## 5 Experimental Result and Analysis
### The Proposed Method Analysis  
Figure 15 shows the time waveforms of the rotor vibration signals corresponds to four rotor states. Then both the ISSD and EMD methods were employed to perform the time-frequency analysis on the rotor vibration signals. Figure 16 shows the ISSD-HT TFS of the four rotor states. From Figure 16, we can find that there are obvious differences among the four rotor fault types. For the normal state, only the 1X harmonic of the rotation frequency, i.e., 50 Hz, could be found and its amplitude is relatively small. The ISSD-HT TFS of the rubbing state is composed of the fundamental frequency and its 2X and 3X harmonics, i.e., 29.33 Hz, 58.66 Hz and 87.99 Hz. For the oil film whirl state, the fundamental frequency and its 0.5X and 1.5X harmonics, i.e., 50 Hz, 25 Hz and 75 Hz, can be detected from the  
Figure 14: The schematic diagram of rubbing.  
ISSD-HT TFS. The main frequency component reflected in the ISSD-HT TFS of the imbalance state include the fundamental frequency (25 Hz), the 2X harmonic frequency (50 Hz), the 3X harmonic frequency (75 Hz) and some other discrete high-frequency components. The ISSD-HT TFS displays the fault characteristics of rotor fault accurately and different fault types can be distinguished apparently. Hence, the energy distribution characteristics of the ISSD-HT TFS can be extracted to distinguish the rotor states.  
Figure 16: The ISSD-HT time–frequency spectrum of (**a**) Normal state; (**b**) rubbing state; (**c**) oil film whirl state; (**d**) imbalance state.  
Figure 15: The waveforms of the signal of (**a**) Normal state; (**b**) rubbing state; (**c**) oil film whirl state; (**d**) imbalance state.  
Figure 17 shows the HHT TFS, i.e., the EMD-HT TFS of the four rotor states. From Figure 17, it can be visible that the energy of the TFS of the four rotor states concentrates near the fundamental frequency, and there are no obvious differences among different states. At the same time, the fault characteristic frequencies of rotor faults are hard to be detected from the EMD-HT TFS due to the serious mode problems. The ISSD-HT TFS describes the fault signatures of rotor faults more accurately compared with the EMD-HT TFS.  
Then, the proposed approach was employed to realize the intelligent fault diagnosis of rotor faults. First, the CFBEE of the ISSD-HT TFS of the four simulated states was calculated by using the calculation method introduced above. Figure 18 shows the cure of the CFBEE (each state includes 40 samples). It is obvious that the tendency of feature distribution for a specific rotor state is almost the same, and different rotor states have different trends. Thus, the state of the rotor can be characterized effectively by using the CFBEE index. To diagnose the state of the rotor automatically, SVM was adopted. The calculated CFBEE as the fault feature vectors were input to SVM for training and classifying. The classification results of the test sample sets obtained using SVM is shown in Figure 19. The category label 1, 2, 3 and 4 respect the normal state, rubbing state, oil film whirl state and imbalance state, respectively. The state diagnosis accuracy of the proposed method is 100%. This indicates the proposed approach is very effective for identifying rotor faults.  
Figure 17: The EMD-HT time–frequency spectrum of (**a**) Normal state; (**b**) rubbing state; (**c**) oil film whirl state; (**d**) imbalance state.