Bayesian Updating: Reducing Epistemic Uncertainty in Hysteretic Degradation Behavior of Steel Tubular Structures
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 8, Issue 3
Abstract
This paper proposes a probabilistic framework for updating the governing parameters in the hysteretic constitutive model for tubular steel with strength degradation. The hysteretic constitutive model is formulated to track the strength degradation due to the local buckling of square hollow steel beam-columns imposed by cyclic loadings with large elastoplastic deformation. Despite various hysteretic laws that have been proposed to model the steel tubular strength degradation, limitations for determining parameter values remain in numerical analysis. The parameters are generally obfuscated by the inevitable epistemic uncertainties from material and geometric properties. The updating process of the material parameters is performed within the Bayesian framework employing the Markov chain Monte Carlo algorithm. The epistemic uncertainty involved in the computational procedure is initially represented as predefined intervals of the uncertain parameters. The proposed Markov chain Monte Carlo (MCMC) algorithm can generate samples from the posterior distributions of the parameters according to the experimental results. The epistemic uncertainty is hence significantly reduced by the Bayesian updating process such that the updated model is feasible to predict the degradation behavior of square hollow steel beam-columns subjected to cyclic loadings. The benchmark example indicates that the proposed framework can find the optimal path for updating key parameter values to accurately assess the condition of steel tubular structures in terms of the degradation behavior.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work is supported by the National Natural Science Function of China (Grant No. 12102036) and the Stateful Support Project of the Science and Industry Bureau of China (Grant No. HTKJ2019KL502011). The corresponding author is grateful for the support of the National Science Foundation of China for Excellent Young Scholars (Overseas Project), and the Fund of Chongqing University (Grant No. T0180). The first and the corresponding authors appreciate the support of the Alexander von Humboldt Stiftung/Foundation (Awards Nos. 1193706 and 1196752).
References
Ahmed, M., Q. Q. Liang, V. I. Patel, and M. N. S. Hadi. 2020. “Computational simulation of eccentrically loaded circular thin-walled concrete-filled double steel tubular slender columns.” Eng. Struct. 213 (Jun): 110571. https://doi.org/10.1016/j.engstruct.2020.110571.
Bai, Y., A. Kawano, K. Odawara, and S. Matsuo. 2012. “Constitutive models for hollow steel tubes and concrete filled steel tubes considering the strength deterioration.” J. Struct. Constr. Eng. 77 (677): 1141–1150. https://doi.org/10.3130/aijs.77.1141.
Bai, Y., and X. Lin. 2015. “Numerical simulation on seismic collapse of thin-walled steel moment frames considering post local buckling behavior.” Thin-Walled Struct. 94 (Sep): 424–434. https://doi.org/10.1016/j.tws.2015.04.033.
Bai, Y., X. Lin, and B. Mou. 2016. “Numerical modeling on post-local buckling behavior of circular and square concrete-filled steel tubular beam columns.” Int. J. Steel Struct. 16 (2): 531–546. https://doi.org/10.1007/s13296-016-6022-0.
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).
Bi, S., M. Broggi, and M. Beer. 2019. “The role of the Bhattacharyya distance in stochastic model updating.” Mech. Syst. Sig. Process. 117 (Feb): 437–452. https://doi.org/10.1016/j.ymssp.2018.08.017.
Birrell, M., R. Astroza, R. Carreño, J. Restrepo, and G. Araya-Letelier. 2021. “Bayesian parameter and joint probability distribution estimation for a hysteretic constitutive model of reinforcing steel.” Struct. Saf. 90 (May): 102062. https://doi.org/10.1016/j.strusafe.2020.102062.
Chen, Y., J. Yan, P. Sareh, and J. Feng. 2020. “Feasible prestress modes for cable-strut structures with multiple self-stress states using particle swarm optimization.” J. Comput. Civ. Eng. 34 (3): 04020003. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000882.
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).
Hackl, J., and J. Kohler. 2016. “Reliability assessment of deteriorating reinforced concrete structures by representing the coupled effect of corrosion initiation and progression by Bayesian networks.” Struct. Saf. 62 (Sep): 12–23. https://doi.org/10.1016/j.strusafe.2016.05.005.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/eqe.495.
Kawano, A., and K. Sakino. 2003. “Seismic resistance of CFT trusses.” Eng. Struct. 25 (5): 607–619. https://doi.org/10.1016/S0141-0296(02)00170-0.
