Rolling bearings play a vital role in the overall operation of rotating machinery. In practice, many learning methods for variable-speed fault diagnosis ignore task-specific decision boundaries, making it very difficult to completely match feature distribution between different domains. Therefore, to overcome this problem, an adversarial domain adaptation of asymmetric mapping with CORAL alignment is presented. The asymmetric mapping feature extractor is able to extract more specific-domain features with obvious distinction. Meanwhile, combining the maximum classifier discrepancy of deep transfer to give an adversarial approach and taking the task-specific decision boundaries into account, class-level alignment between the features of the source domain and target domain can be attempted. To prevent degenerate learning, which is possibly caused by asymmetric mapping and adversarial learning, the model is constrained by deep CORAL alignment to extract more domain-invariant features. Experimental results show that the proposed method can solve the variable-speed (a small span of intermediate vehicle speeds) fault diagnosis problem well, with high transfer accuracy and strong generalization.

In recent years, transfer learning has become more and more favored by scholars from all walks of life. At present, although transfer learning has achieved certain results in the field of fault diagnosis, the use of transfer learning alone may lead to poor transfer effects or even negative transfer due to the sample gap being under variable conditions in the same machinery. Therefore, deep domain adaptation with adversarial idea and coral alignment (DAACA) is proposed in this paper in order to solve the problem. DAACA is briefly summarized below. The domain adaptation with adversarial idea is added on the basis of transfer learning. The deep coral is then appended to further reduce the distribution difference between the data from the source and the target domain, which improves the invariant features of adversarial domain adaptation learning. In addition, a gradient reversal layer is introduced in the method to achieve gradient reversion and avoid the adversarial disadvantage of fixing parameters separately. It can be seen from the experimental results that the DAACA can not only solve the problem caused by the sample gap in variable conditions, but also achieve higher diagnosis accuracy and generalization ability.

Big data condition monitoring in the industrial of internet era is indispensable, and intelligent fault diagnosis plays an important role in it. The adversarial learning method is widely used because of its ability to extract domain invariant features to solve the variable speed fault diagnosis problem. However, its training process is often unstable and difficult to converge to the optimal solution, which brings great challenges to the fault detection of equipment. In view of this exasperating problem, a novel model, called deep domain adversarial method with central moment discrepancy, is proposed. The presented model mainly consists of four modules: a shared weight feature extraction network with wide convolution kernel, a supervised classification network, an adversarial domain classification network, and a CMD alignment network. Adversarial domain classification network is employed to extract features that have both category distinction and domain invariance in the process of mutual game learning between features of source domain and target domain. The CMD alignment network can be devoted to align the higher-order moments of two domain features to constrain the instability in adversarial learning. Through the above regularization method, the model shows a relatively stable and higher accuracy of transferring diagnosis in the non-standardized data. The public test data set and the private data set are applied to validate the model. The results show that the proposed model successfully solves the problem of training instability in adversarial learning and has a relatively high diagnostic accuracy.

At present, most of the fault diagnosis methods with extensive research and good diagnostic effect are based on the premise that the sample distribution is consistent. However, in reality, the sample distribution of rotating machinery is inconsistent due to variable working conditions, and most of the fault diagnosis algorithms have poor diagnostic effects or even invalid. To dispose the above problems, a novel symmetric stacked autoencoder (NSSAE) for adversarial domain adaptation is proposed. Firstly, the symmetric stacked autoencoder network with shared weights is used as the feature extractor to extract features which can better express the original signal. Secondly, adding domain discriminator that constituting adversarial with feature extractor to enhance the ability of feature extractor to extract domain invariant features, thus confusing the domain discriminator and making it unable to correctly distinguish the features of the two domains. Finally, to assist the adversarial training, the maximum mean discrepancy (MMD) is added to the last layer of the feature extractor to align the features of the two domains in the high-dimensional space. The experimental results show that, under the condition of variable speed, the NSSAE model can extract domain invariant features to achieve the transfer between domains, and the transfer diagnosis accuracy is high and the stability is strong.

Image reconstruction represents an important technique applied in various fields such as medicine, biology, materials science, nondestructive testing, and so forth. In this paper, we transform the problem of image reconstruction into the problem of solving linear systems with multiple right-hand sides. Based on the idea of K-means clustering, we propose the global randomized block Kaczmarz method, so as to solve the problem of the linear systems with multiple right-hand sides effectively and use this method to image reconstruction. Theoretical analysis proves the convergence of this method, and the simulation results demonstrate the performance of this method in image reconstruction.

The dataset in the application scenario of existing fault diagnosis methods is often balanced, while the data collected under actual working conditions are often imbalanced. Directly applying existing fault diagnosis methods to this scenario will lead to poor diagnosis effect. In view of the above problems, we proposed a method called dual generative adversarial networks (DGANs) combining conditional assistance and feature enhancement. The method uses data augmentation as a basic strategy to supplement imbalanced datasets by generating high-quality data. Firstly, a new generator is designed to build the basic framework by sharing the dual-branch deconvolutional neural networks, and combining the label auxiliary information and the coral distance loss function to ensure the diversity of generated samples. Secondly, a new discriminator was designed, which is based on deep convolutional neural networks and embedded with auxiliary classifiers, further expanding the function of the discriminator. Thirdly, the self-attention module is introduced into both the generator and the discriminator to enhance deep feature learning and improve the quality of generated samples; finally, the proposed method is experimentally validated on datasets of two different testbeds. The experimental results show that the proposed method can generate fake samples with rich diversity and high quality, using these samples to supplement the imbalanced dataset, the effect of imbalanced fault diagnosis has been substantially improved. This method can be used to solve the problem of fault diagnosis in the case of sample imbalance, which often exists in actual working conditions.