Fault Diagnosis of Rolling Bearing Based on S-Transform and Convolutional Neural Network

Fig. 4. Ten kinds of simulation signal diagrams. (a) Normal signal; (b) OR 0.1778 nm; (c) OR 0.3556 mm; (d) OR 0.5334 mm; (e) B 0.1778 nm; (f) B 0.3556 mm; (g) B 0.5334 mm; (h) IR 0.1778 nm; (i) IR 0.3556 mm; (j) IR 0.5334 mm

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Fig. 5. Time frequency transformation results of 10 kinds of time domain signals. (a) Normal signal; (b) OR 0.1778 nm; (c) OR 0.3556 mm; (d) OR 0.5334 mm; (e) B 0.1778 nm; (f) B 0.3556 mm; (g) B 0.5334 mm; (h) IR 0.1778 nm; (i) IR 0.3556 mm; (j) IR 0.5334 mm

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Fig. 6. Graying results of 10 kinds frequency images. (a) Normal signal; (b) OR 0.1778 nm; (c) OR 0.3556 mm; (d) OR 0.5334 mm; (e) B 0.1778 nm; (f) B 0.3556 mm; (g) B 0.5334 mm; (h) IR 0.1778 nm; (i) IR 0.3556 mm; (j) IR 0.5334 mm

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Fig. 7. Experimental results of two activation functions

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Fig. 8. Experimental results of different networks

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Fig. 9. Performance comparison of 4 types of networks

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Table 1. Experimental data

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Table 1. Experimental data

Type	Bearing condition	Fault diameter /mm	Data length	Number of samples	Load	Speed /(r·min^-1)
1	norm	0	1024	2000	2	1797
2	slight damage to inner ring	0.1778	1024	2000	2	1797
3	moderate damage of inner ring	0.3556	1024	2000	2	1797
4	severe damage of inner ring	0.5334	1024	2000	2	1797
5	slight damage of rolling element	0.1778	1024	2000	2	1797
6	moderate damage of rolling element	0.3556	1024	2000	2	1797
7	rolling weight injury	0.5334	1024	2000	2	1797
8	slight damage of outer ring	0.1778	1024	2000	2	1797
9	slight damage of outer ring	0.3556	1024	2000	2	1797
10	slight damage of outer ring	0.5334	1024	2000	2	1797

Table 2. Fault code

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Table 2. Fault code

Fault location	Fault diameter /mm	Code name	Label
None	0	a	100000000
Rolling element+inner ring	0.1778	b	010000000
Rolling element+outer ring	0.3556	c	001000000
Rolling element+outer ring	0.5334	d	001000000
Inner ring	0.1778	e	000100000
Inner ring	0.3556	f	000010000
Inner ring	0.5334	g	000001000
Outer ring	0.1778	i	000000100
Outer ring	0.3556	j	000000010
Outer ring	0.5334	k	000000001

Table 3. Effects of different learning rates on network performance
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Table 3. Effects of different learning rates on network performance
Learning rate Accuracy /% Training time /s
1 69.64 134
0.1 34.42 128
0.05 73.03 132
0.005 99.87 127
0.001 91.01 144

Table 4. Effects of different Batchsize on network performance
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Table 4. Effects of different Batchsize on network performance
Batchsize Accuracy /% Training time /s
8 99.81 226
16 99.62 141
32 91.38 237
64 88.76 124
128 80.52 138

Table 5. Effects of different convolution kernel on network performance
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Table 5. Effects of different convolution kernel on network performance
Convolution kernel size Accuracy /% Training time /s
3×3 98.7 84
5×5 93.2 98
8×8 92.4 79
12×12 91.8 77

Table 6. Structural parameters of the CNN

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Table 6. Structural parameters of the CNN

Network layer type	Specific parameter	Network layer output
Input	input of time-frequency diagram	32×32
C1	3×3 convolution kernels(32), in steps of 1	30×30×32
S1	maximum pool 2×2 cores, in steps of 1	15×15×32
C2	3×3 convolution kernels(32), in steps of 2	13×13×32
S2	maximum pool 2×2 cores, in steps of 2	7×7×32
FC	1568 nodes	1×1568
Softmax	10-classification	1×10

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Qingrong Wang, Lei Yang, Songsong Wang. Fault Diagnosis of Rolling Bearing Based on S-Transform and Convolutional Neural Network[J]. Laser & Optoelectronics Progress, 2021, 58(22): 2207001

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