Deep transfer-learning-based diagnosis models are promising to apply diagnosis knowledge across related machines, but from which the collected data follow different distribution. To reduce the distribution discrepancy, Gaussian kernel induced maximum mean discrepancy (GK-MMD) is a widely used distance metric to impose constraints on the training of diagnosis models. However, the models using GK-MMD have three weaknesses: 1) GK-MMD may not accurately estimate distribution discrepancy because it ignores the high-order moment distances of data; 2) the time complexity of GK-MMD is high to require much computation cost; 3) the transfer performance of GK-MMD-based diagnosis models is sensitive to the selected kernel parameters. In order to overcome the weaknesses, a distance metric named polynomial kernel induced MMD (PK-MMD) is proposed in this paper. Combined with PK-MMD, a diagnosis model is constructed to reuse diagnosis knowledge from one machine to the other. The proposed methods are verified by two transfer learning cases, in which the health states of locomotive bearings are identified with the help of data respectively from motor bearings and gearbox bearings in laboratories. The results show that PK-MMD enables to improve the inefficient computation of GK-MMD, and the PK-MMD-based diagnosis model presents better transfer results than other methods.

As a deep learning model, a deep belief network (DBN) consists of multiple restricted Boltzmann machines (RBMs). Based on DBN, many intelligent fault diagnosis methods are proposed. However, these methods seldom considered the appearance of new working conditions during the operation of real machines. Varying working conditions lead to a change of feature distributions and finally result in low diagnosis accuracies. Therefore, we propose a distribution-invariant DBN (DIDBN) to learn distribution-invariant features directly from raw vibration data. DIDBN consists of a locally connected RBM (LCRBM) layer, a fully connected RBM layer, and an RBM layer with a mean discrepancy maximum (MDM-RBM). The LCRBM layer is designed with a locally connected structure. By proposing MDM, the MDM-RBM layer is able to obtain features that have close distributions under varying working conditions. Followed by a softmax classifier, DIDBN is able to recognize faults. The proposed method is applied to two diagnosis cases. Results verify that DIDBN is able to learn distribution-invariant features and achieve higher diagnosis accuracies than recently proposed methods. Moreover, the reason why DIDBN is able to learn distribution-invariant features is explained by visualizing the feature learning process.

The early fault characteristics of rolling element bearings carried by vibration signals are quite weak because the signals are generally masked by heavy background noise. To extract the weak fault characteristics of bearings from the signals, an improved spectral kurtosis (SK) method is proposed based on maximum correlated kurtosis deconvolution (MCKD). The proposed method combines the ability of MCKD in indicating the periodic fault transients and the ability of SK in locating these transients in the frequency domain. A simulation signal overwhelmed by heavy noise is used to demonstrate the effectiveness of the proposed method. The results show that MCKD is beneficial to clarify the periodic impulse components of the bearing signals, and the method is able to detect the resonant frequency band of the signal and extract its fault characteristic frequency. Through analyzing actual vibration signals collected from wind turbines and hot strip rolling mills, we confirm that by using the proposed method, it is possible to extract fault characteristics and diagnose early faults of rolling element bearings. Based on the comparisons with the SK method, it is verified that the proposed method is more suitable to diagnose early faults of rolling element bearings.

Deep learning has been applied in intelligent fault diagnosis of machines since it trains deep neural networks to simultaneously learn features and recognize faults. In the intelligent fault diagnosis methods based on deep learning, feature learning and fault recognition are achieved by solving a multi-class classification problem. The multi-class classification, however, has not considered the relationships of fault labels, leading to two weaknesses of these methods. One is that it cannot ensure to learn the correlated features for related faults and the other is that it cannot handle missing label problem. To overcome these weaknesses, we introduce a concept of multi-label classification into intelligent fault diagnosis and propose a deep multi-label learning framework called multi-label convolutional neural network (MLCNN). MLCNN builds the relationship between the labels, and thus it is able to learn the correlated features from mechanical vibration signals and be well trained using the samples with missing labels. A motor bearing diagnosis case and a compound fault diagnosis case are used to verify the proposed method, respectively. The results show that the relationships between features are learned by MLCNN, and the classification accuracies of MLCNN are higher than traditional methods when the missing label problem occurs.

Imbalanced classification using deep learning has attracted much attention in intelligent fault diagnosis of machinery. However, the existing methods use individual deep neural network to extract features and recognize the health conditions under imbalanced dataset, which may easily over-fit the mechanical data and affect the diagnosis accuracy. To deal with this problem, this paper takes the advantages of ensemble learning and proposes an ensemble convolutional neural network (EnCNN) for the intelligent fault diagnosis for machines under imbalanced data. In the proposed method, a convolutional neural network with the input of multi-sensor signals is used as the base classifier. Firstly, the mechanical imbalance dataset is first split into balanced training subsets through under-sampling strategy, and each subset is used to train a base classifier. Then the weight coefficients of each trained base classifier are calculated by G-mean score and anomalous base classifiers are screened using classifier selection. Finally, the base classifiers are integrated into EnCNN through weighted voting strategy. The proposed EnCNN is validated by the imbalanced dataset collected from a machinery fault test bench. By comparing with the related methods, the superiority of EnCNN is verified in intelligent fault diagnosis of machines under imbalanced data.

Transfer learning is a topic that has attracted attention for the intelligent fault diagnosis of bearings since it addresses bearing datasets that have different distributions. However, the traditional intelligent fault diagnosis methods based on transfer learning have the following two shortcomings. (1) The multi-mode structure characteristics of bearing datasets are neglected. (2) Some local regions of the bearing signals may not be suitable for transfer due to signal fluctuation. Therefore, a multi-domain weighted adversarial transfer network is proposed for the cross-domain intelligent fault diagnosis of bearings. In the proposed method, multi-domain adversarial and attention weighting modules are designed to consider bearing multi-mode structure characteristics and solve the influence of local non-transferability regions of signals, respectively. Two diagnosis cases are used to verify the proposed method. The results show that the proposed method is able to extract domain invariant features for different cross-domain diagnosis cases, and thus improves the accuracy of fault identification.