A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders
Abstract
:1. Introduction
- Unknown boundary conditions often challenge the application of time-domain model updating for bridges since the model parameters are often dependent on the boundary conditions. Here, the modal-based model updating is used to identify the boundary conditions first.
- The application of modal-based model updating for damage identification of bridges is limited. This is likely due to the uncertainties in the identified modal signatures that propagate through the parameter estimation process. Therefore, here, the estimation of model parameters for damage identification will be refined through a subsequent time-domain model updating.
- The dynamic measurements can provide more information about the uncertain material parameters compared to the static/pseudo-static responses. Hence, here, the acceleration measurements are used directly in the time-domain model updating.
- To improve the numerical stability and convergence of the model parameters the linear and nonlinear response behavior of the bridge are assimilated through the two-step model updating process.
2. Material, Test Methodology, and Preliminary Results
2.1. Description of the Field Experiment
2.1.1. Testbed Structure
2.1.2. Dynamic Excitation System
2.1.3. Wireless Sensing Network
2.1.4. Forced-Vibration Testing
2.2. Modal Identification
2.3. Finite Element Modeling of the Testbed Structure
3. Two-Step Model Updating: Methodology, Results, and Discussion
3.1. First Step: Modal-Based Model Updating
3.2. Second Step: Time-Domain Model Updating
3.2.1. Identifiability Analysis for Time-Domain Model Updating
3.2.2. Bayesian Inference
3.2.3. Results
4. Conclusions
- Identifiability analysis showed significant mutual dependency between different model parameters. This mutual dependency could lead to weak identifiability of model parameters in the traditional FE model updating process. The proposed two-step model updating helped with this challenge to update the most sensitive model parameters separately using modal-based and time-domain model updating.
- Sequential application of modal-based and time-domain model updating reduced the challenges due to ill-conditioning and modeling errors.
- It was demonstrated that the updated FE model using only modal-based model updating was not capable of reflecting true response behavior of the structure in time domain.
- Concrete compressive strength was correlated with damage/deterioration in the monitored structure and could be used to assess the health condition of the structure. In this study, a 30% reduction in concrete compressive strength from its nominal value correctly showed significant deterioration in the studied girders.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Mode Number | ||||||
---|---|---|---|---|---|---|
1 (Tr *) | 2 (Tr) | 3 (V **) | 4 (Tr) | 5 (V) | 6 (To ***) | |
4.07 | 5.57 | 9.73 | 9.76 | 12.79 | 20.98 | |
1.92 | 1.78 | 2.97 | 0.60 | 1.39 | 2.18 |
Parameter | Parameter Description | Initial Values |
---|---|---|
Concrete compressive strength/Concrete modulus of elasticity for the west girder | 46 MPa/46 GPa | |
Concrete compressive strength/Concrete modulus of elasticity for the east girder | 46 MPa/46 GPa | |
Modulus of elasticity for coupling beams | 30 GPa | |
Rotational stiffness of bearing pads about directions 1 and 2 and 3 | ||
