Effective fault diagnosis is essential to ensure the safe and reliable operation of equipment. In recent years, several transfer learning-based methods for diagnosing faults under variable working conditions have been developed. However, these models are designed to completely match the feature distributions between different domains, which is difficult to accomplish because each domain has unique characteristics. To solve this problem, we propose a framework based on the maximum classifier discrepancy with marginal probability distribution adaptation that focuses on task-specific decision boundaries. Specifically, this method captures ambiguous target samples through the predicted discrepancy between two classifiers for the target samples. Furthermore, marginal probability distribution adaptation facilitates the capture of target samples located far from the source domain, and these target samples are brought closer to the source domain through adversarial training. Experimental results indicate that the proposed method demonstrates higher performance and generalization ability than existing fault diagnosis methods.

Domain adaptive fault diagnosis methods of bearing have made extraordinary achievements in recent years. Among these methods, the vast majority of machine learning problems are balanced classification problems. However, imbalance problems are very common in practical applications. Undersampling and oversampling methods are often used to deal with imbalance problems. Inspired by Wasserstein generative adversarial network (WGAN), a domain adaptive guided WGAN for bearing fault diagnosis under imbalanced samples is proposed in this paper. Firstly, the unbalanced data of each bearing fault is collected, and the data and random noise are generated through WGAN to generate a balanced data set, and the processed data is compared with the real and generated bearing signals through the frequency domain feature distribution. Then, stacked autoencoders (SAE) is used to extract the fault features of the target and source domains, and L2 regularization is added in each layer of fault extractor network to prevent model overfitting. Finally, the domain adaptation guided by maximum mean discrepancy (MMD) is employed to complete the feature alignment of the target and source domains. Therefore, a novel domain adaptive method named WGAN - domain adaptive (DAWGAN) is proposed for imbalanced samples. Two experiments are applied to verify the superiority of the proposed DAWGAN method. The experimental results show that the DAWGAN method can significantly improve the diagnostic accuracy of the bearing, compared with the five comparison methods in this paper, the average increase is more than 10%, and it has better stability. Comparison results of two experiments show that the DAWGAN method can significantly improve the diagnosis accuracy of bearing and has better stability than the other methods. Meanwhile, the calculation time is also shortened by an average of 40% compared with the comparison method.

Transfer learning has been successfully applied in fault diagnosis to solve the difficulty in constructing network models due to the lack of labeled data in practical engineering. The current transfer learning models mainly use the adaptive method to obtain the similarity between source and target domains, but the obtained similarity is incomplete. Inspired by the domain-adversarial mechanism, a novel method called ‘distance guided domain-adversarial network’ (DGDAN) is proposed in this study. DGDAN includes two modules: domain-adversarial network and maximum mean discrepancies (MMD) guided domain adaptation. In this method, a stacked autoencoder (SAE) is used as the feature extractor of the domain-adversarial network to learn domain invariant features, and MMD is used to measure the non-parametric distance of different metric spaces to improve domain alignment. Reduction of the distance of the bottleneck layer of the feature extractor is employed to improve the feature extraction capability of the network. Experimental results show that the classification accuracy rate of DGDAN is more than 98%, and DGDAN has superior robustness and generalization ability.

Domain adaptation-based models for fault classification under variable working conditions have become a research focus in recent years. Previous domain adaptation approaches generally assume identical label spaces in the source and target domains, however, such an assumption may be no longer legitimate in a more realistic situation that requires adaptation from a larger and more diverse source domain to a smaller target domain with less number of fault classes. To address the above deficiencies, we propose a partial transfer fault diagnosis model based on a weighted subdomain adaptation network (WSAN) in this paper. Our method pays more attention to the local data distribution while aligning the global distribution. An auxiliary classifier is introduced to obtain the class-level weights of the source samples, so the network can avoid negative transfer caused by unique fault classes in the source domain. Furthermore, a weighted local maximum mean discrepancy (WLMMD) is proposed to capture the fine-grained transferable information and obtain sample-level weights. Finally, relevant distributions of domain-specific layer activations across different domains are aligned. Experimental results show that our method could assign appropriate weights to each source sample and realize efficient partial transfer fault diagnosis.

Domain adaptation (DA)-based methods for fault diagnosis (FD) of rotating machinery have achieved impressive results in recent years. Most methods hold the assumption that the source domain (SD) and target domain (TD) share the same label space, which is not always satisfied in actual situations. A more practical scenario called partial domain adaptation (PDA) needs to be given more attention, where the transferable knowledge learned from a larger SD is applied to a smaller but relevant TD. A PDA method called class-weighted alignment-based transfer network (CWATN) is proposed in this article to adapt this scenario. A novel weighting method is designed to adapt the data distributions of shared classes. Except for weighted class-level alignment, global-level feature adaptation is also considered to learn more general transferable knowledge. Moreover, a domain discrepancy learning block is plugged in the shared classifier as a residual block, which could enforce the network to learn and measure the discrepancy between SD and TD explicitly, thus improving the result of DA. Three case studies are implemented to verify the superiority of CWATN. Results demonstrate that the proposed method could obtain better diagnostic performance than the selected competitive methods in the PDA scenario.

Random impact interference has always been an important subject in fault diagnosis. In the fast kurtogram (FK), kurtosis is a sparsity index used to locate optimal resonance frequency bands. However, the shortcomings of the kurtosis measure are a tendency to select the random impact with a large amplitude and a relatively weak sparse measure ability, which reduces the accuracy and anti-interference of the FK method. To overcome the effects of random impact interference, this paper proposes a novel bearing fault diagnosis method named the fast nonlinear Hoyergram (FNH), in which the nonlinear Hoyer index is employed to replace kurtosis to improve the fault representation capability under random impulse interference. Firstly, Z -score normalization and a generalized nonlinear sigmoid activation function are used for signal preprocessing, and the scale distribution of the signal is changed to weaken the impact of random impact interference. Secondly, the Hoyer index, which can be viewed as the normalized form of the l 2 / l 1 norm, is used to replace kurtosis to improve the sparsity measure capability. Thirdly, in the Hoyergram, the frequency band with the largest Hoyer value can be chosen as the best resonance frequency band for the squared envelope analysis. Finally, the proposed FNH is compared with the FK method through simulation and experimental signals, and the effectiveness of the proposed method is verified.