In bearing fault diagnosis, due to the insufficient obtained supervised data and the inevitable noise contained in the vibration signals, the problem of clustering bearing fault diagnosis with imbalanced data containing noise is caused. Thanks to the ability to quickly and fully learn boundary information in small samples, the extension neural network-type 2 algorithm (ENN-2) has the potential in imbalanced data clustering and has been gradually applied in fault diagnosis. Therefore, in order to improve the unstable clustering performance of ENN-2 caused by its heavy dependence on input order of samples, a novel algorithm called linked extension neural network (LENN) is developed by redesigning the correlation function and its iterative method, which greatly reduces the clustering iteration epochs of the algorithm. In addition, an evaluation index of clustering quality for this novel algorithm, extension density, is also proposed. After that, a bearing fault diagnosis model of variational mode decomposition (VMD) based denoising and LENN is proposed. Firstly, VMD is used to get intrinsic mode functions (IMFs), and the correlation coefficients of IMFs are calculated for signal denoising. Secondly, the features are extracted from denoised signals and selected by PCA algorithm, and the fault diagnosis is finally completed by LENN. Compared with ENN-2, K-means, FCM, and DBSCAN based models, the proposed model identifies the faults with different severities more accurately and achieves superior diagnostic ability on different imbalance degrees of datasets, which can further lay a foundation for clustering fault diagnosis based on vibration signals.
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