## 4 Experimental Verification
### Analysis Result of the Outer Race Fault Signal  
The acquisition time from 12 February 2004 10:32:39 to 19 February 2004 06:22:39 was for the performance degradation of outer race faults in bearing 1. Literature [3] gives the root mean square (RMS) value for the entire life cycle, which indicates the change of the bearings in the different periods of performance. The whole life cycle can be divided into three parts. At first, bearing operation keeps steady at the 0 th-4 th days (see phase I). Then the RMS increases to a certain level at the 5 th day (see phase II). Some fluctuations appear in the temporal interval of the 5 th and 6 th days. Finally, a sharp \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Signal** & **Operation** & **MMBCSOICE** & **MPODSOISE** & **MPOCSOISE** & **MMBDSOICE** \\ \hline \multirow{6}{*}{Signal one} & Before de-noising & 4.3483 & 4.3483 & 4.3483 & 4.3483 \\  & After de-noising & **24.1932** & 7.6607 & 7.6607 & 7.6607 \\  & Number & 5 & 4 & 4 & 4 \\  & Before de-noising & \(-\)5.1941 & \(-\)5.1941 & \(-\)5.1941 & \(-\)5.1941 \\  & After de-noising & **18.5129** & 6.5913 & 6.5913 & 6.5913 \\  & Number & 6 & 4 & 4 & 4 \\  & Before de-noising & \(-\)11.2147 & \(-\)11.2147 & \(-\)11.2147 & \(-\)11.2147 \\  & After de-noising & **4.2480** & \(-\)0.0627 & \(-\)0.0627 & 3.4739 \\  & Number & 7 & 2 & 2 & 4 \\ \hline \multirow{6}{*}{Signal two} & Before de-noising & 3.4937 & 3.4937 & 3.4937 & 3.4937 \\  & After de-noising & **14.2194** & 6.0736 & 6.0736 & 6.0736 \\ \cline{1-1}  & Number & 5 & 4 & 4 & 4 \\ \cline{1-1}  & Before de-noising & \(-\)2.5269 & \(-\)2.5269 & \(-\)2.5269 & \(-\)2.5269 \\ \cline{1-1}  & After de-noising & **13.1688** & 5.8545 & 5.8545 & 5.8545 \\ \cline{1-1}  & Number & 5 & 4 & 4 & 4 \\ \cline{1-1}  & Before de-noising & \(-\)8.5475 & \(-\)8.5475 & \(-\)8.5475 & \(-\)8.5475 \\ \cline{1-1}  & After de-noising & **10.5862** & 4.7850 & 9.2128 & 4.7850 \\ \cline{1-1}  & Number & 5 & 4 & 6 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of signal-to-noise ratio (SNR) and effective number of singular values about two de-noised signals. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Bearing Designation** & **The Inner-Race Fault Frequency** & **The Outer-Race Fault Frequency** & **The Rolling Element Fault Frequency** & **The Ball Fundamental** & **Spin Frequency** \\ \hline ZA-2155 of & \(f_{\mathrm{1}}\,\mathrm{(Hz)}\) & \(f_{\mathrm{O}}\,\mathrm{(Hz)}\) & \(f_{\mathrm{B}}\,\mathrm{(Hz)}\) & \(f_{\mathrm{c}}\,\mathrm{(Hz)}\) & \(f_{\mathrm{BS}}\,\mathrm{(Hz)}\) \\ Rexnord & 296.9 & 236.4 & 139.9 & 14.8 & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Corresponding parameters of the experimental bearings. rise occurs after half of the 6 th day (see phase III). The changing trend of RMS over time illustrates the intrinsic characteristics of the damage propagating process: small spalls or cracks are formed and later smoothed by the continuous rolling contact in the failure of the initial state. When the damage spreads over a wider area, the vibration level rises again [5]. This paper extracted the data on the damage of the outer race in bearing 1 which chose 19 February 2004 00:42 as the occurrence of the early failure time. Next, 2480 samples were collected and time and frequency analysis was conducted. First of all, we depicted the Time-domain waveform of the early out race fault in bearing 1 in Figure 6, what we can see from the figure that the failure signal is submerged by the noise and the waveform is so confused that it is impossible to extract the tiny components of the early fault signal. Figure 7 demonstrated the de-noised result based on four methods. It is obvious that the de-noised signal in Figure 7b is cleaner than others, and the vibration of the fault signal has been recovered.