# A Novel Rolling Bearing Fault Diagnosis and Severity Analysis Method
## 6 Experiments and Results
### Fault Detection Experiment  
To demonstrate the effectiveness of the fast SampEn algorithm for rolling bearing fault detection, fault detection experiments are conducted in this section. When the SampEn is used to detect dynamical changes in vibration time series, the vibration signal should be partitioned into several non-overlapping segments with a suitable length. As discussed in Section 2, the length of the time series \(\mathbf{N}\) has enormous implications for the calculation time. Thus, setting an appropriate length \(\mathbf{N}\) is important for the SampEn calculational efficiency. Obviously, the length \(\mathbf{N}\) should not be too large because the calculation time would be too long. However, \(\mathbf{N}\) should not be too small because the SampEn value would not be effective for the fault detection of rolling bearings. [PERSON] et al. set \(N=2400\) and successfully detected and diagnosed a rolling bearing fault [36]. [PERSON] et al. [37] and [PERSON] et al. [38] respectively set \(N=4096\) and \(N=2000\) with a sampling frequency of 20 kHz. [PERSON] et al. set \(N=2400\) with a sampling frequency of 12 kHz [15]. In comparison, this study sets \(N=2400\), which not only conserves the calculation time but also produces reasonable statistical validity. The embedding dimension can be set as \(m=1\) or \(m=2\). To detect the dynamics of the change in the vibration signal and realize fault detection, set \(m=2\). The value of the similarity tolerance \(r\) affects the sensitivity degree of the SampEn to the time series complexity. The smaller the value of \(r\) is, the greater the impact of noise in the calculation results. However, the larger the value of \(r\) is, the more detailed the information loss in the time series. Therefore, the similarity tolerance is set to 0.1, which can detect the complexity changes more effectively than other settings. According to the discussion above, this study set \(N=2400\); the first 120,000 points of each original collected signal were divided into 50 segments and all of the vibration signals under different conditions are partitioned into 2400 non-overlapping segments. The SampEn values for all 2400 samples are calculated and are shown in Figure 6.  
In Figure 6, the SampEn values of samples with a fault are larger than those of the normal samples. In other words, samples with a fault have more complexity than normal samples. When the rolling bearing is working in normal conditions, the vibration mainly stems from the coupling between mechanical parts and the environmental noise, which have a certain regularity, so the SampEn values are relatively small. In contrast, when faults occur, the vibration signal of the bearing becomes more complex due to the introduction of some uncertain components. As a result, the SampEn values significantly change. The appropriate threshold value is set to 0.3, which can distinctly divide the samples with faults from normal samples irrespective of the fault diameter and the load, as shown in Figure 6. As a result, the SampEn value of the vibration signal can be an effective method to detect bearing faults. However, the SampEn value alone cannot be used to distinguish between three types of faults from Figure 6. It also cannot be used to illustrate the fault diameter. Therefore, it is necessary to further analyze the vibration signals, extract more features, and then use an effective classifier to identify the fault type and the fault diameter. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Fault Type**} & \multirow{2}{*}{**Fault Diameter (in)**} & \multicolumn{4}{c}{**Load (hp)**} \\ \cline{3-6}  & & 0 & 1 & 2 & 3 \\ \hline Normal & — & ✓ & ✓ & ✓ & ✓ \\ BF & 0.007 & ✓ & ✓ & ✓ & ✓ \\  & 0.014 & ✓ & ✓ & ✓ & ✓ \\  & 0.021 & ✓ & ✓ & ✓ & ✓ \\  & 0.028 & ✓ & ✓ & ✓ & ✓ \\ IRF & 0.007 & ✓ & ✓ & ✓ & ✓ \\  & 0.014 & ✓ & ✓ & ✓ & ✓ \\  & 0.021 & ✓ & ✓ & ✓ & ✓ \\  & 0.028 & ✓ & ✓Several complexity analysis algorithms of time-domain data have also been selected to handle the same sample sets in this paper.