints on the generated fake data under the basic GAN framework. Spectral normalization constraints are imposed on the output of each layer of the neural network of the discriminator to realize the Lipschitz continuity condition so as to avoid vanishing or exploding gradients. Finally, based on the generated data and the original S & I dataset, seven kinds of bearing fault datasets are made, and the prediction results of the Bi-directional Long Short-Term Memory (BiLSTM) model is verified. The results show that the data generated by ACGAN-SN can significantly promote the performance of the fault diagnosis model under the S & I fault samples.

Intelligent fault diagnosis of rolling bearings under non-stationary and time-varying speed conditions is still a challenging task. At the same time, a reasonable explanation for an intelligent diagnosis model based on features is currently lacking. Therefore, we exploit an explainable one-dimensional convolutional neural network (1DCNN) model by combining with the demodulated frequency features of vibration signals and apply it to the fault classification of rolling bearings under time-varying speed conditions. First, the speed signals obtained by the speed encoder were transformed into generalized demodulation operator (GDO). Second, combined with the sensitive frequency band and GDO, the generalized demodulation algorithm was used to extract the frequency features from the amplitude envelope of the vibration signal. Subsequently, the proposed lightweight 1DCNN was trained to classify the frequency features and identify the health states of the rolling bearing. Finally, the local interpretable model-agnostic explanations model was utilized to explain the proposed model based on the features which own weight. It is found that the internal classification mechanism of the lightweight 1DCNN is realized according to the distribution of fault features, which is consistent with the process of human brain analysis. Two kinds of time-varying speed datasets which come from the University of Ottawa and XJTU are tested and verified. The results show that compared with other intelligent fault diagnosis methods, the identification error of the proposed method is lower and the diagnosis stability is better. The average diagnostic accuracy was 96.26% and 99.82%, respectively.

The transient pulses caused by local faults of rolling bearings are an important measurement information for fault diagnosis. However, extracting transient pulses from complex nonstationary vibration signals with a large amount of background noise is challenging, especially in the early stage. To improve the anti-noise ability and detect incipient faults, a novel signal de-noising method based on enhanced time-frequency manifold (ETFM) and kurtosis-wavelet dictionary is proposed. First, to mine the high-dimensional features, the C-C method and Cao’s method are combined to determine the embedding dimension and delay time of phase space reconstruction. Second, the input parameters of the liner local tangent space arrangement (LLTSA) algorithm are determined by the grid search method based on Renyi entropy, and the dimension is reduced by manifold learning to obtain the ETFM with the highest time-frequency aggregation. Finally, a kurtosis-wavelet dictionary is constructed for selecting the best atom and eliminating the noise and reconstruct the defective signal. Actual simulations showed that the proposed method is more effective in noise suppression than traditional algorithms and that it can accurately reproduce the amplitude and phase information of the raw signal.

Interpretability plays a crucial role in the application of neural networks for fault diagnosis. Integrating preprocessing methods into neural networks can enhance interpretability while preserving their ‘end-to-end’ characteristics. However, when only redesigning the first layer, subsequent structures still exhibit limited transparency. Additionally, traditional convolution structure is ill-suited for analyzing the readable feature maps derived from vibration signals. To address these challenges, this paper proposes a novel convolution structure for the parameterized signal processing function of the first-layer convolution kernel. This structure incorporates channel mixing for feature augmentation, designs a condensed feature encoder for aggregating and compressing features channel-by-channel, ensures the interpretability of feature map processing, and obtains condensed feature codes to propose smooth activation layer-wise relevance propagation (SA-LRP) method that to perform interpretability analysis. Additionally, cubic feature screening is implemented for diagnostic classification to improve structural fitness. We design experiments using multiple datasets to test various indicators of the structure. The results confirm that connecting our convolution architecture for subsequent analysis outperforms other convolution architectures for the convolution kernel of the first-layer parameterized signal processing function. The interpretability of the model is evaluated through SA-LRP method and validates the interpretability of the model.