## 4 Applications to Gear and Bearing Fault Classification  
### Application to Processing of Case Western Reserve University Bearing Data  
Through numerical simulations, the proposed method based on the smooth local subspace projection method and PE can be applied to the signal which contains a frequency modulated signal in this section. The fault bearing data from the _Case Western Reserve University Bearing Data Center Website_[53] is used to verify the proposed method. The website provides a large collection of experimental bearing data that  
Figure 21: Time domain plot of noisy FM signal.  
Figure 22: PE values of noisy FM signal along with time.  
are related to faulty bearings, and among those, the data for faulty bearings are acquired by using electric spark machining. In this paper, inner race, ball, and outer race fault data of rolling bearings are adopted. The sampling frequency in the experiment is 12000 Hz, and the rotational speed is 1730 rpm. Experimental fault bearing type is 6205-2 RS JEM SKF, and its specific parameters are shown in Table 3.  
The test equipment of _Case Western Reserve University_ (Cleveland, OHIO, USA) includes two motors, a coupling (containing torque sensor and encoder), and other related devices. An accelerometer is placed on the testing site to collect the acceleration signal that can be used for bearing fault analysis. The schematic diagram of a signal acquisition device and a picture are shown in Figure 23.  
The collected signals, such as rolling bearings of defect on inner race, ball and outer race, contain a lot of noises, so it is difficult to classify the fault conditions of rolling bearing. The time domain plots of one set of gear signals are shown in Figures 24-26.  
It can be seen from Figures 24-26 that the spectral analysis of these groups of signals cannot show the difference between different kinds of rolling bearing faults. Hence, the smooth local subspace projection method is applied to denoise 12 groups of signals for 10 times iteration denoising, and PE values of original vibration signals and denoised vibration signals are calculated, to conduct a fault classification of rolling bearings.  
The results are shown in Figures 27 and 28, respectively.  
Through the permutation entropies of original signals and denoised signals above, it can show that before the smooth local subspace projection denoising, the PE values of one working condition are not distinguished from another working condition. All the PE values are aliasing, as shown in Figure 27. However, after the bearing vibration signals are denoised by the local projection method, the entropies of gear signals of four kinds of working conditions are distinguished very clearly. As shown in Figure 28, the PE values of the vibration signals of a ball defect bearing are the smallest, in range from 3.26 to 3.58, and their mean value is 3.34; the PE values of vibration signals of an inner race defect range from 3.64 to 3.78, and their mean value is 3.70; the PE values of vibration signals of the outer race defect range from 3.99 to 4.23, and their mean value is 4.12. The PE values of different fault types have different mean values and ranges, which can be applied to classify different kinds of mechanical fault types.  
Figure 26: The time domain plot of outer race defect.  
Figure 25: The time domain plot of inner race defect.  
signals. Hence, it can come to a conclusion that rolling bearings with different kinds of defect can be classified by the proposed method based on the proposed smooth local subspace projection method, using the logarithmic weighting function and PE. To sum up, the application researches demonstrate the effectiveness of the proposed method in the fault classification of rolling bearings.