Uncertainty Quantification in the Assessment of Progressive Damage in a 7-Story Full-Scale Building Slice
Publication: Journal of Engineering Mechanics
Volume 139, Issue 12
Abstract
In this paper, Bayesian linear finite-element (FE) model updating is applied for uncertainty quantification (UQ) in the vibration-based damage assessment of a 7-story RC building slice. This structure was built and tested at full scale on the University of California at San Diego-Network for Earthquake Engineering Simulation shake table: progressive damage was induced by subjecting it to a set of historical earthquake ground motion records of increasing intensity. At each damage stage, modal characteristics, such as natural frequencies and mode shapes, were identified through low-amplitude vibration testing; these data are used in the Bayesian FE model updating scheme. To analyze the results of the Bayesian scheme and gain insight into the information contained in the data, a comprehensive uncertainty and resolution analysis is proposed and applied to the 7-story building test case. The Bayesian UQ approach and subsequent resolution analysis are shown to be effective in assessing uncertainty in FE model updating. Furthermore, it is demonstrated that the Bayesian FE model updating approach provides insight into the regularization of its often ill-posed deterministic counterpart.
Get full access to this article
View all available purchase options and get full access to this article.
References
Beck, J., and Au, S.-K. (2002). “Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation.” J. Eng. Mech., 128(4), 380–391.
Beck, J., and Katafygiotis, L. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 124(4), 455–461.
Beck, J., and Yuen, K.-V. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 130(2), 192–203.
Box, G., and Tiao, G. (1973). Bayesian inference in statistical analysis, Addison-Wesley, Boston.
Ching, J., and Chen, Y.-C. (2007). “Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging.” J. Eng. Mech., 133(7), 816–832.
Cox, R. (1946). “Probability, frequency and reasonable expectation.” Am. J. Phys., 14(1), 1–13.
Duijndam, A. (1988). “Bayesian estimation in seismic inversion. Part II: Uncertainty analysis.” Geophys. Prospect., 36(8), 899–918.
Filippou, F., and Constantinides, M. (2004). “FEDEASlab getting started guide and simulation examples.” Technical Rep. NEESgrid-2004-22.
Friswell, M., and Mottershead, J. (1995). Finite element model updating in structural dynamics, Kluwer, Dordrecht, Netherlands.
Gamerman, D. (1997). Markov chain Monte Carlo: Stochastic simulation for Bayesian inference, Chapman & Hall, London.
Haario, H., Laine, M., Mira, A., and Saksman, E. (2006). “DRAM: Efficient adaptive MCMC.” Stat. Comput., 16(4), 339–354.
Haario, H., Saksman, E., and Tamminen, J. (2001). “An adaptive metropolis algorithm.” Bernouilli, 7(2), 223–242.
Heylen, W., Lammens, S., and Sas, P. (1997). Modal analysis theory and testing, Dept. of Mechanical Engineering, Katholieke Univ. Leuven, Leuven, Belgium.
Jaynes, E. (1957). “Information theory and statistical mechanics.” Phys. Rev., 106(4), 620–630.
Jaynes, E. (2003). Probability theory. The logic of science, Cambridge University Press, Cambridge, U.K.
Katafygiotis, L., and Beck, J. (1998). “Updating models and their uncertainties. II: Model identifiability.” J. Eng. Mech., 124(4), 463–467.
Mathworks. (2012). MATLAB R2012b (v8.0) optimization toolbox user's guide, Natick, MA.
Mehta, M. (2004). Random matrices, 3rd Ed., Elsevier, San Diego.
Moaveni, B., Barbosa, A., Conte, J., and Hemez, F. (2007). “Uncertainty analysis of modal parameters obtained from three system identification methods.” Proc., IMAC-XXV, Int. Conf. on Modal Analysis, Society for Experimental Mechanics, Bethel, CT.
Moaveni, B., Barbosa, A. R., Conte, J. P., and Hemez, F. (2013). “Uncertainty analysis of system identification results obtained for a seven story building slice tested on the UCSD-NEES shake table.” Struct. Contr. Health Monit.,.
Moaveni, B., Conte, J., and Hemez, F. (2009). “Uncertainty and sensitivity analysis of damage identification results obtained using finite element model updating.” Comput. Aided Civ. Infrastruct. Eng., 24(5), 320–334.
Moaveni, B., He, X., Conte, J., and Restrepo, J. (2010). “Damage identification study of a seven-story full-scale building slice tested on the UCSD-NEES shake table.” Struct. Saf., 32(5), 347–356.
Moaveni, B., He, X., Conte, J., Restrepo, J., and Panagiotou, M. (2011). “System identification study of a 7-story full-scale building slice tested on the USCD-NEES shake table.” J. Eng. Mech., 137(6), 705–717.
