## 3 Experiment and Analysis Results
### Analysis Results  
The historical data of similar equipment under the working conditions of a rotational speed of 2100 r/min and radial force of 12 kN are selected for study, and the original vibration data are cleaned. Different wavelet bases have different time-frequency characteristics, so different wavelets can obtain different results in denoising the same signal. Since a compact support and smoothness of the wavelet cannot be achieved at the same time, various factors must be considered comprehensively, and an eclectic method must be adopted to select the wavelet basis to better process the noisy signal. Thirty-seven kinds of commonly used wavelet bases are selected to reduce the noise of the signal, labelled 1-37, and the corresponding serial numbers are listed in Table 2. The signal to noise ratio (_SNR_), root mean square error (_RMSE_) and correlation coefficient of the noise-reduced signal are analyzed, as shown in Figure 3.  
Generally, the higher the _SNR_ of the signal is, the closer the noise reduction signal is to the energy of the real signal. The smaller the _RMSE_ is, the smaller the deviation between the denoising signal \begin{table}
\begin{tabular}{c c} \hline \hline
**Serial Number** & **Wavelet Base** \\ \hline
1 & haar \\
2-11 & db1, db2, db3, db4, db5, db6, db7, db8, db9, db10 \\
12-18 & sym2, sym3, sym4, sym5, sym6, sym7, sym8 \\
19-23 & coif1, coif2, coif3, coif4, coif5 \\
24-36 & bior1.1, bior1.3, bior1.5, bior2.2, bior2.4, bior2.6, bior2.8, bior3.5, bior3.7, bior3.9, bior4.4, bior5.5, bior6.8 \\
37 & dmey \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Commonly used wavelet bases and corresponding sequence numbers. Figure 3: Signal to noise ratio (SNR) and root mean square error (RMSE) of noise reduction for the different wavelet bases. Figure 2: Bearing test stand. and the actual signal is, the better the smoothness and denoising effect are. The closer the correlation coefficient is to 1, the better the similarity between the noise filtering signal waveform and the actual signal waveform is and the lower the distortion degree is. Through analysis of these 37 kinds of wavelets, it is found that the db10, sym8, coif5, and dmey wavelets attain better noise reduction effects on the signals used in this case. The number of layers of wavelet decomposition also affect the noise reduction effect. The original signal is denoised by 2- to 8-layer wavelets, as shown in Figure 4. According to the analysis, when the number of decomposed layers is small, the SNR of the signal is high, the RMSE is small, and the correlation coefficient is high. Numerically speaking, the denoising effect is the best, but from the waveform point of view, the signal still contains much noise after denoising with a small number of layers. With the increase in the number of decomposition layers, the waveform of the denoising signal is smoother, but the distortion degree is higher. As shown in Table 3 and Figure 5, three layers are the optimal number of decomposition layers, which not only effectively eliminates noise but also retains the information in the signal as much as possible. Therefore, it is important to choose the number of decomposition layers properly to reduce noise when wavelet decomposition is  
The soft threshold, hard threshold, and fixed threshold are also compared and analyzed, as summarized in Table 4. Four kinds of wavelet basis functions are adopted to reduce noise, among which the hard threshold method is the best, the fixed threshold method attains the second best effect, and the soft threshold method performs the worst. Finally, the hard threshold denoising method of dmey wavelet 3-layer decomposition is applied to denoise the signal. A total of 52 features are extracted from the noise-reduced signal, as shown in Table 5. Among them, wavelet packet energy and energy entropy are decomposed through dmey wavelet 4-layer decomposition.