Technical Papers
Mar 10, 2022

Model Updating Using Hierarchical Bayesian Strategy Employing B-WIM Calibration Data

Publication: Journal of Bridge Engineering
Volume 27, Issue 5

Abstract

Bridge weigh-in-motion (B-WIM) systems are employed for monitoring traffic weights, providing useful information for management decisions. Many applications were proposed based on the information collected, such as calculation of influence lines and damage detection. In this work, an additional application is addressed, to perform model updating of structural parameters from information collected during the calibration of B-WIM systems. The goal of model updating techniques is to adjust the model parameters in order to achieve better agreement between predicted and experimental responses. Therefore, the resulting updated model is able to provide valuable information for decision makers. For many civil engineering applications, the updated parameters may have an inherent variability during the execution of the experimental procedure, since some external effects, such as environmental conditions, may change considerably along the process. To account for this inherent variability properly, a hierarchical Bayesian strategy is adopted. Results for both numerically simulated signals and a real engineering calibration procedure indicate that the proposed hierarchical Bayesian model updating approach is able to perform suitable estimates.

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Data Availability Statement

The following data that support the findings of this study are available from the corresponding author upon reasonable request: the dataset of numerical simulations for bridge response and codes for performing the hierarchical Bayesian model updating.

Acknowledgments

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brasil (CAPES) (finance code 001) and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ) (Grant No. 307133/2020-6).