Mosegaard, K., and Tarantola, A. (1995). “Monte Carlo sampling of solutions to inverse problems.” J. Geophys. Res., 100(B7), 12431–12447.
Mottershead, J., and Friswell, M. (1993). “Model updating in structural dynamics: A survey.” J. Sound Vibrat., 167(2), 347–375.
Muto, M., and Beck, J. (2008). “Bayesian updating and model class selection for hysteretic structural models using stochastic simulation.” J. Vibrat. Control, 14(1–2), 7–34.
Panagiotou, M., Restrepo, J., and Conte, J. (2011). “Shake table test of a full-scale 7-story building slice. Phase I: Rectangular wall.” J. Struct. Eng., 137(6), 691–704.
Papadimitriou, C. (2004). “Optimal sensor placement for parametric identification of structural systems.” J. Sound Vibrat., 278(4–5), 923–947.
Papadimitriou, C., Beck, J., and Au, S. (2000). “Entropy-based optimal sensor location for structural model updating.” J. Vibrat. Control, 6(5), 781–800.
Papadimitriou, C., Beck, J., and Katafygiotis, L. (1997). “Asymptotic expansions for reliability and moments of uncertain systems.” J. Eng. Mech., 123(12), 1219–1229.
Peeters, B., and De Roeck, G. (2001). “Stochastic system identification for operational modal analysis: A review.” J. Dynam. Syst. Measure. Control, 123(4), 659–667.
Reynders, E., and De Roeck, G. (2008). “Reference-based combined deterministic-stochastic subspace identification for experimental and operational modal analysis.” Mech. Syst. Signal Process., 22(3), 617–637.
Reynders, E., Pintelon, R., and De Roeck, G. (2008). “Uncertainty bounds on modal parameters obtained from stochastic subspace identification.” Mech. Syst. Signal Process., 22(4), 948–969.
Rytter, A. (1993). “Vibration based inspection of civil engineering structures.” Ph.D. thesis, Aalborg Univ., Aalborg, Denmark.
Schevenels, M., Lombaert, G., Degrande, G., and François, S. (2008). “A probabilistic assessment of resolution in the SASW test and its impact on the prediction of ground vibrations.” Geophys. J. Int., 172(1), 262–275.
Sibilio, E., Ciampoli, M., and Beck, J. (2007). “Structural health monitoring by Bayesian upating.” Proc., ECCOMAS Thematic Conf. on Comput. Methods in Struct. Dynam. and Earthq. Eng., M. Papadrakakis, D. C. Charmpis, N. D. Lagros, and Y. Tsompanakis, eds., Rethymno, Greece.
Sohn, H., and Law, K. (1997). “A Bayesian probabilistic approach for structure damage detection.” Earthquake Eng. Struct. Dynam., 26(12), 1259–1281.
Soize, C. (2000). “A nonparametric model of random uncertainties for reduced matrix models in structural dynamics.” Probab. Eng. Mech., 15(3), 277–294.
Soize, C. (2003). “Probabilités et modélisation des incertitudes: Éléments de base et concepts fondamentaux.” Séminaire de formation de l'école doctorale MODES, Paris.
Soize, C. (2008). “Construction of probability distributions in high dimensions using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices.” Int. J. Numer. Methods Eng., 76(10), 1583–1611.
Soize, C. (2010). “Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions.” Int. J. Numer. Methods Eng., 81(8), 939–970.
Soize, C. (2013). “Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances.” J. Sound Vibrat., 332(10), 2379–2395.
Tarantola, A. (2005). Inverse problem theory and methods for model parameter estimation, SIAM, Philadelphia.
Teughels, A., Maeck, J., and De Roeck, G. (2002). “Damage assessment by FE model updating using damage functions.” Comp. Struct., 80(25), 1869–1879.
Vanik, M., Beck, J., and Au, S. (2000). “Bayesian probabilistic approach to structural health monitoring.” J. Eng. Mech., 126(7), 738–745.
Yuen, K.-V. (2010a). Bayesian methods for structural dynamics and civil engineering, 1st Ed., Wiley, Singapore.
Yuen, K.-V. (2010b). “Recent developments of Bayesian model class selection and applications in civil engineering.” Struct. Saf., 32(5), 338–346.
Yuen, K.-V., and Katafygiotis, L. (2002). “Bayesian modal updating using complete input and incomplete response noisy measurements.” J. Eng. Mech., 128(3), 340–350.
Yuen, K.-V., Katafygiotis, L., Papadimitriou, C., and Mickleborough, N. (2001). “Optimal sensor placement methodology for identification with unmeasured excitation.” J. Dynam. Syst. Measure. Control, 123(4), 677–686.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 12 • December 2013
Pages: 1818 - 1830
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Sep 7, 2012
Accepted: Feb 15, 2013
Published online: Feb 18, 2013
Published in print: Dec 1, 2013
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.