Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays
Abstract
1. Introduction
2. Materials and Methods
2.1. UGW Theory
2.2. Selection of the Excitation Frequency
2.3. Design of Piezoelectric Sensor Array
2.4. Principle of a BP Neural Network
2.5. Evaluation Metrics for Model Performance
3. Experiments and Systems
3.1. The Experimental System
3.2. Experiment
4. Feature Definition and Extraction
5. Evaluation Model Based on Multi-Path Reconstruction
6. Conclusions
7. Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Rail Type | Elastic Modulus (Pa) | Poisson’s Ratio (α) | Density (kg/m3) | Grid Length (m) | Excitation Signal Frequency (kHz) |
---|---|---|---|---|---|
CHN60 | 2.1 × 1011 | 0.29 | 7850 | 8.6 × 10-4 | 350 |
Evaluation Metric | Expression | Parameter Description |
---|---|---|
RMSE | is the ideal value, and N is the total amount of data. | |
is the ideal value. | ||
P_Rr010 | is the total number of test samples. | |
P_Rr005 | is the total number of test samples. |
Dimensional Feature Parameters | Dimensionless Feature Parameters | ||
---|---|---|---|
Feature Parameters | Expressions | Feature Parameters | Expressions |
Maximum value | Kurtosis | ||
Minimum value | Skewness | ||
Average value | Waveform factor | ||
Square root amplitude | Peak factor | ||
Variance biased | Impulse factor | ||
Standard deviation | Margin factor | ||
Root mean square | Clearance factor |
Feature Parameters | Expressions | Feature Parameters | Expressions |
---|---|---|---|
Centroid frequency | Root mean square frequency | ||
Mean frequency | Root variance frequency |
Path | RMSE | R2 | P_Rr010 | P_Rr005 | Path | RMSE | R2 | P_Rr010 | P_Rr005 |
---|---|---|---|---|---|---|---|---|---|
E1-R1 | 2.2233 | 0.7529 | 37.50% | 15.63% | E3-R1 | 1.5075 | 0.8855 | 37.50% | 18.75% |
E1-R2 | 1.4772 | 0.9015 | 53.13% | 40.63% | E3-R2 | 1.8944 | 0.8199 | 34.38% | 25.00% |
E1-R3 | 1.9551 | 0.8091 | 53.13% | 28.13% | E3-R3 | 0.4755 | 0.9890 | 81.25% | 59.38% |
E1-R4 | 0.6664 | 0.9782 | 87.50% | 59.38% | E3-R4 | 1.8411 | 0.8307 | 43.75% | 31.25% |
E2-R1 | 1.4222 | 0.9077 | 43.75% | 15.63% | E4-R1 | 0.8257 | 0.9660 | 78.13% | 37.50% |
E2-R2 | 1.6733 | 0.8602 | 56.25% | 21.88% | E4-R2 | 1.8289 | 0.8380 | 43.75% | 31.25% |
E2-R3 | 0.7039 | 0.9751 | 81.25% | 62.50% | E4-R3 | 0.4366 | 0.9910 | 100% | 84.38% |
E2-R4 | 0.7460 | 0.9735 | 81.38% | 68.75% | E4-R4 | 1.1635 | 0.9326 | 62.50% | 53.13% |
Path | RMSE | R2 | P_Rr010 | P_Rr005 |
---|---|---|---|---|
E-R(optimal) | 0.3762 | 0.9932 | 100% | 87.50% |
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Yang, Y.; Wang, P.; Song, T.-L.; Jiang, Y.; Zhou, W.-T.; Xu, W.-L. Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays. Sensors 2022, 22, 7023. https://doi.org/10.3390/s22187023
Yang Y, Wang P, Song T-L, Jiang Y, Zhou W-T, Xu W-L. Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays. Sensors. 2022; 22(18):7023. https://doi.org/10.3390/s22187023
Chicago/Turabian StyleYang, Yuan, Ping Wang, Tian-Lang Song, Yi Jiang, Wen-Tao Zhou, and Wei-Lei Xu. 2022. "Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays" Sensors 22, no. 18: 7023. https://doi.org/10.3390/s22187023
APA StyleYang, Y., Wang, P., Song, T.-L., Jiang, Y., Zhou, W.-T., & Xu, W.-L. (2022). Evaluation of the Transverse Crack Depth of Rail Bottoms Based on the Ultrasonic Guided Waves of Piezoelectric Sensor Arrays. Sensors, 22(18), 7023. https://doi.org/10.3390/s22187023