Due to the data distribution discrepancy, fault diagnosis models, trained with labeled data in one scene, likely fails in classifying by unlabeled data acquired from the other scenes. Transfer learning is capable to generalize successful application trained in one scene to the fault diagnosis in the other scenes. However, the existing transfer methods do not pay much attention to reduce adaptively marginal and conditional distribution biases, and also ignore the degree of contribution between both biases and among network layers, which limit classification performance and generalization in reality. To overcome these weaknesses, we establish a new fault diagnosis model, called subdomain adaptation transfer learning network (SATLN). First, two convolutional building blocks were stacked to extract transferable features from raw data. Then, the pseudo label learning is amended to construct target subdomain of each class. Furthermore, a subdomain adaptation is combined with domain adaptation to reduce both marginal and conditional distribution biases simultaneously. Finally, a dynamic weight term is applied for adaptive adjustment of the contributions from both discrepancies and each network layers. The SATLN method is tested with six transfer tasks. The results demonstrate the effectiveness and superiority of the SATLN in the cross-domain fault diagnosis field.

The selection of variational mode decomposition (VMD) parameters usually adopts the empirical method, trial-and-error method or single-objective optimization method. The above method cannot achieve the global optimal effect. Therefore, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters of VMD, and it is applied to the composite fault diagnosis of the gearbox. The specific steps are: Firstly, symbol dynamic entropy (SDE) can effectively remove background noise, and use state mode probability and state transition to preserve fault information. Power spectral entropy (PSE) reflects the complexity of signal frequency composition. Therefore, the SDE and PSE are selected as fitness functions, and then the Pareto frontier optimal solution set is obtained by the MOPSO algorithm. Finally, the optimal combination of VMD parameters (k, α) is obtained by normalization. The improved VMD is used to analyze the simulation signal and gear box fault signal. The effectiveness of the proposed method is verified by comparing with the ensemble em-pirical mode decomposition (EEMD).

Minimum entropy deconvolution (MED) is widely used in the gearbox fault diagnosis because it can enhance the energy of the impact signal. However, it is sensitive to single abnormal impulsive oscillation. This is because it takes kurtosis as the objective function and solves the optimal filter by iteration. In addition, the filter length is not adaptive and needs to be determined artificially. This paper proposes a maximum kurtosis spectral entropy deconvolution (MKSED) method and applies it to bearing fault diagnosis. Considering that the kurtosis spectral entropy has the advantage of highlighting the continuous impact oscillation, the kurtosis spectral entropy is chosen as the objective function of deconvolution. At the same time, kurtosis spectral entropy is also used as the fitness function of improved local particle swarm optimization algorithm (LPSO), and the filter length is optimized by LPSO, which makes that MKSED adaptively determines the length of the filter while solving the deconvolution, so that it can accurately extract the continuous pulse signal. The results of the simulation signal analysis show that the proposed MKSED method is superior to MED, and the proposed method is applied to bearing fault diagnosis, which verifies its ability to extract continuous impact.

Semi-observable systems are referred to as a kind of widely used industrial equipment whose physical degradation state is only observable via shutdown inspection. To monitor the degradation process of semi-observable systems online, different types of sensors are generally employed to collect monitoring signals. Lots of studies have been conducted to fuse multi-sensor signals to predict remaining useful life (RUL). Majority of them, however, ignored the partially available state observations which can be viewed as ground truth measurements of physical degradation. To deal with this problem, this paper proposes a multi-sensor data-driven RUL prediction method for semi-observable systems, which leverages degradation information from online multi-sensor signals as well as offline state observations. This method is developed based on a generalizable state-space model combined with particle filtering (PF) framework. In the framework, a state transition function is used to describe the degradation process of system states. A multi-dimensional measurement function is constructed to describe the mapping between states and multi-sensor signals. To enhance the performance of prediction, an algorithm named prioritized sensor group selection (PSGS) is also proposed to select the optimal sensor group for RUL prediction. The effectiveness of the proposed method is demonstrated using an experiment of cutting tool wear.

In the era of big data, data‐driven methods mainly based on deep learning have been widely used in the field of intelligent fault diagnosis. Traditional neural networks tend to be more subjective when classifying fault time‐frequency graphs, such as pooling layer, and ignore the location relationship of features. The newly proposed neural network named capsules network takes into account the size and location of the image. Inspired by this, capsules network combined with the Xception module (XCN) is applied in intelligent fault diagnosis, so as to improve the classification accuracy of intelligent fault diagnosis. Firstly, the fault time‐frequency graphs are obtained by wavelet time‐frequency analysis. Then the time‐frequency graphs data which are adjusted the pixel size are input into XCN for training. In order to accelerate the learning rate, the parameters which have bigger change are punished by cost function in the process of training. After the operation of dynamic routing, the length of the capsule is used to classify the types of faults and get the classification of loss. Then the longest capsule is used to reconstruct fault time‐frequency graphs which are used to measure the reconstruction of loss. In order to determine the convergence condition, the three losses are combined through the weight coefficient. Finally, the proposed model and the traditional methods are, respectively, trained and tested under laboratory conditions and actual wind turbine gearbox conditions to verify the classification ability and reliable ability.