Adaptive Sampling-Based Bayesian Model Updating for Bridges Considering Substructure Approach
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 9, Issue 3
Abstract
During long-term bridge monitoring, model updating is necessary because it provides the basis for accurate condition assessment and damage detection. In this study, an adaptive sampling-based Bayesian model updating method for bridges is developed considering a substructure approach. First, the substructuring method is considered to solve eigenvalue problems. By reducing the size of the characteristic equations, the substructure approach overcomes poor algorithm performance, nonconvergence of results, and inefficient model updating caused by the large number of updated parameters when updating a large-scale system. Then Bayesian model updating is applied to quantify the uncertainty existing in bridge model updating and to obtain the posterior probability density function (PDF) of updating parameters that can be further used in different fields of engineering. By introducing the affine-invariant ensemble sampler (AIES) to replace the traditional Metropolis-Hastings (MH) sampler, an adaptive transitional Markov chain Monte Carlo algorithm is proposed to obtain the posterior probability of parameters with high efficiency. Application to a bridge structure demonstrates that the proposed method is efficient and useful in engineering problems.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This research was jointly supported by the National Natural Science Foundation of China (Grant Nos. 52250011, 52222807, and 12002224) and Fundamental Research Funds for the Central Universities (Grant Nos. DUT22ZD213 and DUT22QN235).
References
Beck, J. L., and S.-K. Au. 2002. “Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation.” J. Eng. Mech. 128 (4): 380–391. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:4(380).
Betz, W., I. Papaioannou, and D. Straub. 2016. “Transitional Markov chain Monte Carlo: Observations and improvements.” J. Eng. Mech. 142 (5): 04016016. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001066.
Ching, J., and Y.-C. Chen. 2007. “Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging.” J. Eng. Mech. 133 (7): 816–832. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:7(816).
Ching, J., and J.-S. Wang. 2016. “Application of the transitional Markov chain Monte Carlo algorithm to probabilistic site characterization.” Eng. Geol. 203 (Mar): 151–167. https://doi.org/10.1016/j.enggeo.2015.10.015.
Craig, R. R., and M. C. C. Bampton. 1968. “Coupling of substructures for dynamic analyses.” AIAA J. 6 (7): 1313–1319. https://doi.org/10.2514/3.4741.
Del Moral, P., A. Doucet, and A. Jasra. 2006. “Sequential Monte Carlo samplers.” J. R. Stat. Soc. B 68 (3): 411–436. https://doi.org/10.1111/j.1467-9868.2006.00553.x.
Efraimidis, P., and P. Spirakis. 2016. “Weighted random sampling.” In Encyclopedia of algorithms, edited by M. Y. Kao, 2365–2367. New York: Springer.
Foreman-Mackey, D., D. W. Hogg, D. Lang, and J. Goodman. 2013. “EMCEE: The MCMC hammer.” Publ. Astron. Soc. Pac. 125 (925): 306–312. https://doi.org/10.1086/670067.
Gallier, J. 2011. Geometric methods and applications: For computer science and engineering. New York: Springer.
Goodman, J., and J. Weare. 2010. “Ensemble samplers with affine invariance.” Commun. Appl. Math. Comput. Sci. 5 (1): 65–80. https://doi.org/10.2140/camcos.2010.5.65.
Hastings, W. K. 1970. “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika 57 (1): 97–109. https://doi.org/10.1093/biomet/57.1.97.
Hou, F., J. Goodman, D. W. Hogg, J. Weare, and C. Schwab. 2012. “An affine-invariant sampler for exoplanet fitting and discovery in radial velocity data.” Astrophys. J. 745 (2): 198. https://doi.org/10.1088/0004-637X/745/2/198.
Hurty, W. C. 1965. “Dynamic analysis of structural systems using component modes.” AIAA J. 3 (4): 678–685. https://doi.org/10.2514/3.2947.
Lye, A., A. Cicirello, and E. Patelli. 2021. “Sampling methods for solving Bayesian model updating problems: A tutorial.” Mech. Syst. Signal Process. 159 (Oct): 107760. https://doi.org/10.1016/j.ymssp.2021.107760.
Lye, A., A. Cicirello, and E. Patelli. 2022. “An efficient and robust sampler for Bayesian inference: Transitional ensemble Markov chain Monte Carlo.” Mech. Syst. Signal Process. 167 (Mar): 108471. https://doi.org/10.1016/j.ymssp.2021.108471.
MacNeal, R. H. 1971. “A hybrid method of component mode synthesis.” Comput. Struct. 1 (4): 581–601. https://doi.org/10.1016/0045-7949(71)90031-9.
Ortiz, G. A., D. A. Alvarez, and D. Bedoya-Ruíz. 2015. “Identification of Bouc–Wen type models using the transitional Markov Chain Monte Carlo method.” Comput. Struct. 146 (Jan): 252–269. https://doi.org/10.1016/j.compstruc.2014.10.012.
