# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 7 Conclusions  
In this paper, a novel fault diagnosis and severity analysis for rolling bearings based on the fast sample entropy, the wavelet packet energy entropy, and the multiclass relevance vector machine is presented.  
1. The time complexity of the vibration signal increases when a fault occurs in the rolling bearing. To improve the real-time performance of the fault detection process, a fast sample entropy algorithm based on a kd tree is adopted. The rolling bearing failure can be effectively identified by calculating the fast sample entropy of the vibration signal and this fault detection method can effectively improve the real-time performance of fault detection process.
2. Considering that the vibration signals are complex and exhibit non-stationarity and non-linearity, the wavelet packet energy entropy is adopted as the fault feature extraction method. First, the wavelet packet transform decomposes the fault signal into different frequency bands. Then, the wavelet packet energy entropy values of the reconstructed signals of each node in the last level of the wavelet packet are calculated and the fault feature vector is generated. The wavelet packet energy entropy can effectively extract the fault information of a rolling bearing vibration signal with good feature description performance and the extracted feature vector has strong separability.
3. The fault feature vectors are fed into a multiclass relevance vector machine classifier to identify the fault type as well as the fault severity. The results of the experiments in this paper, which take into account multiple combinations of fault types and fault diameters, show that the proposed method can diagnose the fault type as well as the fault severity with high accuracy.  
This paper provides a novel fault diagnosis and fault severity analysis method and an effective exploration method for fault severity analysis on the basis of accurate identification of fault types. In this paper, the classifier method is used to analyze the fault severity of rolling bearings; the future research will focus on the analysis of the fault severity by means of a prediction method and the influence of fault location on bearing fault diagnosis [39].  
[PERSON] designed the method and wrote this paper. [PERSON] and [PERSON] performed the experiments. [PERSON] analyzed the data and proofread the manuscript.  
This work received financial support from the National Natural Science Foundation of China (No. 61803128).  
**Acknowledgments:** Thanks for the Bearing Data Center of Case Western Reserve University to supply the rolling bearing data set. Thanks to [PERSON] of Harbin Institute of Technology for the preliminary work of this paper.  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Nomenclature**  
AM Amplitude-modulated  
ApEn Approximate entropy  
CEEMD Complete ensemble empirical mode decomposition  
EMD Empirical mode decomposition  
EEMD Ensemble empirical mode decomposition  
FFT Fast Fourier transform  
FM Frequency-modulated  
FE Fuzzy entropy  
IMFs Intrinsic mode functions  
LMD Local mean decomposition  
HMM Markov modeling  
mRVM Multiclass relevance vector machine  
PE Permutation entropy  
PFs Product functions  
PCA Principle component analysis