## 4 Experimental Investigations
### Obtain the Measured Signals and Classification Results  
The four different faulty signals are collected, including shaft unbalance, misalignment, rub-impact and the combination of rub-impact and unbalance. Figure 10 shows the four faults of the shaft in the experimental operation. In order to conduct the unbalance fault, we add a bob-weight (2 g) mounted on the disk, as shown in Figure 10a. Figure 10b shows the metal washer (which change the height and angle of shaft) added to the bottle of the motor to simulate the misalignment fault. We operate the rub-impact fault of the shaft using a screw contacting the shaft surface, as shown in Figure 10c. Figure 10d shows the combination of rub-impact and unbalance. The vibration signals of shaft unbalance, misalignment, rub-impact and the combination of rub-impact and unbalance are shown in Figure 11a-d, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Combinations Number** & \(x+\) & \(x-\) & \(y+\) & \(y-\) & \(\rho(x,y)\) \\ \hline \multirow{3}{*}{A} & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \(K\): 15.3 \(\times\) 10\({}^{7}\) & \(K\): 25.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1400 & C: 1000 & C: 1500 & C: 900 & \\ \hline \multirow{3}{*}{B} & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1400 & C: 1000 & C: 1500 & C: 900 & \\ \hline \multirow{3}{*}{C} & \(K\): 18.3 \(\times\) 10\({}^{7}\) & \(K\): 28.5 \(\times\) 10\({}^{7}\) & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1400 & C: 1000 & C: 1500 & C: 900 & \\ \hline \multirow{3}{*}{D} & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \(K\): 15.3 \(\times\) 10\({}^{7}\) & \(K\): 25.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1500 & C: 1100 & C: 1600 & C: 1000 & \\ \hline \multirow{3}{*}{E} & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1500 & C: 1100 & C: 1600 & C: 1000 & \\ \hline \multirow{3}{*}{F} & \(K\): 18.3 \(\times\) 10\({}^{7}\) & \(K\): 28.5 \(\times\) 10\({}^{7}\) & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1500 & C: 1100 & C: 1600 & C: 1000 & \\ \hline \multirow{3}{*}{G} & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \(K\): 15.3 \(\times\) 10\({}^{7}\) & \(K\): 25.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1600 & C: 1200 & C: 1700 & C: 1100 & \\ \hline \multirow{3}{*}{H} & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \(K\): 16.3 \(\times\) 10\({}^{7}\) & \(K\): 26.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1600 & C: 1200 & C: 1700 & C: 1100 & \\ \hline \multirow{3}{*}{I} & \(K\): 18.3 \(\times\) 10\({}^{7}\) & \(K\): 28.5 \(\times\) 10\({}^{7}\) & \(K\): 17.3 \(\times\) 10\({}^{7}\) & \(K\): 27.5 \(\times\) 10\({}^{7}\) & \\ \cline{2-6}  & C: 1600 & C: 1200 & C: 1700 & C: 1100 & \\ \hline \hline \end{tabular} \({}^{1}\)\(K\) (N/m), C (N\(\cdot\)m/s).  
\end{table} 
Table 4: The nine different combinations of stiffness and damping coefficients and the corresponding \(\rho(x,y)\)\({}^{1}\). Figure 11: The measured signals with different kinds of faults. (**a**) The measured signals with unbalance fault; (**b**) the measured signals with misalignment fault; (**c**) the measured signals with rub-impact fault; (**d**) the measured signals with the combination of rub-impact and unbalance fault. Figure 10: Four faults of a shaft in the experimental operation. (**a**) Unbalance; (**b**) misalignment; (**c**) rub-impact; (**d**) the combination of rub-impact and unbalance. The 8000 data points collected for the different faults are divide into 20 segments, respectively, and each corresponding segment contains 400 data points.