Weak fault diagnosis of rolling bearing based on FRFT and DBN

Figures & data

Figure 1. Time-frequency plane rotated by an angle.

Figure 2. Filtering in fractional domain.

Figure 3. Original signal.

Figure 4. Signal with noise.

Figure 5. Three-dimensional diagram of signal after fractional Fourier signal.

Figure 6. FRFT filtering.

Figure 7. Filtered signal.

Figure 8. Structure of RBM.

Figure 9. Schematic diagram of DBN structure.

Figure 10. Flow chart of fault diagnosis.

Figure 11. Normal data waveform.

Figure 12. General fault data waveform.

Figure 13. Weak fault data waveform.

Table 1. Bearing sample data.

Data category	Fault category	Fault description	Fault degree
1	Normal data		Normal
2	Cage break	Cut off	General fault
3	Spalling of the rolling element	About 1 mm^2, in the middle of the raceway
4	Spalling on the inner ring	About 1 mm^2, in the middle of the raceway
5	Spalling on the outer ring	About 1 mm^2, in the middle of the raceway
6	Cage break	1/4 of the cage	Weak fault
7	Spalling of the rolling element	About 0.5 mm^2, slightly deviated
8	Spalling on the inner ring	About 0.5 mm^2, slightly deviated
9	Spalling on the outer ring	About 0.5 mm^2, slightly deviated

Figure 14. Three-dimensional diagram of cage fault data FRFT.

Figure 15. Comparison diagram of cage fault data.

Figure 16. Other types of general fault filtering waveform.

Figure 17. Weak fault filtering waveform.

Table 2. Two sample datasets.

Data set	Data category	Training set	Test set	Total
A	Original data	3240	1080	4320
B	FRFT	3240	1080	4320

Figure 18. Comparison of accuracy rate of data sets A and B.

Table 3. Average diagnosis accuracy rate of each type of fault.

Fault type	Set A (%)	Set B (%)
Normal	100	100
General fault of cage	74.08	91.58
General fault of rolling element	85.50	99.42
General fault of inner ring	91.75	96.50
General fault of outer ring	97.42	93.08
Weak fault of cage	52.83	87.75
Weak fault of rolling element	52.33	95.75
Weak fault of inner ring	85.58	99.41
Weak fault of outer ring	57.33	87.41
Total	77.44	94.5