Due to the effectiveness of anomaly/outlier detection, one-class algorithms have been extensively studied in the past. The representatives include the shallow-structure methods and deep networks, such as the one-class support vector machine (OC-SVM), one-class extreme learning machine (OC-ELM), deep support vector data description (Deep SVDD), and multilayer OC-ELM (ML-OCELM/MK-OCELM). However, existing algorithms are generally built on the minimum mean-square-error (mse) criterion, which is robust to the Gaussian noises but less effective in dealing with large outliers. To alleviate this deficiency, a robust maximum correntropy criterion (MCC)-based OC-ELM (MC-OCELM) is first proposed and then further extended to a hierarchical network to enhance its capability in characterizing complex and large data (named HC-OCELM). The gradient derivation combining with a fixed-point iterative updation scheme is adopted for the output weight optimization. Experiments on many benchmark data sets are conducted for effectiveness validation. Comparisons to many state-of-the-art approaches are provided for the superiority demonstration.

Bearings are important part of aerospace equipments. Therefore, bearings fault diagnosis and fault detection is necessary for the safe operation. Generally, the bearing are core component and runs in a complex and heavy background noise environment. Thence, the bearing signals will be overwhelmed by noise. At present, the diagnosis methods of bearings are based on the experience of experts which costs a lot of labor and time-consuming. Consequently, to address these inadequacies, a novel method based on variational mode decomposition (VMD) algorithms and Alexnet neural network has been presented. Firstly, it decomposes the nonstationary bearing signals into intrinsic mode functions adaptively. However, background noise will seriously affect the number of signal decompositions and reduce accuracy even over-decomposition. Thence, this paper proposed the hierarchical fuzzy entropy method to adaptively extract weak fault characteristics of bearings. Then Alexnet neural network has been utilized to learn the relationship of fault features and bearings health conditions. The architecture of Alexnet diagnosis model is convenient and efficient. Finally, two tentative dataset are adopted to verify the effectiveness and feasibility of the method proposed in this article. The results show that the presented method has a higher fault diagnosis accuracy rate than traditional convolutional neural networks.