Kurata, M., M. Nakashima, and K. Suita. 2005. “Effect of column base behaviour on the seismic response of steel moment frames.” J. Earthquake Eng. 9 (2): 415–438. https://doi.org/10.1142/S136324690500247X.
Li, X., and M. Kurata. 2018. “Probabilistic updating of fishbone model for assessing seismic damage to beam-column connections in steel moment-resisting frames.” Comput.-Aided Civ. Infrastruct. Eng. 34 (9): 790–805. https://doi.org/10.1111/mice.12429.
Lignos, D. G., H. Krawinkler, and A. S. Whittaker. 2011. “Prediction and validation of sidesway collapse of two scale models of a 4-story steel moment frame.” Earthquake Eng. Struct. Dyn. 40 (7): 807–825. https://doi.org/10.1002/eqe.1061.
Lin, X., M. Kato, L. Zhang, and M. Nakashima. 2018. “Quantitative investigation on collapse margin of steel high-rise buildings subjected to extremely severe earthquakes.” Earthquake Eng. Eng. Vib. 17 (3): 445–457. https://doi.org/10.1007/s11803-018-0454-9.
Luque, J., and D. Straub. 2016. “Reliability analysis and updating of deteriorating systems with dynamic Bayesian networks.” Struct. Saf. 62 (Sep): 34–46. https://doi.org/10.1016/j.strusafe.2016.03.004.
Lye, A., A. Cicirello, and E. Patelli. 2021. “Sampling methods for solving Bayesian model updating problems: A tutorial.” Mech. Syst. Sig. Process. 159 (Oct): 107760. https://doi.org/10.1016/j.ymssp.2021.107760.
Ma, Y., J. Zhang, L. Wang, and Y. Liu. 2013. “Probabilistic prediction with Bayesian updating for strength degradation of RC bridge beams.” Struct. Saf. 44 (Sep): 102–109. https://doi.org/10.1016/j.strusafe.2013.07.006.
Mottershead, J. E., M. Link, and M. I. Friswell. 2011. “The sensitivity method in finite element model updating: A tutorial.” Mech. Syst. Sig. Process. 25 (7): 2275–2296. https://doi.org/10.1016/j.ymssp.2010.10.012.
Mou, B., Y. Bai, and V. Patel. 2020. “Post-local buckling failure of slender and over-design circular CFT columns with high-strength materials.” Eng. Struct. 210 (May): 110197. https://doi.org/10.1016/j.engstruct.2020.110197.
Nakashima, M., and D. Liu. 2005. “Instability and complete failure of steel columns subjected to cyclic loading.” J. Eng. Mech. 131 (6): 559–567. https://doi.org/10.1061/(ASCE)0733-9399(2005)131:6(559).
Pourreza, F., M. Mousazadeh, and C. Basim. 2021. “An efficient method for incorporating modeling uncertainties into collapse fragility of steel structures.” Struct. Saf. 88 (Jan): 102009. https://doi.org/10.1016/j.strusafe.2020.102009.
Rocchetta, R., M. Broggi, Q. Huchet, and E. Patelli. 2018. “On-line Bayesian model updating for structural health monitoring.” Mech. Syst. Sig. Process. 103 (Mar): 174–195. https://doi.org/10.1016/j.ymssp.2017.10.015.
Song, X. 2020. “Parameterized fragility analysis of steel frame structure subjected to blast loads using Bayesian logistic regression method.” Struct. Saf. 87 (Nov): 102000. https://doi.org/10.1016/j.strusafe.2020.102000.
Wang, Z. 2008. “A preliminary report on the Great Wenchuan Earthquake.” Earthquake Eng. Eng. Vibr. 7 (2): 225–234.
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© 2022 American Society of Civil Engineers.
History
Received: Aug 31, 2021
Accepted: Apr 9, 2022
Published online: Jul 12, 2022
Published in print: Sep 1, 2022
Discussion open until: Dec 12, 2022
ASCE Technical Topics:
- Analysis (by type)
- Bayesian analysis
- Chemical degradation
- Chemical processes
- Chemistry
- Continuum mechanics
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Environmental engineering
- Material mechanics
- Material properties
- Materials engineering
- Mathematics
- Motion (dynamics)
- Parameters (statistics)
- Solid mechanics
- Statistical analysis (by type)
- Statistics
- Steel structures
- Strength of materials
- Structural behavior
- Structural engineering
- Structures (by type)
- Uncertainty principles
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