Figure 1.
Winding force analysis diagram. The arrow indicates the direction of displacement.
Figure 1.
Winding force analysis diagram. The arrow indicates the direction of displacement.
Figure 2.
Schematic diagram (a) and physical diagram (b) of FBG acceleration induction.
Figure 2.
Schematic diagram (a) and physical diagram (b) of FBG acceleration induction.
Figure 3.
Transformer vibration signal acquisition system based on FBG.
Figure 3.
Transformer vibration signal acquisition system based on FBG.
Figure 4.
Vibration signal demodulation system.
Figure 4.
Vibration signal demodulation system.
Figure 5.
Fixed position of the sensor.
Figure 5.
Fixed position of the sensor.
Figure 6.
Signal pre-processing process.
Figure 6.
Signal pre-processing process.
Figure 7.
CEEMDAN-MRAL fault diagnosis method.
Figure 7.
CEEMDAN-MRAL fault diagnosis method.
Figure 8.
Structure diagram of CBAM.
Figure 8.
Structure diagram of CBAM.
Figure 9.
LSTM structure diagram.
Figure 9.
LSTM structure diagram.
Figure 10.
Residual Block 1 structure diagram (a) and Residual Block 2 structure diagram (b).
Figure 10.
Residual Block 1 structure diagram (a) and Residual Block 2 structure diagram (b).
Figure 11.
Improved structure diagram of Residual Block 1 (a) and Residual Block 2 (b).
Figure 11.
Improved structure diagram of Residual Block 1 (a) and Residual Block 2 (b).
Figure 12.
MRAL-Net network architecture.
Figure 12.
MRAL-Net network architecture.
Figure 13.
(a). Vibration in the time and frequency domains during normal time. (b). Vibrating time- and frequency–domain signals when windings are loose. (c). Vibration time and frequency domain signals when the core is loose. (d). Vibration of time- and frequency-domain signals when the core and windings are loose.
Figure 13.
(a). Vibration in the time and frequency domains during normal time. (b). Vibrating time- and frequency–domain signals when windings are loose. (c). Vibration time and frequency domain signals when the core is loose. (d). Vibration of time- and frequency-domain signals when the core and windings are loose.
Figure 14.
IMFs obtained by normal signal decomposition.
Figure 14.
IMFs obtained by normal signal decomposition.
Figure 15.
Line chart of SE, VCR, and CC of each IMF component.
Figure 15.
Line chart of SE, VCR, and CC of each IMF component.
Figure 16.
The reconstructed SNR, RMSE, CC, and R of each IMF.
Figure 16.
The reconstructed SNR, RMSE, CC, and R of each IMF.
Figure 17.
SNR, RMSE, CC, and R at 5 dB (a), 10 dB (b), and 15 dB (c).
Figure 17.
SNR, RMSE, CC, and R at 5 dB (a), 10 dB (b), and 15 dB (c).
Figure 18.
Waterfall diagram of the denoising effect of the three methods.
Figure 18.
Waterfall diagram of the denoising effect of the three methods.
Figure 19.
Undenoised MTF image (a) and denoised MTF image (b).
Figure 19.
Undenoised MTF image (a) and denoised MTF image (b).
Figure 20.
(a) Accuracy of the training set, (b) loss rate of the training set, (c) accuracy of the validation set, and (d) loss rate of the validation set.
Figure 20.
(a) Accuracy of the training set, (b) loss rate of the training set, (c) accuracy of the validation set, and (d) loss rate of the validation set.
Figure 21.
(a) Box plot of the accuracy of the training set, (b) box plot of the loss rate of the training set, (c) box plot of the accuracy of the validation set, (d) box plot of the loss rate of the validation set.
Figure 21.
(a) Box plot of the accuracy of the training set, (b) box plot of the loss rate of the training set, (c) box plot of the accuracy of the validation set, (d) box plot of the loss rate of the validation set.
Figure 22.
The average accuracy of the five network models corresponding to the four states.
Figure 22.
The average accuracy of the five network models corresponding to the four states.
Figure 23.
Ablation test results.
Figure 23.
Ablation test results.
Figure 24.
Comparison of the accuracy of the five networks combined with time-frequency analysis methods.
Figure 24.
Comparison of the accuracy of the five networks combined with time-frequency analysis methods.
Table 1.
Parameters of each network layer.
Table 1.
