Figure 1.
A flowchart outlining the proposed method.
Figure 1.
A flowchart outlining the proposed method.
Figure 2.
Schematic diagram showing the three-layer wavelet packet decomposition.
Figure 2.
Schematic diagram showing the three-layer wavelet packet decomposition.
Figure 3.
Schematic diagram showing a convolution autoencoder network.
Figure 3.
Schematic diagram showing a convolution autoencoder network.
Figure 4.
Schematic diagram showing the dilated causal convolution operation.
Figure 4.
Schematic diagram showing the dilated causal convolution operation.
Figure 5.
Schematic diagram showing the residual block in TCN.
Figure 5.
Schematic diagram showing the residual block in TCN.
Figure 6.
Multi-step forecasting. (a) Recursive multi-step prediction. (b) Direct multi-step forecasting.
Figure 6.
Multi-step forecasting. (a) Recursive multi-step prediction. (b) Direct multi-step forecasting.
Figure 7.
Rolling bearing full life test bench.
Figure 7.
Rolling bearing full life test bench.
Figure 8.
Lifetime vibration signal of the 1#bearing.
Figure 8.
Lifetime vibration signal of the 1#bearing.
Figure 9.
Variation trend in time domain feature of 1#bearing. (a) Dimensional time domain features. (b) Dimensionless time domain features.
Figure 9.
Variation trend in time domain feature of 1#bearing. (a) Dimensional time domain features. (b) Dimensionless time domain features.
Figure 10.
Variation trend in the frequency domain feature of 1#bearing.
Figure 10.
Variation trend in the frequency domain feature of 1#bearing.
Figure 11.
Variation trend in the time–frequency domain features of 1#bearing.
Figure 11.
Variation trend in the time–frequency domain features of 1#bearing.
Figure 12.
Comprehensive evaluation index of characteristics of 1#bearing.
Figure 12.
Comprehensive evaluation index of characteristics of 1#bearing.
Figure 13.
The contribution rate of the top 10 principal components of 1#bearing.
Figure 13.
The contribution rate of the top 10 principal components of 1#bearing.
Figure 14.
The cumulative contribution rate of the principal components of 1#bearing.
Figure 14.
The cumulative contribution rate of the principal components of 1#bearing.
Figure 15.
Variation trend in the top 4 principal components of 1#bearing.
Figure 15.
Variation trend in the top 4 principal components of 1#bearing.
Figure 16.
HI constructed using different methods of 1#bearing.
Figure 16.
HI constructed using different methods of 1#bearing.
Figure 17.
Performance degradation prediction for the 1#bearing based on different methods.
Figure 17.
Performance degradation prediction for the 1#bearing based on different methods.
Figure 18.
The structure of RCF-A machine.
Figure 18.
The structure of RCF-A machine.
Figure 19.
Schematic diagram showing the shaft box of an RCF-A machine. 1: Accompanying axle box and 2: spindle box.
Figure 19.
Schematic diagram showing the shaft box of an RCF-A machine. 1: Accompanying axle box and 2: spindle box.
Figure 20.
The installation position of the accelerometer. 1: Specimen; 2: accompanying specimen; 3: acceleration sensor; and 4: fuel injection pipe.
Figure 20.
The installation position of the accelerometer. 1: Specimen; 2: accompanying specimen; 3: acceleration sensor; and 4: fuel injection pipe.
Figure 21.
The control interface of the RCF-A machine.
Figure 21.
The control interface of the RCF-A machine.
Figure 22.
Comparison of specimen before and after the test. (a) Before the test and (b) after the test. 1: Pitting and 2: crack spalling.
Figure 22.
Comparison of specimen before and after the test. (a) Before the test and (b) after the test. 1: Pitting and 2: crack spalling.
Figure 23.
Fatigue damage and evolution process of the specimen surface. (a) Normal status; (b) pitting; (c) cracks appear; (d) crack propagation; (e) further crack growth; and (f) flaking occurs.
Figure 23.
Fatigue damage and evolution process of the specimen surface. (a) Normal status; (b) pitting; (c) cracks appear; (d) crack propagation; (e) further crack growth; and (f) flaking occurs.
Figure 24.
Vibration signal during the whole life cycle of the specimen.
Figure 24.
Vibration signal during the whole life cycle of the specimen.
Figure 25.
Variation trend in time domain feature of specimen. (a) Dimensional feature. (b) Dimensionless features.
Figure 25.
Variation trend in time domain feature of specimen. (a) Dimensional feature. (b) Dimensionless features.
Figure 26.
Variation trend in the frequency domain feature of specimen.
Figure 26.
Variation trend in the frequency domain feature of specimen.
Figure 27.
Variation trend in the time–frequency domain features of specimen.
Figure 27.
Variation trend in the time–frequency domain features of specimen.
Figure 28.
Comprehensive evaluation index value of each feature of specimen.
Figure 28.