References

Ballesteros, G. C., P. Angelikopoulos, C. Papadimitriou, and P. Koumoutsakos. 2014. “Bayesian hierarchical models for uncertainty quantification in structural dynamics.” In Vulnerability, uncertainty, and risk: Quantification, mitigation, and management, 1615–1624. Reston, VA: ASCE.
Behmanesh, I., and B. Moaveni. 2016. “Accounting for environmental variability, modeling errors, and parameter estimation uncertainties in structural identification.” J. Sound Vib. 374: 92–110. https://doi.org/10.1016/j.jsv.2016.03.022.
Behmanesh, I., B. Moaveni, G. Lombaert, and C. Papadimitriou. 2015. “Hierarchical Bayesian model updating for structural identification.” Mech. Syst. Sig. Process. 64–65: 360–376. https://doi.org/10.1016/j.ymssp.2015.03.026.
Brownjohn, J. M. W., P. Moyo, P. Omenzetter, and Y. Lu. 2003. “Assessment of highway bridge upgrading by dynamic testing and finite-element model updating.” J. Bridge Eng. 8 (3): 162–172. https://doi.org/10.1061/(ASCE)1084-0702(2003)8:3(162).
Cantero, D. 2021. “Moving point load approximation from bridge response signals and its application to bridge weigh-in-motion.” Eng. Struct. 233 (9): 111931. https://doi.org/10.1016/j.engstruct.2021.111931.
Cantero, D., and A. González. 2015. “Bridge damage detection using weigh-in-motion technology.” J. Bridge Eng. 20 (5): 04014078. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000674.
Cantero, D., R. Karoumi, and A. González. 2015. “The virtual axle concept for detection of localised damage using bridge weigh-in-motion data.” Eng. Struct. 89: 26–36. https://doi.org/10.1016/j.engstruct.2015.02.001.
Carraro, F., M. S. Gonçalves, R. H. Lopez, L. F. F. Miguel, and A. M. Valente. 2019. “Weight estimation on static B-WIM algorithms: A comparative study.” Eng. Struct. 198 (8): 109463. https://doi.org/10.1016/j.engstruct.2019.109463.
Catbas, F. N., R. Zaurin, M. Gul, and H. B. Gokce. 2012. “Sensor networks, computer imaging, and unit influence lines for structural health monitoring: Case study for bridge load rating.” J. Bridge Eng. 17 (4): 662–670. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000288.
DNIT (Departamento Nacional de Infraestrutura de Transportes). 2012. Quadro de fabricantes de veículos. Rio de Janeiro, Brazil. https://www.gov.br/dnit/pt-br/rodovias/operacoes-rodoviarias/pesagem/QFV2.
Durbin, J., and G. S. Watson. 1950. “Testing for serial correlation in least squares regression: I.” Biometrika 37 (3/4): 409–428. https://doi.org/10.2307/2332391.
Frøseth, G. T., A. Rønnquist, D. Cantero, and O. Øiseth. 2017. “Influence line extraction by deconvolution in the frequency domain.” Comput. Struct. 189 (3): 21–30. https://doi.org/10.1016/j.compstruc.2017.04.014.
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis, 3rd ed. London: Chapman and Hall/CRC.
Gonçalves, M. S., F. Carraro, and R. H. Lopez. 2021. “A B-WIM algorithm considering the modeling of the bridge dynamic response.” Eng. Struct. 228 (1): 111533. https://doi.org/10.1016/j.engstruct.2020.111533.
Gonçalves, M. S. 2021. “Vehicle-bridge dynamics simulation considering inherent variability in structural properties.” Mendeley Data, v1. https://doi.org/10.17632/9j2wngpdg3.1.
Gonçalves, M. S., R. H. Lopez, E. Oroski, and A. M. Valente. 2022. “A Bayesian algorithm with second order autoregressive errors for B-WIM weight estimation.” Eng. Struct. 250 (8): 113353. https://doi.org/10.1016/j.engstruct.2021.113353.
He, W., X. Liang, L. Deng, X. Kong, and H. Xie. 2021. “Axle configuration and weight sensing for moving vehicles on bridges based on the clustering and gradient method.” Remote Sens. 13 (17): 3477. https://doi.org/10.3390/rs13173477.
He, W., T. Ling, E. J. O’Brien, and L. Deng. 2019. “Virtual axle method for bridge weigh-in-motion systems requiring no axle detector.” J. Bridge Eng. 24 (9): 04019086. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001474.
Heitner, B., F. Schoefs, E. J. O’Brien, A. Žnidarič, and T. Yalamas. 2020. “Using the unit influence line of a bridge to track changes in its condition.” J. Civ. Struct. Health Monit. 10 (4): 667–678. https://doi.org/10.1007/s13349-020-00410-7.
Helmi, K., T. Taylor, and F. Ansari. 2015. “Shear force–based method and application for real-time monitoring of moving vehicle weights on bridges.” J. Intell. Mater. Syst. Struct. 26 (5): 505–516. https://doi.org/10.1177/1045389X14529612.
Ieng, S.-S. 2015. “Bridge influence line estimation for bridge weigh-in-motion system.” J. Comput. Civ. Eng. 29 (1): 06014006. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000384.
ISO. 1995. Mechanical vibration–road surface profiles–reporting of measured data. ISO 8606:1995. Geneva: ISO.
Ivanković, A. M., D. Skokandić, A. Žnidarič, and M. Kreslin. 2019. “Bridge performance indicators based on traffic load monitoring.” Struct. Infrastruct. Eng. 15 (7): 899–911. https://doi.org/10.1080/15732479.2017.1415941.
Jacob, B., E. O’Brien, and S. Jehaes. 2002. Weigh-in-motion of road vehicles: Final report of the COST 323 action. COST 323, Paris.
James, G., D. Witten, T. Hastie, and R. Tibshirani. 2013. An introduction to statistical learning. New York: Springer.
Junges, P. 2017. “Análise de fadiga em pontes curtas de concreto armado a partir de dados de sistemas B-WIM.” Ph.D. thesis, Univ. Federal de Santa Catarina.
Khan, M. S., C. Caprani, S. Ghosh, and J. Ghosh. 2021. “Value of strain-based structural health monitoring as decision support for heavy load access to bridges.” Struct. Infrastruct. Eng. https://doi.org/10.1080/15732479.2021.1890140.
Kwag, S., and B. S. Ju. 2020. “Application of a Bayesian hierarchical model to system identification of structural parameters.” Eng. Comput. 36 (2): 455–474. https://doi.org/10.1007/s00366-019-00708-1.
Lansdell, A., W. Song, and B. Dixon. 2017. “Development and testing of a bridge weigh-in-motion method considering nonconstant vehicle speed.” Eng. Struct. 152 (5): 709–726. https://doi.org/10.1016/j.engstruct.2017.09.044.
