Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes
Abstract
:1. Introduction
2. Higher Mode Identification
3. Kriging Model
4. Particle Swarm Optimization
5. Model Updating with Kriging Model
6. Model Updating Verification for Jalón Viaduct
6.1. Bridge Description and Summary of OMA
6.2. Updating Parameters Selection
6.3. Kriging Model Establishment
6.4. Model Updating
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Mode | Type | Initial FE Model | Ambient Vibration | Free-Ambient Vibration | ||||
---|---|---|---|---|---|---|---|---|
fa,ini (Hz) | fea (Hz) | (%) | fef | (%) | MPC | MAC | ||
1 | 1st↔ | 0.601 | 0.648 | 0.75 | 0.648 | 0.69 | 0.94 | 0.973 |
2 | 2nd↔ | 1.182 | 1.238 | 0.81 | 1.219 | 1.34 | 0.96 | 0.977 |
3 | 3rd↔ | 2.201 | 2.230 | 1.00 | 2.186 | 1.53 | 0.85 | 0.926 |
4 | 1st↕ | 3.264 | 3.279 | 0.42 | 3.267 | 0.40 | 0.96 | 0.985 |
5 | 4th↔ | 3.595 | 3.536 | 1.37 | 3.493 | 0.70 | 0.93 | 0.964 |
6 | 2nd↕ | 3.788 | 3.758 | 0.54 | 3.783 | 0.61 | 0.98 | 0.986 |
8 | 4th↕ | 4.421 | 4.471 | 0.66 | 4.452 | 0.48 | 0.98 | 0.969 |
10 | 5th↕ | 5.015 | 5.056 | 0.57 | 5.045 | 0.62 | 0.97 | 0.969 |
12 | 6th↕ | 5.996 | 6.036 | 0.69 | 6.027 | 0.70 | 0.91 | 0.911 |
Mode | Type | Initial FE Model | Free-Ambient Vibration | |||
---|---|---|---|---|---|---|
fa,ini (Hz) | fef | (%) | MPC | MAC | ||
9 | 5th↔ | 5.211 | 4.917 | 0.74 | 0.94 | 0.958 |
11 | 1st↺ | 5.717 | 5.309 | 0.73 | 0.85 | 0.865 |
13 | 6th↔ | 7.554 | 7.455 | 0.70 | 0.87 | 0.499 |
14 | 2nd↺ | 9.290 | 8.420 | 0.96 | 0.83 | 0.701 |
15 | 7th↔ | 10.180 | 9.329 | 0.96 | 0.79 | 0.649 |
Updating Parameters | Initial Value | Updated Value | Difference (%) |
---|---|---|---|
E1 (104 MPa) | 4.00 | 3.85 | −3.8 |
D1 (103 kg/m3) | 2.50 | 2.36 | −5.6 |
E2 (102 MPa) | 2.80 | 2.42 | −13.6 |
D2 (103 kg/m3) | 1.70 | 1.86 | 9.4 |
S1 (105 kN/m) | 2.00 | 3.29 | 64.5 |
S5 (105 kN/m) | 2.00 | 3.43 | 71.5 |
Mode | Mode Type | Experimental (Free–Ambient) | Initial FE Model | Updated FE Model | ||||
---|---|---|---|---|---|---|---|---|
fef (Hz) | fa,ini (Hz) | Difference (%) | MAC | fa,up (Hz) | Difference (%) | MAC | ||
1 | 1st↔ | 0.648 | 0.601 | 7.25 | 0.973 | 0.634 | 2.18 | 0.978 |
2 | 2nd↔ | 1.219 | 1.182 | 3.04 | 0.977 | 1.196 | 1.92 | 0.983 |
3 | 3rd↔ | 2.186 | 2.201 | −0.69 | 0.926 | 2.191 | −0.24 | 0.962 |
4 | 1st↕ | 3.267 | 3.264 | 0.09 | 0.985 | 3.234 | 1.00 | 0.996 |
5 | 4th↔ | 3.493 | 3.595 | −2.92 | 0.964 | 3.558 | −1.85 | 0.986 |
6 | 2nd↕ | 3.783 | 3.788 | −0.13 | 0.986 | 3.757 | 0.70 | 0.990 |
8 | 4th↕ | 4.452 | 4.421 | 0.70 | 0.969 | 4.461 | −0.20 | 0.973 |
9 | 5th↔ | 4.917 | 5.211 | −5.98 | 0.958 | 5.127 | −4.28 | 0.989 |
10 | 5th↕ | 5.045 | 5.015 | 0.59 | 0.969 | 5.047 | −0.04 | 0.986 |
11 | 1st↺ | 5.309 | 5.717 | −7.69 | 0.865 | 5.372 | −1.18 | 0.929 |
12 | 6th↕ | 6.027 | 5.966 | 1.01 | 0.911 | 5.966 | 1.02 | 0.889 |
13 | 6th↔ | 7.455 | 7.554 | −1.33 | 0.499 | 7.497 | −0.56 | 0.585 |
14 | 2nd↺ | 8.420 | 9.290 | −10.33 | 0.701 | 9.043 | −7.40 | 0.791 |
15 | 7th↔ | 9.329 | 10.180 | −9.12 | 0.649 | 10.121 | −8.49 | 0.828 |
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Qin, S.; Zhang, Y.; Zhou, Y.-L.; Kang, J. Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes. Sensors 2018, 18, 1879. https://doi.org/10.3390/s18061879
Qin S, Zhang Y, Zhou Y-L, Kang J. Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes. Sensors. 2018; 18(6):1879. https://doi.org/10.3390/s18061879
Chicago/Turabian StyleQin, Shiqiang, Yazhou Zhang, Yun-Lai Zhou, and Juntao Kang. 2018. "Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes" Sensors 18, no. 6: 1879. https://doi.org/10.3390/s18061879
APA StyleQin, S., Zhang, Y., Zhou, Y.-L., & Kang, J. (2018). Dynamic Model Updating for Bridge Structures Using the Kriging Model and PSO Algorithm Ensemble with Higher Vibration Modes. Sensors, 18(6), 1879. https://doi.org/10.3390/s18061879