Parameters of each network layer.
| Kernel Size | Strides | Padding | Repeat | Output | Output Channels |
---|
Conv | 7 × 7 | 2 | 3 | | 112 × 112 | 64 |
CBAM | 1 × 1/7 × 7 | | | | 112 × 112 | 64 |
Maxpool | 3 × 3 | 2 | 1 | | 56 × 56 | 64 |
Residual1 | 3 × 3 | 1 | 1 | 2 | 56 × 56 | 64 |
Residual2 | 3 × 3 | 2 | 1 | | 28 × 28 | 128 |
Residual3 | 3 × 3 | 1 | 1 | | 28 × 28 | 128 |
Residual4 | 3 × 3 | 2 | 1 | | 14 × 14 | 256 |
Residual5 | 3 × 3 | 1 | 1 | | 14 × 14 | 256 |
Residual6 | 3 × 3 | 2 | 1 | | 7 × 7 | 512 |
Residual7 | 3 × 3 | 1 | 1 | | 7 × 7 | 512 |
AvgPool | | | | | 1 × 1 | 512 |
Flatten | | | | | 1 | 512 |
LSTM1 | | | | | 128 | |
LSTM2 | | | | | 128 | |
Linear | | | | | 4 | |
Table 2.
Number of samples in the training and test sets.
Table 2.
Number of samples in the training and test sets.
| Training Sample | Validation Sample | Testing Sample | Total Sample |
---|
Normal | 1440 | 360 | 400 | 2200 |
Iron core loosening | 1440 | 360 | 400 | 2200 |
Winding loosening | 1440 | 360 | 400 | 2200 |
Iron core and winding loose | 1440 | 360 | 400 | 2200 |
Table 3.
SE, VCR, and CC values of each IMF component.
Table 3.
SE, VCR, and CC values of each IMF component.
| IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | IMF9 | IMF10 |
---|
SE | 1.9798 | 1.6196 | 0.6316 | 0.6289 | 0.2782 | 0.0678 | 0.0953 | 0.0538 | 0.0254 | 0.0092 |
VCR | 0.0461 | 0.0124 | 0.3065 | 0.0380 | 0.5652 | 0.0263 | 0.0043 | 0.0008 | 0.0002 | 0.0003 |
CC | 0.0024 | 0.0161 | 0.5860 | 0.3916 | 0.7481 | 0.1521 | 0.0120 | 0.0037 | 0.0031 | 0.0039 |
Table 4.
Accuracy and loss rate of each model after stabilization.
Table 4.
Accuracy and loss rate of each model after stabilization.
Model | The Average Accuracy of the Training Set | The Average Accuracy of the Validation Set | The Training Set Average Loss Rate | Validation Set Average Loss Rate |
---|
MRAL-Net | 0.9986 | 0.9764 | 0.0041 | 0.1157 |
Resnet-18 | 0.9970 | 0.9655 | 0.0093 | 0.1264 |
GoogLeNet | 0.9759 | 0.9501 | 0.0685 | 0.1272 |
Alexnet | 0.9822 | 0.9411 | 0.0455 | 0.2624 |
LeNet | 0.9559 | 0.9449 | 0.1121 | 0.1385 |
Table 5.
Time spent on training each model.
Table 5.
Time spent on training each model.
Model | MRAL-Net | Resnet-18 | GoogLeNet | Alexnet | LeNet |
---|
Times | 1705 s | 1892 s | 2146 s | 1538 s | 1355 s |
Table 6.
Confusion matrix and precision, recall, and F1 score of the proposed method.
Table 6.
Confusion matrix and precision, recall, and F1 score of the proposed method.
MRAL-Net | Prediction Label | Precision | Recall | F1-Score |
---|
0 | 1 | 2 | 3 |
---|
True label | 0 | 400 | 0 | 0 | 0 | 1 | 1 | 1 |
1 | 0 | 386 | 0 | 14 | 0.9674 | 0.9650 | 0.9662 |
2 | 0 | 0 | 400 | 0 | 0.9852 | 1 | 0.9925 |
3 | 0 | 13 | 6 | 381 | 0.9646 | 0.9525 | 0.9585 |
Accuracy | 97.9375% | — |
Table 7.
Performance of the five network models corresponding to the four states.
Table 7.
Performance of the five network models corresponding to the four states.
| Precision | Recall | F1 Score |
---|
MRAL-Net | 0.9830 | 0.9794 | 0.9812 |
Resnet-18 | 0.9754 | 0.9744 | 0.9749 |
GoogLeNet | 0.9763 | 0.9756 | 0.9759 |
Alexnet | 0.9699 | 0.9694 | 0.9696 |
LeNet | 0.9424 | 0.9381 | 0.9402 |
Table 8.
Comparison of this model with the reference model.
Table 8.
Comparison of this model with the reference model.
| Precision | Recall | F1 Score | Accuracy |
---|
This method | 0.9830 | 0.9794 | 0.9812 | 0.9794 |
Ref. [16] | 0.9700 | 0.9694 | 0.9697 | 0.9694 |
Ref. [17] | 0.9765 | 0.9731 | 0.9748 | 0.9731 |
Ref. [21] | 0.9541 | 0.9538 | 0.9539 | 0.9537 |
Ref. [25] | 0.9559 | 0.9556 | 0.9557 | 0.9556 |