# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 1 Introduction
used the multi-scale permutation entropy to calculate the PE values at different time scales and generate the fault feature vector of a rolling bearing vibration signal [20]. [PERSON] et al. proposed a feature extraction method of vibration signals based on improved LMD and PE to highlight the fault characteristics [18]. [PERSON] et al. presented a fault feature extraction method based on the hierarchical fuzzy entropy for extracting the characteristics of a non-linear and non-stationary vibration signal in complex operating conditions [15]. Although all of the above methods have had achievements in rolling bearing fault diagnosis, the accuracy of these fault diagnosis methods needs to be improved. In particular, the description of different fault severity levels is an urgent problem that needs to be solved. Therefore, a high-performance fault feature extraction method for rolling bearing should be effectively conducted before performing fault identification. After feature extraction, an appropriate classification algorithm should be used to achieve fault type identification. As an effective predictor and classifier, neural network has been successfully applied in mechanical fault prediction and diagnosis [21]. The support vector machine (SVM) is a powerful classifier [22] that is currently one of the most widely used classifiers in rolling bearing fault diagnosis. However, the classification performance of SVMs is related to the setting of a penalty factor value. Improper setting of the penalty factor leads to an over-fitting problem when the number of training samples is large. A linear increase in the number of support vectors leads to a significant increase in the test time. The relevance vector machine (RVM) introduced by [PERSON] in 2001 has the same function as the SVM, but it is a new type of machine-learning method based on the sparse Bayesian framework [23]. The classification accuracy of the RVM is no less than that of the SVM. Compared with SVMs, RVMs have special advantages in solving the classification problem [24; 25]; the penalty factor is assigned automatically in RVMs, not subjectively by users, the sparsity of RVMs is better than that of SVMs, making them more suitable for online monitoring, and the kernel functions of RVM algorithms are no longer constrained by the Mercer theorem. It is worth mentioning that the RVM provides a probabilistic interpretation of its outputs. However, similar to the SVM, the RVM is also a binary classification algorithm; when dealing with multiclass issues, it usually transforms them into a series of binary classification problems, which may cause an accumulative error and overlapping classification. A multiclass relevance vector machine (mRVM) is proposed by [PERSON], which extendsthe original RVM to multiclass issues by introducing auxiliary variables, which act as intermediate regression targets, thus realizing the classification of multiclasses by outputting the estimation of class membership probabilities [26; 27]. [PERSON] et al. applied an mRVM to the on-line fault diagnosis of an analogue circuit and obtained promising results [28]. [PERSON] et al. presented a novel fault diagnosis strategy based on principal component analysis (PCA) and mRVM, and the simulation results have validated that the mRVM is useful in multi-fault diagnosis, producing results superior to those of the SVM [29]. The above studies have shown that the mRVM has excellent multi-classification performance and can provide a very good tool for the fault diagnosis and severity analysis of rolling bearings. Through the above analysis, a novel fault diagnosis and severity analysis method based on fast sample entropy (SampEn), wavelet packet energy entropy (WPEE), and multiclass relevance vector machine (mRVM) is presented for rolling bearings. The SampEn can effectively detect the dynamic changes of the vibration signal and can be applied to detect the rolling bearing faults.