Abstract
This paper presents Hierarchical Bayesian model updating of a 10-story building model based on the identified modal parameters. The identified modal parameters are numerically simulated using a frame model (exact model) of the considered 10-story building and then polluted with Gaussian white noise. Stiffness parameters of a simplified shear model~- representing modeling errors - are considered as the updating parameters. In the Hierarchical Bayesian framework, the stiffness parameters are assumed to follow a probability distribution (e.g., normal) and the parameters of this distribution are updated as hyperparameters. The error functions are defined as the difference between model-predicted and identified modal parameters of the first few modes and are also assumed to follow a predefined distribution (e.g., normal) with unknown parameters (mean and covariance) which will also be estimated as hyperparameters. The Metropolis-Hastings within Gibbs sampler is employed to estimate the updating parameters and hyperparameters. The uncertainties of structural parameters as well as error functions are propagated in predicting the modal parameters and response time histories of the building.
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References
Friswell, M., Mottershead, J.E.: Finite Element Model Updating in Structural Dynamics. Springer Science & Business Media, 2013
Brownjohn, J.M., Xia, P.-Q.: Dynamic assessment of curved cable-stayed bridge by model updating. J. Struct. Eng. 126, 252–260 (2000)
Teughels, A., De Roeck, G.: Structural damage identification of the highway bridge Z24 by FE model updating. J. Sound Vib. 278, 589–610 (2004)
Reynders, E., Roeck, G.D., Gundes Bakir, P., Sauvage, C.: Damage identification on the Tilff bridge by vibration monitoring using optical fiber strain sensors. J. Eng. Mech. 133, 185–193 (2007)
Song, M., Yousefianmoghadam, S., Mohammadi, M.E., Moaveni, B., Stavridis, A., Wood, R.L.: An application of finite element model updating for damage assessment of a two-story reinforced concrete building and comparison with lidar. Struct. Health Monit. Nov 7:1475921717737970 (2017)
Alampalli, S.: Effects of testing, analysis, damage, and environment on modal parameters. Mech. Syst. Signal Process. 14, 63–74 (2000)
Clinton, J.F., Bradford, S.C., Heaton, T.H., Favela, J.: The observed wander of the natural frequencies in a structure. Bull. Seismol. Soc. Am. 96, 237–257 (2006)
Moaveni, B., Behmanesh, I.: Effects of changing ambient temperature on finite element model updating of the Dowling Hall Footbridge. Eng. Struct. 43, 58–68 (2012)
Sohn, H.: A Bayesian probabilistic approach for structure damage detection. Earthq. Eng. Struct. Dyn. 26(12), 1259–1281 (1997)
Beck, J.L., Katafygiotis, L.S.: Updating models and their uncertainties. I: Bayesian statistical framework. J. Eng. Mech. 124, 455–461 (1998)
Ching, J., Beck, J.L.: New Bayesian model updating algorithm applied to a structural health monitoring benchmark. Struct. Health Monit. 3, 313–332 (2004)
Yuen, K.V., Beck, J.L., Au, S.K.: Structural damage detection and assessment by adaptive Markov chain Monte Carlo simulation. Struct. Control. Health Monit. 11, 327–347 (2004)
Muto, M., Beck, J.L.: Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. J. Vib. Control. 14, 7–34 (2008)
Ntotsios, E., Papadimitriou, C., Panetsos, P., Karaiskos, G., Perros, K., Perdikaris, P.C.: Bridge health monitoring system based on vibration measurements. Bull. Earthq. Eng. 7, 469 (2009)
Behmanesh, I., Moaveni, B., Papadimitriou, C.: Probabilistic damage identification of a designed 9-story building using modal data in the presence of modeling errors. Eng. Struct. 131, 542–552 (2017)
Behmanesh, I., Moaveni, B., Lombaert, G., Papadimitriou, C.: Hierarchical Bayesian model updating for structural identification. Mech. Syst. Signal Process. 64, 360–376 (2015)
Jiang, X., Mahadevan, S.: Bayesian hierarchical uncertainty quantification by structural equation modeling. Int. J. Numer. Methods Eng. 80, 717–737 (2009)
Ballesteros, G., Angelikopoulos, P., Papadimitriou, C., Koumoutsakos, P.: Bayesian hierarchical models for uncertainty quantification in structural dynamics. Vulnerability Uncertain Risk Quantification, Mitigation Manage. 1615–1624 (2014)
Nagel, J.B., Sudret, B.: Hamiltonian Monte Carlo and borrowing strength in hierarchical inverse problems. ASCE-ASME J Risk. Uncertain. Eng. Sys. Part A Civ. Eng. 2, B4015008 (2015)
Wu, S., Angelikopoulos, P., Papadimitriou, C., Moser, R., Koumoutsakos, P.: A hierarchical Bayesian framework for force field selection in molecular dynamics simulations. Phil. Trans. R. Soc. A. 374, 20150032 (2016)
Behmanesh, I., Moaveni, B.: Accounting for environmental variability, modeling errors, and parameter estimation uncertainties in structural identification. J. Sound Vib. 374, 92–110 (2016)
Huang, Y., Beck, J.L., Li, H.: Bayesian system identification based on hierarchical sparse Bayesian learning and Gibbs sampling with application to structural damage assessment. Comput. Methods Appl. Mech. Eng. 318, 382–411 (2017)
Roberts, G.O., Rosenthal, J.S.: Optimal scaling for various Metropolis-Hastings algorithms. Stat. Sci. 16, 351–367 (2001)
Acknowledgements
Partial support of this study by the National Science Foundation Grant 1254338 is gratefully acknowledged. The opinions, findings, and conclusions expressed in this paper are those of the authors and do not necessarily represent the views of the sponsors and organizations involved in this project.
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Song, M., Behmanesh, I., Moaveni, B., Papadimitriou, C. (2019). Hierarchical Bayesian Calibration and Response Prediction of a 10-Story Building Model. In: Barthorpe, R. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-74793-4_20
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DOI: https://doi.org/10.1007/978-3-319-74793-4_20
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