###### Abstract  
Rolling bearing is of great importance in modern industrial products, the failure of which may result in accidents and economic losses. Therefore, fault diagnosis of rolling bearing is significant and necessary and can enhance the reliability and efficiency of mechanical systems. Therefore, a novel fault diagnosis method for rolling bearing based on semi-supervised clustering and support vector data description (SVDD) with adaptive parameter optimization and improved decision strategy is proposed in this study. First, variational mode decomposition (VMD) was applied to decompose the vibration signals into sets of intrinsic mode functions (IMFs), where the decomposing mode number \(K\) was determined by the central frequency observation method. Next, fuzzy entropy (FuzzyEn) values of all IMFs were calculated to construct the feature vectors of different types of faults. Later, training samples were clustered with semi-supervised fuzzy C-means clustering (SSPCM) for fully exploiting the information inside samples, whereupon a small number of labeled samples were able to provide sufficient data distribution information for subsequent SVDD algorithms and improve its recognition ability. Afterwards, SVDD with improved decision strategy (ID-SVDD) that combined with k-nearest neighbor was proposed to establish diagnostic model. Simultaneously, the optimal parameters \(C\) and \(\sigma\) for ID-SVDD were searched by the newly proposed sine cosine algorithm improved with adaptive updating strategy (ASCA). Finally, the proposed diagnosis method was applied for engineering application as well as contrastive analysis. The obtained results reveal that the proposed method exhibits the best performance in all evaluation metrics and has advantages over other comparison methods in both precision and stability. rolling bearing; fault diagnosis; variational mode decomposition; fuzzy entropy; semi-supervised clustering; k-nearest neighbor decision strategy; adaptive sine cosine algorithm; support vector data description +
Footnote †: journal: Applied  
how to recognize and diagnose rolling bearing faults remains one of the main concerns in preventing failures of mechanical systems [2]. However, rolling bearing is prone to failure due to the complex operating conditions, such as improper assembly, poor lubrication, water and foreign body invasion, corrosion or overload [3]. Therefore, effective methods need to be proposed to diagnosis a fault of rolling bearing, which can promote the reliability of industrial manufacture. Owing to the rich information carried by vibration signals, most of fault diagnosis methods for rolling bearings rely on analyzing vibration signals [4; 5], the resistance of the bearing can be measured using electrodynamic sensors or laser vibrometers [6]. Considering that vibration signals are commonly non-stationary, it is difficult to extract critical features directly from fault signals. To solve this problem, various non-stationary signal processing methods are proposed in previous studies. For instance, wavelet transform (WT) is a self-adaptive signal decomposition method [7], which inherits and develops the idea of localization of short-time Fourier transform and is an ideal tool for time-frequency analysis, but its generalization will be restricted once a wavelet basis is chosen. Empirical mode decomposition (EMD) has a strong ability to deal with non-stationary signals and does not need to pre-set any basis function [8], but its performance is affected by end effects and mode mixing. To overcome these defects, an improved version of EMD, ensemble empirical mode decomposition (EEMD), is proposed by introducing a noise-assisted analysis method [9], which is also increases the computational cost and cannot completely neutralize the added noise. Unlike the above methods, variational mode decomposition (VMD) is a novel quasi-orthogonal signal decomposition method which overcomes the generalization problem of WT or mode mixing and end effects of EMD and EEMD [10].