Vertical stiffness of bearing pads in direction 3 | ||
Transverse stiffness of bearing pads in direction 1 | ||
Longitudinal stiffness of bearing pads in direction 2 | ||
Damping coefficient for bearing pads in direction 3 | ||
Damping ratio for mode 1 | 0.02 | |
Damping ratio for mode 2 | 0.02 |
Parameter | ||||||
---|---|---|---|---|---|---|
Updated value | 39 MPa/39 GPa | 39 MPa/39 GPa | 28.23 GPa |
Data I.D. | Layout | Target Load Amplitude | Excitation Frequencies | Data I.D. | Layout | Target Load Amplitude | Excitation Frequencies |
---|---|---|---|---|---|---|---|
1-1 | 1 | 445 N | 9.73 Hz and 12.86 Hz | 2-1 | 2 | 445 N | 9.73 Hz and 12.86 Hz |
1-2 | 1 | 2225 N | 9.73 Hz and 12.86 Hz | 2-2 | 2 | 2225 N | 9.73 Hz and 12.86 Hz |
1-3 | 1 | 4450 N | 9.73 Hz and 12.86 Hz | 2-3 | 2 | 4450 N | 9.73 Hz and 12.86 Hz |
9.73 Hz Excitation Frequency | 12.86 Hz Excitation Frequency | ||||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Data I.D. | CH # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
1-1 | Prior | 201 | 75 | 74 | 80 | 66 | 170 | 76 | 74 | 83 | 46 | 161 | 63 | 63 | 70 | 67 | 202 | 67 | 68 | 72 | 97 |
Posterior | 172 | 14 | 9 | 22 | 27 | 192 | 22 | 17 | 28 | 28 | 132 | 16 | 15 | 22 | 40 | 153 | 11 | 11 | 23 | 57 | |
1-2 | Prior | 163 | 107 | 110 | 102 | 127 | 119 | 101 | 102 | 99 | 101 | 300 | 112 | 117 | 103 | 164 | 565 | 133 | 140 | 109 | 269 |
Posterior | 24 | 11 | 10 | 10 | 22 | 34 | 10 | 9 | 8 | 21 | 72 | 23 | 24 | 24 | 30 | 133 | 20 | 21 | 13 | 55 | |
1-3 | Prior | 191 | 128 | 134 | 116 | 165 | 137 | 114 | 118 | 108 | 130 | 429 | 146 | 156 | 126 | 235 | 1111 | 193 | 205 | 141 | 480 |
Posterior | 24 | 11 | 12 | 20 | 21 | 46 | 11 | 13 | 18 | 18 | 90 | 33 | 35 | 35 | 41 | 254 | 27 | 28 | 20 | 93 | |
2-1 | Prior | 312 | 61 | 58 | 71 | 55 | 259 | 63 | 60 | 75 | 30 | 590 | 30 | 27 | 46 | 124 | 236 | 30 | 26 | 51 | 84 |
Posterior | 191 | 8 | 8 | 18 | 46 | 213 | 17 | 14 | 23 | 50 | 312 | 7 | 4 | 22 | 68 | 133 | 9 | 9 | 22 | 54 | |
2-2 | Prior | 229 | 78 | 78 | 84 | 66 | 187 | 78 | 77 | 85 | 40 | 388 | 54 | 52 | 64 | 80 | 250 | 55 | 54 | 66 | 117 |
Posterior | 139 | 11 | 9 | 20 | 46 | 172 | 18 | 15 | 20 | 60 | 236 | 7 | 7 | 17 | 65 | 175 | 9 | 7 | 26 | 72 | |
2-3 | Prior | 109 | 611 | 64 | 46 | 114 | 104 | 62 | 66 | 43 | 128 | 124 | 38 | 34 | 36 | 17 | 54 | 33 | 33 | 49 | 33 |
Posterior | 83 | 8 | 7 | 17 | 52 | 99 | 12 | 11 | 11 | 61 | 180 | 9 | 10 | 13 | 49 | 177 | 10 | 9 | 21 | 82 |
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Malekghaini, N.; Ghahari, F.; Ebrahimian, H.; Bowers, M.; Ahlberg, E.; Taciroglu, E. A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders. Buildings 2023, 13, 420. https://doi.org/10.3390/buildings13020420
Malekghaini N, Ghahari F, Ebrahimian H, Bowers M, Ahlberg E, Taciroglu E. A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders. Buildings. 2023; 13(2):420. https://doi.org/10.3390/buildings13020420
Chicago/Turabian StyleMalekghaini, Niloofar, Farid Ghahari, Hamed Ebrahimian, Matthew Bowers, Eric Ahlberg, and Ertugrul Taciroglu. 2023. "A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders" Buildings 13, no. 2: 420. https://doi.org/10.3390/buildings13020420
APA StyleMalekghaini, N., Ghahari, F., Ebrahimian, H., Bowers, M., Ahlberg, E., & Taciroglu, E. (2023). A Two-Step FE Model Updating Approach for System and Damage Identification of Prestressed Bridge Girders. Buildings, 13(2), 420. https://doi.org/10.3390/buildings13020420