Deep learning models often use a flat softmax layer to classify samples after feature extraction in visual classification tasks. However, it is hard to make a single decision of finding the true label from massive classes. In this scenario, hierarchical classification is proved to be an effective solution and can be utilized to replace the softmax layer. A key issue of hierarchical classification is to construct a good label structure, which is very significant for classification performance. Several works have been proposed to address the issue, but they have some limitations and are almost designed heuristically. In this article, inspired by fuzzy rough set theory, we propose a deep fuzzy tree model which learns a better tree structure and classifiers for hierarchical classification with theory guarantee. Experimental results show the effectiveness and efficiency of the proposed model in various visual classification datasets.

Recently, deep learning techniques have been successfully used for bearing remaining useful life (RUL) prediction. However, the degradation pattern of bearings can be much different from each other, which leads to the trained model usually not being able to work well for RUL prediction of a new bearing. As a method that can adapt a model trained on source datasets to a different but relative unlabeled target dataset, transfer learning shows the potential to solve this problem. Therefore, we propose a two-stage transfer regression (TR)-based bearing RUL prediction method. Firstly, the incipient fault point (IFP) is detected by a convolutional neural network (CNN) classifier to identity the start time of degradation stage and label the training samples. Then, a transfer regression CNN with multiloss is constructed for RUL prediction, including regression loss, classification loss, maximum mean discrepancy (MMD) and regularization loss, which can not only extract fault information from fault classification loss for RUL prediction, but also minimize the probability distribution distance, thus helping the method to be trained in a domain-invariant way via the transfer regression algorithm. Finally, real data collected from run-to-failure bearing experiments are analyzed by the TR-based CNN method. The results and comparisons with state-of-the-art methods demonstrate the superiority and reliable performance of the proposed method for bearing RUL prediction.

The issues of actuator fault reconstruction, sensor fault reconstruction, and state estimation are considered in this article for Markovian jump systems, using a novel adaptive observer approach. First, by utilizing coordinate transformation technology, the original plant is decoupled into two subplants. The actuator faults and sensor faults are separated in different subplants. Then, two novel observers are proposed, respectively. With the two proposed adaptive observers, state estimation, sensor faults, and actuator faults reconstruction can be achieved. Finally, a numerical example is employed to verify the effectiveness of the theoretical results and to make comparisons with some existing fault reconstruction schemes.

This paper studies the event-triggered $H_{\mathrm{\infty }}$ control problem for networked switched systems with a mixed time and state-dependent switching law. By the event-triggering strategies, only necessary samplings of feedback signals are determined to be released. The advantages are that redundant transmissions and updates can be reduced. By the adopted switching law, each sub-system will work for a minimum dwell time, and then a state-dependent switching starts to work. Specifically, by using discrete event-triggering strategies and considering the effects of transmission delays, a time-delay closed-loop switched system is first established. Then, by utilising multiple Lyapunov functions method, sufficient conditions are presented to ensure the stability of the closed-loop switched system with a certain $H_{\mathrm{\infty }}$ performance level. In particular, since the switching instants and the event-triggered instants may be coupled, typical cases are discussed in detail. Moreover, the co-design conditions for state-feedback sub-controller gains and event-triggering parameters are developed. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Reliability is of great significance in ensuring the safe operation of modern industry, which mainly relies on data analysis and life tests. However, as the life of mechanical systems becomes increasingly longer with the rapid development of the manufacturing industry, the collection of historical failure data becomes progressively more time-consuming. In this paper, a few-shot reliability assessment approach is proposed in order to overcome the dependence on historical data. Firstly, the vibration response of a bearing was illustrated. Then, based on a vibration response analysis, a morphological component analysis (MCA) method based on sparse representation theory was used to decompose vibration signals and extract impulse signals. After the impulse components’ reconstruction, their statistical indexes were utilized as the input observation vector of a Mixture of Gaussians Hidden Markov Model (MoG-HMM) for a reliability estimation. Finally, the experimental dataset of an aerospace bearing was analyzed via the proposed method. The comparison results illustrate the effectiveness of the proposed method of a few-shot reliability assessment.