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• A capsule auto-encoder model, which can extract vector features, is proposed. • The model can achieve good results by using only a small number of samples. • The proposed method can significantly reduce the training time. • The proposed method has good anti-noise ability under the noisy environment. Both of traditional intelligent fault diagnosis (TIFD) based on artificial features and modern intelligent fault diagnosis (MIFD) based on deep learning have made healthy progress in recent times. But, the bulk of methods neglects the actual application environments of intelligent diagnosis: (1) There are only few samples of faults, which greatly limit the popularity of TIFD and MIFD. Therefore, it is urgent to develop intelligent models with the ability of few-shot learning. (2) The performance degradation will occur when the equipment runs for a long time, which requires intelligent diagnosis models to possess the ability of quick updating. In order to remedy these shortcomings, a capsule auto-encoder model based on auto-encoder and capsule network, namely CaAE, is proposed for intelligent fault diagnosis. By constructing a capsule auto-encoder, various meaningful feature capsules are extracted from the input data, and then these capsules are fused adaptively into status capsules by the dynamic routing algorithm to represent health statuses. After that, status capsules are fed into the classifier to distinguish health statuses. The extraction of feature capsules enhances the model's ability of mining information, which reduces the dependence of CaAE on the number of samples and compresses training time by reducing layers of the network. The loss function in the model introduces the penalty for the samples classified correctly and the constraints on the capsule auto-encoder, which make the model fast in training and excellent in feature extracting. A bearing dataset is utilized to validate the performance of the proposed CaAE. The results indicate that CaAE is suitable for few-shot learning and quick updating of intelligent models. In addition, the model can also achieve satisfactory results under noisy environment. [ABSTRACT FROM AUTHOR]

Abstract: The performance degradation assessment based on the support vector data description (SVDD) has been receiving more attention recently. However, there are three main drawbacks to this approach. First, the SVDD is sensitive to outliers and may result in an over-fitting problem. Second, the initial status model, which is not changed as time goes on, does not effectively reflect the latest status of the bearing. Third, the previous assessment indicator only contains distance information without spatial position information. To address these critical issues, a novel one-class classifier called the rough support vector data description (RSVDD) is proposed based on the rough set notion. Then, the incremental rough support vector data description (IRSVDD) is designed based on the RSVDD. Finally, the new assessment indicator and assessment process are proposed. The effectiveness of the proposed methods is validated through experiments. [Copyright &y& Elsevier]

The development of non-linear dynamic theory brought a new method for recognising and predicting the complex non-linear dynamic behaviour. Fractal dimension can quantitatively describe the non-linear behaviour of vibration signal. In the present paper, the capacity dimension, information dimension and correlation dimension are applied to classify various fault types and evaluate various fault conditions of rolling element bearing, and the classification performance of each fractal dimension and their combinations are evaluated by using SVMs. Experiments on 10 fault data sets showed that the classification performance of the single fractal dimension is quite poor on most data sets, and for a given data set, each fractal dimension exhibited different classification ability, this indicates that various fractal dimensions contain various fault information. Experiments on different combinations of the fractal dimensions demonstrated that the combination of all these three fractal dimensions gets the highest score, but the classification performance is still poor on some data sets. In order to improve the classification performance of the SVM further, 11 time-domain statistical features are introduced to train the SVM together with three fractal dimensions, and the classification performance of the SVM is improved significantly. At the same time, experimental results showed that the classification performance of the SVM trained with 11 time-domain statistical features in tandem with three fractal dimensions outperforms that of the SVM trained only with 11 time-domain statistical features or with three fractal dimensions. [Copyright &y& Elsevier]

• An improved dynamic model of ball bearing is proposed. • This model considers bearing deformations and ball-inner raceway separation. • A prediction method for the initial values is applied to solve dynamic model. • The influence of deformations and ball-inner raceway separation is discussed. In actual operation conditions, the bearing deformations caused by the change of assembly state play a major role in bearing dynamic performance, and the ball-inner raceway separation due to the insufficient preload or excessive external loads is also a key issue that limits the bearing service. In this paper, an improved nonlinear dynamic model of ball bearing considering bearing deformations and ball-inner raceway separation is proposed. Firstly, the relationships between the bearing deformations and bearing-shaft assembly state are directly derived according to the deformation compatibility condition, and the interaction and relative motions among various bearing components under the ball-inner raceway separation conditions are analyzed. Then a prediction method for the initial iterative values is used to calculate the dynamic model, and the calculation results are compared with the experimental data for verification. Finally, the variations of bearing deformations, contact properties, and cage skid under different factors are investigated. It is found that the bearing deformations affect the contact properties of ball-raceway, and the appropriate preload effectively improves the bearing service characteristics, especially under the ball-inner raceway separation conditions. [ABSTRACT FROM AUTHOR]

• A 5 DOFs nonlinear dynamics model of four-point contact ball bearing was proposed. • The dynamic contact feature of FCPBB with complex operating conditions were investigated. • The interaction between balls and raceway may changes from 2-point to 3-point contact with pure axial load. • The ball may experience 2-point contact, 3-point contact and 4-point contact in one revolution in case of combined loads. Four-contact-point ball bearing (FCPBB), with a special double half inner ring structure, presents dynamic multi-point contact characteristics in service. The dynamic contact feature, such as 2-point, 3-point or even 4-point contact phenomena between balls and bearing raceway, lead to completely different bearing friction, heat generation and wear rates. Considering the oil film traction effect, the traction and contact equations for ball and four raceways were proposed, and the changes of bearing dynamic contact feature with complex operating conditions, such as high speed-slight load, combined axial-radial load, were investigated. As bearing preload increases, the interaction between the ball and raceway gradually changes from 3-point to 2-point contact. In this process, the PV factor in outer sub-contact area first increases and then decreases, which is the key factor in bearing friction loss. In case of combined load, the ball may experience 2-point contact, 3-point contact and 4-point contact in one revolution. Besides, when two-point contact occurs, the main-contact area has the largest PV value; when four-point contact occurs, the sub-contact area has the largest PV value. [ABSTRACT FROM AUTHOR]

• Bearing thermal characteristic with different oil-air supply methods was compared. • Field synergy principle was used to explain bearing internal flow and lubrication. • It was found that lateral oil-air flow is better for bearing at certain speeds. High precision models were established to investigate airflow pattern and lubrication performance inside bearing cavity with different oil-air supply methods. The coupling technique of Level-Set function and VOF method was used to track the oil-air interface, and the migration and diffusion process of oil droplets inside bearing cavity were obtained. A high-speed oil-air lubrication test rig was designed and set up, bearing temperature rise with outer ring and lateral oil-air lubrication methods at different rotation speeds were tested and compared. Finally, combined with the internal flow and temperature field distribution, the synergistic analysis was applied and the lubricant flow and heat dissipation performance of bearing internal cavity and key areas were all estimated. [ABSTRACT FROM AUTHOR]