Lydon, M., S. E. Taylor, D. Robinson, A. Mufti, and E. Brien. 2016. “Recent developments in bridge weigh in motion (B-WIM).” J. Civ. Struct. Health Monit. 6 (1): 69–81. https://doi.org/10.1007/s13349-015-0119-6.
Ma, Y., L. Wang, J. Zhang, Y. Xiang, and Y. Liu. 2014. “Bridge remaining strength prediction integrated with Bayesian network and in situ load testing.” J. Bridge Eng. 19 (10): 04014037. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000611.
Moses, F. 1979. “Weigh-in-motion system using instrumented bridges.” J. Transp. Eng. 105 (3): 233–249. https://doi.org/10.1061/TPEJAN.0000783.
Múčka, P. 2017. “Simulated road profiles according to iso 8608 in vibration analysis.” J. Test. Eval. 46 (1): 20160265. https://doi.org/10.1520/JTE1801-EB.
O’Brien, E. J., J. M. W. Brownjohn, D. Hester, F. Huseynov, and M. Casero. 2021. “Identifying damage on a bridge using rotation-based bridge weigh-in-motion.” J. Civ. Struct. Health Monit. 11 (1): 175–188. https://doi.org/10.1007/s13349-020-00445-w.
O’Brien, E. J., M. Quilligan, and R. Karoumi. 2006. “Calculating an influence line from direct measurements.” Proc. Inst. Civ. Eng. Bridge Eng. 159 (1): 31–34.
O’Brien, E. J., C. W. Rowley, A. Gonzalez, and M. F. Green. 2009. “A regularised solution to the bridge weigh-in-motion equations.” Int. J. Heavy Veh. Syst. 16 (3): 310–327. https://doi.org/10.1504/IJHVS.2009.027135.
O’Brien, E. J., L. Zhang, H. Zhao, and D. Hajializadeh. 2018. “Probabilistic bridge weigh-in-motion.” Can. J. Civ. Eng. 45 (8): 667–675. https://doi.org/10.1139/cjce-2017-0508.
Okasha, N. M., D. M. Frangopol, and A. D. Orcesi. 2012. “Automated finite element updating using strain data for the lifetime reliability assessment of bridges.” Reliab. Eng. Syst. Saf. 99 (6): 139–150. https://doi.org/10.1016/j.ress.2011.11.007.
Oliveira, C. B. L., M. Greco, and T. N. Bittencourt. 2019. “Analysis of the Brazilian federal bridge inventory.” Rev. IBRACON Estrut. Mater. 12 (1): 1–13. https://doi.org/10.1590/s1983-41952019000100002.
Press, S. J. 2002. Subjective and objective Bayesian statistics: Principles, models, and applications, 2nd ed. Hoboken, NJ: John Wiley & Sons.
Quilligan, M. 2003. “Bridge weigh-in motion: Development of a 2-d multi-vehicle algorithm.” Licentiate thesis, KTH Royal Institute of Technology.
Rowley, C., A. Gonzalez, E. J. O’Brien, and A. Znidaric. 2008. “Comparison of conventional and regularized bridge weigh-in-motion algorithms.” In Proc., Int. Conf. on Heavy Vehicles, 221–230. Hoboken, NJ: John Wiley & Sons.
Schlune, H., M. Plos, and K. Gylltoft. 2009. “Improved bridge evaluation through finite element model updating using static and dynamic measurements.” Eng. Struct. 31 (7): 1477–1485. https://doi.org/10.1016/j.engstruct.2009.02.011.
Sedehi, O., C. Papadimitriou, and L. S. Katafygiotis. 2019. “Probabilistic hierarchical Bayesian framework for time-domain model updating and robust predictions.” Mech. Syst. Sig. Process. 123: 648–673. https://doi.org/10.1016/j.ymssp.2018.09.041.
Sedehi, O., C. Papadimitriou, and L. S. Katafygiotis. 2020. “Data-driven uncertainty quantification and propagation in structural dynamics through a hierarchical Bayesian framework.” Probab. Eng. Mech. 60: 103047. https://doi.org/10.1016/j.probengmech.2020.103047.
Simoen, E., G. De Roeck, and G. Lombaert. 2015. “Dealing with uncertainty in model updating for damage assessment: A review.” Mech. Syst. Sig. Process. 56–57 (2): 123–149. https://doi.org/10.1016/j.ymssp.2014.11.001.
Song, M., B. Moaveni, C. Papadimitriou, and A. Stavridis. 2019. “Accounting for amplitude of excitation in model updating through a hierarchical Bayesian approach: Application to a two-story reinforced concrete building.” Mech. Syst. Sig. Process. 123: 68–83. https://doi.org/10.1016/j.ymssp.2018.12.049.
Yoshida, I., H. Sekiya, and S. Mustafa. 2021. “Bayesian bridge weigh-in-motion and uncertainty estimation.” ASCE-ASME J. Risk Uncertainty Eng. Syst. Part A: Civ. Eng. 7 (1): 04021001. https://doi.org/10.1061/AJRUA6.0001118.
Yu, Y., C. Cai, and L. Deng. 2016. “State-of-the-art review on bridge weigh-in-motion technology.” Adv. Struct. Eng. 19 (9): 1514–1530. https://doi.org/10.1177/1369433216655922.
Yu, Y., C. Cai, and L. Deng. 2018. “Nothing-on-road bridge weigh-in-motion considering the transverse position of the vehicle.” Struct. Infrastruct. Eng. 14 (8): 1108–1122. https://doi.org/10.1080/15732479.2017.1401095.
Žnidarič, A., and J. Kalin. 2020. “Using bridge weigh-in-motion systems to monitor single-span bridge influence lines.” J. Civ. Struct. Health Monit. 10 (5): 743–756. https://doi.org/10.1007/s13349-020-00407-2.

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 27Issue 5May 2022

History

Received: Apr 5, 2021
Accepted: Jan 22, 2022
Published online: Mar 10, 2022
Published in print: May 1, 2022
Discussion open until: Aug 10, 2022

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Authors

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Center for Optimization and Reliability in Engineering (CORE), Civil Engineering Dept., Univ. Federal de Santa Catarina, Florianópolis, SC, Brazil (corresponding author). ORCID: https://orcid.org/0000-0002-3691-2752. Email: [email protected]
Center for Optimization and Reliability in Engineering (CORE), Civil Engineering Dept., Univ. Federal de Santa Catarina, Florianópolis, SC, Brazil. ORCID: https://orcid.org/0000-0001-9037-0176.
Amir Mattar Valente
Laboratório de Transportes e Logística (LabTrans), Univ. Federal de Santa Catarina, Florianópolis, SC, Brazil.

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  • An analytically tractable solution for hierarchical Bayesian model updating with variational inference scheme, Mechanical Systems and Signal Processing, 10.1016/j.ymssp.2022.110060, 189, (110060), (2023).

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