Ouyang, J., and Y. Liu. 2022. “Model updating for slope stability assessment in spatially varying soil parameters using multi-type observations.” Mech. Syst. Signal Process. 171 (May): 108906. https://doi.org/10.1016/j.ymssp.2022.108906.
Roberts, G. O., A. Gelman, and W. R. Gilks. 1997. “Weak convergence and optimal scaling of random walk Metropolis algorithms.” Ann. Appl. Probab. 7 (1): 110–120. https://doi.org/10.1214/aoap/1034625254.
Roberts, G. O., and J. S. Rosenthal. 2001. “Optimal scaling for various Metropolis-Hastings algorithms.” Stat. Sci. 16 (4): 351–367. https://doi.org/10.1214/ss/1015346320.
Rubin, S. 1975. “Improved component-mode representation for structural dynamic analysis.” AIAA J. 13 (8): 995–1006. https://doi.org/10.2514/3.60497.
Sehgal, S., and H. Kumar. 2016. “Structural dynamic model updating techniques: A state of the art review.” Arch. Comput. Methods Eng. 23 (3): 515–533. https://doi.org/10.1007/s11831-015-9150-3.
Simoen, E., G. De Roeck, and G. Lombaert. 2015. “Dealing with uncertainty in model updating for damage assessment: A review.” Mech. Syst. Signal Process. 56–57 (May): 123–149. https://doi.org/10.1016/j.ymssp.2014.11.001.
Simpson, A., and B. Tabarrok. 1968. “On Kron’s eigenvalue procedure and related methods of frequency analysis.” Q. J. Mech. Appl. Math. 21 (1): 1–39. https://doi.org/10.1093/qjmam/21.1.1.
Tian, W., S. Weng, and Y. Xia. 2022. “Model updating of nonlinear structures using substructuring method.” J. Sound Vib. 521 (Mar): 116719. https://doi.org/10.1016/j.jsv.2021.116719.
Wang, J., and L. S. Katafygiotis. 2014. “Reliability-based optimal design of linear structures subjected to stochastic excitations.” Struct. Saf. 47 (Mar): 29–38. https://doi.org/10.1016/j.strusafe.2013.11.002.
Wang, Y., and J. Solomon. 2019. “Intrinsic and extrinsic operators for shape analysis.” In Handbook of numerical analysis, 41–115. Amsterdam, Netherlands: Elsevier.
Yan, W.-J., D. Chronopoulos, C. Papadimitriou, S. Cantero Chinchilla, and G.-S. Zhu. 2020. “Bayesian inference for damage identification based on analytical probabilistic model of scattering coefficient estimators and ultrafast wave scattering simulation scheme.” J. Sound Vib. 468 (Mar): 115083. https://doi.org/10.1016/j.jsv.2019.115083.
Yang, X.-M., C.-X. Qu, T.-H. Yi, H.-N. Li, and H. Liu. 2020. “Modal analysis of a bridge during high-speed train passages by enhanced variational mode decomposition.” Int. J. Struct. Stab. Dyn. 20 (13): 2041002. https://doi.org/10.1142/S0219455420410023.
Yang, X.-M., T.-H. Yi, C.-X. Qu, H.-N. Li, and H. Liu. 2019. “Automated eigensystem realization algorithm for operational modal identification of bridge structures.” J. Aerosp. Eng. 32 (2): 04018148. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000984.
Yi, T.-H., X.-J. Yao, C.-X. Qu, and H.-N. Li. 2019. “Clustering number determination for sparse component analysis during output-only modal identification.” J. Eng. Mech. 145 (1): 04018122. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001557.
Zhang, Z., X. Liu, Y. Zhang, M. Zhou, and J. Chen. 2020. “Time interval of multiple crossings of the Wiener process and a fixed threshold in engineering.” Mech. Syst. Signal Process. 135 (Jan): 106389. https://doi.org/10.1016/j.ymssp.2019.106389.
Zhu, H., J. Li, W. Tian, S. Weng, Y. Peng, Z. Zhang, and Z. Chen. 2021. “An enhanced substructure-based response sensitivity method for finite element model updating of large-scale structures.” Mech. Syst. Signal Process. 154 (Jun): 107359. https://doi.org/10.1016/j.ymssp.2020.107359.
Zhu, H., J. Li, S. Weng, F. Gao, and Z. Chen. 2019. “Calculation of structural response and response sensitivity with improved substructuring method.” J. Aerosp. Eng. 32 (3): 04019016. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000996.
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© 2023 American Society of Civil Engineers.
History
Received: Feb 23, 2023
Accepted: May 12, 2023
Published online: Jun 29, 2023
Published in print: Sep 1, 2023
Discussion open until: Nov 29, 2023
ASCE Technical Topics:
- Adaptive systems
- Algorithms
- Analysis (by type)
- Bayesian analysis
- Bridge engineering
- Bridge tests
- Engineering fundamentals
- Field tests
- Mathematics
- Model accuracy
- Models (by type)
- Parameters (statistics)
- Statistical analysis (by type)
- Statistics
- Structural engineering
- Structures (by type)
- Substructures
- Systems engineering
- Systems management
- Tests (by type)
Authors
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