Rolling bearings are the vital components of large electromechanical equipment, thus it is of great significance to develop intelligent fault diagnoses for them to improve equipment operation reliability. In this paper, a fault diagnosis method based on refined composite multiscale reverse dispersion entropy (RCMRDE) and random forest is developed. Firstly, rolling bearing vibration signals are adaptively decomposed by variational mode decomposition (VMD), and then the RCMRDE values of 25 scales are calculated for original signal and each decomposed component as the initial feature set. Secondly, based on the joint mutual information maximization (JMIM) algorithm, the top 15 sensitive features are selected as a new feature set and feed into random forest model to identify bearing health status. Finally, to verify the effectiveness and superiority of the presented method, actual data acquisition and analysis are performed on the bearing fault diagnosis experimental platform. These results indicate that the presented method can precisely diagnose bearing fault types and damage degree, and the average identification accuracy rate is 97.33%. Compared with the refine composite multiscale dispersion entropy (RCMDE) and multiscale dispersion entropy (MDE), the fault diagnosis accuracy is improved by 2.67% and 8.67%, respectively. Furthermore, compared with the RCMRDE method without VMD decomposition, the fault diagnosis accuracy is improved by 3.67%. Research results prove that a better feature extraction technique is proposed, which can effectively overcome the deficiency of existing entropy and significantly enhance the ability of fault identification.

Deep learning can be applied in the field of fault diagnosis without an accurate mechanism model. However, the accurate diagnosis of minor faults using deep learning is limited by the training sample size. In the case that only a small number of noise-polluted samples is available, it is crucial to design a new learning mechanism for the training of deep neural networks to make it more powerful in feature representation. The new learning mechanism for deep neural networks model is accomplished by designing a new loss function such that accurate feature representation driven by consistency of trend features and accurate fault classification driven by consistency of fault direction both can be secured. In such a way, a more robust and more reliable fault diagnosis model using deep neural networks can be established to effectively discriminate those faults with equal or similar membership values of fault classifiers, which is unavailable for traditional methods. Validation for gearbox fault diagnosis shows that 100 training samples polluted with strong noise are adequate for the proposed method to successfully train deep neural networks to achieve satisfactory fault diagnosis accuracy, while more than 1500 training samples are required for traditional methods to achieve comparative fault diagnosis accuracy.

Federated learning is an effective means to combine model information from different clients to achieve joint optimization when the model of a single client is insufficient. In the case when there is an inter-client data imbalance, it is significant to design an imbalanced federation aggregation strategy to aggregate model information so that each client can benefit from the federation global model. However, the existing method has failed to achieve an efficient federation strategy in the case when there is an imbalance mode mismatch between clients. This paper aims to design a federated learning method guided by intra-client imbalance degree to ensure that each client can receive the maximum benefit from the federation model. The degree of intra-client imbalance, measured by gain of a class-by-class model update on the federation model based on a small balanced dataset, is used to guide the designing of federation strategy. An experimental validation for the benchmark dataset of rolling bearing shows that a 23.33% improvement of fault diagnosis accuracy can be achieved in the case when the degree of imbalance mode mismatch between clients is prominent.

The efficiency of deep learning-based fault diagnosis methods for bearings is affected by the sample size of the labeled data, which might be insufficient in the engineering field. Self-training is a commonly used semi-supervised method, which is usually limited by the accuracy of features for unlabeled data screening. It is significant to design an efficient training mechanism to extract accurate features and a novel feature fusion mechanism to ensure that the fused feature is capable of screening. A novel training mechanism of multi-scale recursion (MRAE) is designed for Autoencoder in this article, which can be used for accurate feature extraction with a small amount of labeled data. An attention gate-based fusion mechanism was constructed to make full use of all useful features in the sense that it can incorporate distinguishing features on different scales. Utilizing large numbers of unlabeled data, the proposed multi-scale recursive semi-supervised deep learning fault diagnosis method with attention gate (MRAE-AG) can efficiently improve the fault diagnosis performance of DNNs trained by a small number of labeled data. A benchmark dataset from the Case Western Reserve University bearing data center was used to validate this novel method which shows that 7.76% accuracy improvement can be achieved in the case when only 10 labeled samples was available for supervised training of the DNN-based fault diagnosis model.

Aiming at the problem that the vibration signals of rolling bearings working in a harsh environment are mixed with many harmonic components and noise signals, while the traditional sparse representation algorithm takes a long time to calculate and has a limited accuracy, a bearing fault feature extraction method based on the ensemble empirical mode decomposition (EEMD) algorithm and improved sparse representation is proposed. Firstly, an improved orthogonal matching pursuit (adapOMP) algorithm is used to separate the harmonic components in the signal to obtain the filtered signal. The processed signal is decomposed by EEMD, and the signal with a kurtosis greater than three is reconstructed. Then, Hankel matrix transformation is carried out to construct the learning dictionary. The K-singular value decomposition (K-SVD) algorithm using the improved termination criterion makes the algorithm have a certain adaptability, and the reconstructed signal is constructed by processing the EEMD results. Through the comparative analysis of the three methods under strong noise, although the K-SVD algorithm can produce good results after being processed by the adapOMP algorithm, the effect of the algorithm is not obvious in the low-frequency range. The method proposed in this paper can effectively extract the impact component from the signal. This will have a positive effect on the extraction of rotating machinery impact features in complex noise environments.

A convolutional neural network can extract features from high-dimensional data, but the convolution operation has a high time complexity and requires a large amount of computation. For equipment with a high sampling frequency, fault diagnosis methods based on convolutional neural networks cannot meet the requirements of online fault diagnosis. To solve this problem, this study proposes a fault diagnosis method for multi-source heterogeneous information fusion based on two-level transfer learning. This method aims to fully utilize multi-source heterogeneous information and external domain data, construct a two-level transfer mechanism to fuse multi-source heterogeneous information, avoid convolutional operations, and achieve real-time fault diagnosis. Its main work is to build a feature extraction network model of screenshots, design a mechanism for transfer from the feature extraction model using screenshots to the deep learning model using one-dimensional sequence signals, and complete the transfer from a convolutional neural network to a deep neural network. After two-level transfer, the fault diagnosis model not only integrates the characteristics of one-dimensional sequence signals and screenshots but also avoids convolution operations and has a low time complexity. The effectiveness of the proposed method is verified using a gearbox dataset and a bearing dataset.