# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 6 Experiments and Results
### Fault Feature Extraction Experiment  
If the rolling bearing has faults, the fault feature should be extracted for further fault identification. In this paper, the WPEE is used to describe fault characteristics. To illustrate the effectiveness of the proposed feature extraction method, the relevant experiments are conducted in this section. Figure 7 shows the vibration signal decomposed by the WPT with a load of 0 hp and a fault diameter of 0.007 in under a ball fault. The experimental vibration signal is from Bearing Data Center of Case Western Reserve University and the sampling frequency is 12 kHz. The selection of a wave basis not only has a great influence on the effectiveness of signal decomposition and fault feature extraction, but also further affects the accuracy of the rolling bearing fault diagnosis results. Generally, an orthogonal basis should be selected in the wavelet packet transformation and the common orthogonal basis functions are those of the Harr, Daubechies, Coiflets, Symlets, and Meyer families. Daubechies (abbreviated to \(dbN\), where \(N\) denotes the number of wavelet order) wavelets can be applied to different signals by changing the order of the wavelet. In this study, \(dbN\) is selected as the wavelet basis for wavelet packet analysis and the vibration signal under rolling bearing failure state is decomposed and analyzed by setting the appropriate order \(N\). As shown in Figure 7, the WPT can effectively decompose the vibration signal of a rolling bearing under a ball fault into a series \begin{table}
\begin{tabular}{c c c} \hline \hline
**Complexity Analysis Algorithm** & **Can Detect Faults?** & **Average Running Time (s)** \\ \hline Approximate entropy & N & NA \\ Permutation entropy & Y & 2.573 \\ Fuzzy entropy & Y & 41.851 \\ Sample entropy & Y & 0.744 \\ Fast sample entropy & Y & 0.273 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The average running time of several complexity analysis algorithms applied in rolling bearing fault detection. Figure 6: The SampEn values for all 2400 samples under different working conditions. of decomposed signals over different frequency ranges and the spectrum of each node is distinctly different. The fault characteristics of the vibration signal are contained in the decomposed signals and the WPEEs of the vibration signal are used as the feature vector. Figure 7: Vibration signal decomposed by WPT with a load of 0 hp and a fault diameter of 0.007 in under a ball fault. (**a**) Three-level wavelet decomposition tree; (**b**) decomposed signals corresponding to each node; (**c**) spectrum diagram of the decomposed vibration signal corresponding to each node. The dimension of the feature vector is important for fault identification. If the number of wavelet packet levels is 5, the dimension of the feature vector is 32, which is too large to use machine-learning algorithms for fault identification. Moreover, if the number of wavelet packet levels is 3, the dimension of the feature vector is 8, which cannot highlight some features of the rolling bearing. To guarantee the analysis precision and speed, a 4-level WPT is chosen; the number of nodes after decomposition is 16 and the original vibration signals are decomposed into 16 sub-signals. After the signal is decomposed by the wavelet packet, the energy entropy of the reconstructed signal of each node is calculated and the feature vector is formed according to the node order. Then, each sample is represented by a 16-dimensional vector. The type of wavelet basis also has a certain influence on the analysis of the vibration signal; \"db10\" is chosen as the wavelet basis in this paper. The WPEE feature extraction results under different fault types of rolling bearings for a load of 2 hp are shown in Figure 7. Figure 7a presents the WPEE of a ball fault (BF) with different fault diameters, Figure 7b shows the WPEE of an inner race fault (IRF) with different fault diameters and Figure 7c shows the WPEE of an outer race fault (ORF) with different fault diameters.