Seismic Damage Identification Method for Curved Beam Bridges Based on Wavelet Packet Norm Entropy
Abstract
:1. Introduction
2. Basic Theory
2.1. Wavelet Packet Transform
2.2. Lp Norm
2.3. Information Entropy
3. Damage Identification Method
3.1. Damage Identification Index
3.2. Damage Identification Steps
4. Dynamic Analysis of CCRFB
4.1. Establish a CCRFB Finite Element Model
4.2. Set Damage Scenarios
4.3. Enter Ground Motion Acceleration
4.4. Measured Dynamic Response
5. Damage Identification for CCRFB
5.1. Choose Optimal Dynamic Response
5.2. Select Optimal Wavelet Packet Parameters
5.3. Select Valid p Values
5.4. Damage Identification Results
6. Discussion
6.1. Compare Identification Index Der
6.2. Noise Resistance Analysis
6.3. Effect of Seismic Excitation
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Damage Location | Stiffness Reduction Rate | Damage Scenarios | Damage Location | Stiffness Reduction Rate | Damage Scenarios |
---|---|---|---|---|---|
I, II | 0% | 1 | |||
I | 5% | 2 | II | 5% | 9 |
I | 10% | 3 | II | 10% | 10 |
I | 15% | 4 | II | 15% | 11 |
I | 20% | 5 | II | 20% | 12 |
I | 25% | 6 | II | 25% | 13 |
I | 30% | 7 | II | 30% | 14 |
I | 35% | 8 | II | 35% | 15 |
Lower Damage I (EWWPNE) | Upper Damage II (SEWWPNE) | |
---|---|---|
Damage warning value | 3.8000 × 10−2 | 5.9645 × 10−4 |
Scenario | MRR(%) | FRR(%) | NII(%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SNR(dB) | SNR(dB) | SNR(dB) | ||||||||||
20 | 30 | 40 | 50 | 20 | 30 | 40 | 50 | 20 | 30 | 40 | 50 | |
2 | 8.92 | 2.03 | 0.00 | 0.00 | 14.42 | 7.76 | 2.56 | 0.00 | 77.95 | 90.37 | 97.44 | 100.00 |
3 | 5.21 | 1.70 | 0.00 | 0.00 | 10.27 | 5.47 | 0.80 | 0.00 | 85.06 | 92.92 | 99.20 | 100.00 |
4 | 1.09 | 0.04 | 0.00 | 0.00 | 8.71 | 3.28 | 0.10 | 0.00 | 90.29 | 96.68 | 99.90 | 100.00 |
5 | 0.02 | 0.00 | 0.00 | 0.00 | 3.55 | 1.29 | 0.00 | 0.00 | 96.43 | 98.71 | 100.00 | 100.00 |
6 | 0.00 | 0.00 | 0.00 | 0.00 | 1.08 | 1.06 | 0.00 | 0.00 | 98.92 | 98.94 | 100.00 | 100.00 |
7 | 0.00 | 0.00 | 0.00 | 0.00 | 0.53 | 0.25 | 0.00 | 0.00 | 99.47 | 99.75 | 100.00 | 100.00 |
8 | 0.00 | 0.00 | 0.00 | 0.00 | 0.09 | 0.00 | 0.00 | 0.00 | 99.91 | 100.00 | 100.00 | 100.00 |
Scenario | MRR(%) | FRR(%) | NII(%) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
SNR(dB) | SNR(dB) | SNR(dB) | ||||||||||
40 | 50 | 60 | 70 | 40 | 50 | 60 | 70 | 40 | 50 | 60 | 70 | |
9 | 12.34 | 4.55 | 1.07 | 0.48 | 17.29 | 3.34 | 2.45 | 1.12 | 72.50 | 92.26 | 96.51 | 98.40 |
10 | 9.28 | 2.29 | 0.02 | 0.00 | 13.70 | 1.46 | 0.43 | 0.20 | 78.29 | 96.28 | 99.55 | 99.80 |
11 | 7.90 | 1.15 | 0.00 | 0.00 | 10.55 | 0.83 | 0.02 | 0.00 | 82.38 | 98.03 | 99.98 | 100.00 |
12 | 3.89 | 0.05 | 0.00 | 0.00 | 7.01 | 0.46 | 0.00 | 0.00 | 89.37 | 99.49 | 100.00 | 100.00 |
13 | 0.77 | 0.00 | 0.00 | 0.00 | 4.96 | 0.01 | 0.00 | 0.00 | 94.31 | 99.99 | 100.00 | 100.00 |
14 | 0.06 | 0.00 | 0.00 | 0.00 | 3.01 | 0.00 | 0.00 | 0.00 | 96.93 | 100.00 | 100.00 | 100.00 |
15 | 0.00 | 0.00 | 0.00 | 0.00 | 2.11 | 0.00 | 0.00 | 0.00 | 97.89 | 100.00 | 100.00 | 100.00 |
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Deng, T.; Huang, J.; Cao, M.; Li, D.; Bayat, M. Seismic Damage Identification Method for Curved Beam Bridges Based on Wavelet Packet Norm Entropy. Sensors 2022, 22, 239. https://doi.org/10.3390/s22010239
Deng T, Huang J, Cao M, Li D, Bayat M. Seismic Damage Identification Method for Curved Beam Bridges Based on Wavelet Packet Norm Entropy. Sensors. 2022; 22(1):239. https://doi.org/10.3390/s22010239
Chicago/Turabian StyleDeng, Tongfa, Jinwen Huang, Maosen Cao, Dayang Li, and Mahmoud Bayat. 2022. "Seismic Damage Identification Method for Curved Beam Bridges Based on Wavelet Packet Norm Entropy" Sensors 22, no. 1: 239. https://doi.org/10.3390/s22010239