Comprehensive evaluation index value of each feature of specimen.
Figure 29.
The contribution rate of the top 10 principal components of specimen.
Figure 29.
The contribution rate of the top 10 principal components of specimen.
Figure 30.
The cumulative contribution rate of the principal components of specimen.
Figure 30.
The cumulative contribution rate of the principal components of specimen.
Figure 31.
Variation trend in the top 4 principal components of specimen.
Figure 31.
Variation trend in the top 4 principal components of specimen.
Figure 32.
HI constructed using different methods of specimen.
Figure 32.
HI constructed using different methods of specimen.
Figure 33.
Prediction results of the different prediction models.
Figure 33.
Prediction results of the different prediction models.
Figure 34.
Prediction results obtained using TCN under different prediction step sizes.
Figure 34.
Prediction results obtained using TCN under different prediction step sizes.
Table 1.
Time domain feature parameters.
Table 1.
Time domain feature parameters.
No. | Feature | Calculation Formula |
---|
Dimensional Time Domain Features |
f1 | mean | |
f2 | rms value | |
f3 | variance | |
f4 | absolute mean | |
f5 | root amplitude | |
f6 | peak | |
f7 | peak to peak | |
Dimensionless time domain features |
f8 | skewness index | |
f9 | kurtosis index | |
f10 | peak indicator | |
f11 | margin indicator | |
f12 | impulse indicator | |
f13 | waveform indicator | |
Table 2.
Frequency domain feature parameters.
Table 2.
Frequency domain feature parameters.
No. | Feature | Calculation Formula |
---|
f14 | frequency amplitude mean | |
f15 | frequency amplitude variance | |
f16 | first-order center of gravity | |
f17 | second-order center of gravity | |
f18 | rms frequency | |
f19 | frequency domain features 1 | |
f20 | frequency domain features 2 | |
f21 | frequency domain features 3 | |
f22 | frequency domain features 4 | F9 = F4/F3 |
f23 | frequency domain features 5 | |
f24 | frequency domain features 6 | |
f25 | frequency domain features 7 | |
Table 3.
The network architecture and parameters of CAE.
Table 3.
The network architecture and parameters of CAE.
Network Layer | Dimensions Entered | Size of Convolution Kernel | Number of Convolution Kernels | Dimensions of the Output |
---|
Convolutional layer 1 | 4 × 1 | 2 × 1 | 5 | 3 × 5 |
Convolutional layer 2 | 3 × 5 | 2 × 1 | 5 | 2 × 3 |
Convolutional layer 3 | 2 × 3 | 2 × 1 | 1 | 1 × 1 |
Transpose convolutional layer 1 | 1 × 1 | 2 × 1 | 4 | 2 × 4 |
Transpose convolutional layer 2 | 2 × 4 | 2 × 1 | 4 | 3 × 4 |
Transpose convolutional layer 3 | 3 × 4 | 2 × 1 | 2 | 4 × 1 |
Table 4.
Performance of the HI constructed using different methods.
Table 4.
Performance of the HI constructed using different methods.
Evaluation Indicator | CAE-HI | AE-HI | GMM-HI |
---|
Monotonicity | 0.2513 | 0.2411 | 0.1801 |
Trend | 0.9462 | 0.9430 | 0.9454 |
Table 5.
Evaluation metrics for the different prediction models.
Table 5.
Evaluation metrics for the different prediction models.
Evaluation Indicator | Predictive Model |
---|
TCN | LSTM | GRU |
---|
RMSE | 0.0257 | 0.0385 | 0.0366 |
MAE | 0.0187 | 0.0264 | 0.0234 |
Table 6.
Working conditions.
Table 6.
Working conditions.
Specimen Material | Rotational Speed (r/min) | Slip Rate | Radial Load (N) | Sampling |
---|
Main Shaft (Specimen) | Accompanying Shaft (Accompanying Specimen) | Frequency (kHz) | Single Sample Duration (s) | Sampling Interval (min) |
---|
40Cr | 1000 | 1100 | 10% | 2071 | 10 | 1 | 2 |
Table 7.
Evaluation index for the different prediction models.
Table 7.
Evaluation index for the different prediction models.
Evaluation Indicators | Predictive Model |
---|
TCN | GRU | LSTM |
---|
RMSE | 0.0146 | 0.0555 | 0.0744 |
MAE | 0.0105 | 0.0308 | 0.0423 |
Table 8.
Evaluation index for TCN model under different prediction step size.
Table 8.
Evaluation index for TCN model under different prediction step size.
Evaluation Indicator | 1#Bearing | Specimen |
---|
Prediction Step Size |
---|
3 | 4 | 5 | 3 | 4 | 5 |
---|
RMSE | 0.0257 | 0.0333 | 0.0418 | 0.0146 | 0.0259 | 0.0393 |
MAE | 0.0187 | 0.0243 | 0.0305 | 0.0105 | 0.0164 | 0.0270 |