Fault diagnosis of rolling element bearings is an effective technology to ensure the steadiness of rotating machineries. Most of the existing fault diagnosis algorithms are supervised methods and generally require sufficient labeled data for training. However, the acquisition of labeled samples is often laborious and costly in practice, whereas there are abundant unlabeled samples which also imply health information of bearings. Thus, it is worthwhile to develop semi-supervised methods of fault diagnosis to make effective use of the plentiful unlabeled samples. Nevertheless, considering the normal data are much more than the faulty ones, the problem of imbalanced data exists among unlabeled samples for fault diagnosis. Besides, in practice, bearings often work under uncertain and variable operation conditions, which would also have negative influence on fault diagnosis. To solve these issues, a novel hybrid method for bearing fault diagnosis is proposed in this paper: (1) Inspired by visibility graph, a novel fault feature extraction method named visibility graph feature (VGF) is proposed. The obtained features by VGF are natively insensitive to variable conditions, which has been validated by a simulation experiment in this paper; (2) On basis of VGF, to deal with imbalanced unlabeled data, graph-based rebalance semi-supervised learning (GRSSL) for fault diagnosis is proposed. In GRSSL, a graph based on a weighted sparse adjacency matrix is constructed by the k-nearest neighbors and Gaussian Kernel weighting algorithm by means of the samples. Then, a bivariate cost function over classification and normalized label variable is built up to rebalance the importance of labels. Finally, the proposed VGF-GRSSL method was verified by data collected from Case Western Reserve University Bearing Data Center. The experiment results show that the proposed method of bearing fault diagnosis performs effectively to deal with the imbalanced unlabeled data under variable conditions.

This study investigates a critical hazard identification method for railway accident prevention. A new accident causation network is proposed to model the interaction between hazards and accidents. To realize consistency between the most likely and shortest causation paths in terms of hazards to accidents, a method for measuring the length between adjacent nodes is proposed, and the most-likely causation path problem is first transformed to the shortest causation path problem. To identify critical hazard factors that should be alleviated for accident prevention, a novel critical hazard identification model is proposed based on a controllability analysis of hazards. Five critical hazard identification methods are proposed to select critical hazard nodes in an accident causality network. A comparison of results shows that the combination of an integer programming-based critical hazard identification method and the proposed weighted direction accident causality network considering length has the best performance in terms of accident prevention.