Markov Chain Monte Carlo-Based Method for Flaw Detection in Beams
Publication: Journal of Engineering Mechanics
Volume 133, Issue 12
Abstract
A Bayesian inference methodology using a Markov chain Monte Carlo (MCMC) sampling procedure is presented for estimating the parameters of computational structural models. This methodology combines prior information, measured data, and forward models to produce a posterior distribution for the system parameters of structural models that is most consistent with all available data. The MCMC procedure is based upon a Metropolis-Hastings algorithm that is shown to function effectively with noisy data, incomplete data sets, and mismatched computational nodes/measurement points. A series of numerical test cases based upon a cantilever beam is presented. The results demonstrate that the algorithm is able to estimate model parameters utilizing experimental data for the nodal displacements resulting from specified forces.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under Contract No. DOEW-7405-ENG-48.
References
Aines, R., et al. (2002). “The stochastic engine initiative: Improving prediction of behavior in geologic environments we cannot directly observe.” Rep. No. UCRL-ID-148221, Lawrence Livermore National Laboratory, Livermore, Calif.
Beck, J. L. (1989). “Statistical system identification of structures.” Proc., 5th Int. Conf. Structural Safety and Reliability, ASCE, N.Y., 1395–1402.
Beck, J. L., 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. L., and Yuen, K.-V. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 130(2), 192–203.
Collins, J. D., Hart, G. C., Hasselman, T. K., and Kennedy, B. (1974). “Statistical identification of structures.” AIAA J., 12, 185–190.
Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevitz, D. W. (1996). “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review.” Tech. Rep. No. LA-13070-MS, Los Alamos National Laboratory, Los Alamos, N.M.
Friswell, M. I., and Mottershead, J. E. (1995). Finite-element model updating in structural dynamics, Kluwer Academic, Boston.
Glaser, R. E., Hanley, W. G., Lee, C. L., and Nitao, J. J. (2003). “A Markov chain Monte Carlo based method for system identification.” Rep. No. UCRL-JC-150494, Lawrence Livermore National Laboratory, Livermore, Calif.
Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, 57, 97–109.
Karlin, S., and Taylor, H. M. (1975). A first course in stochastic processes, Academic, San Diego.
Metropolis, N., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equations of state calculations by fast computing machines.” J. Chem. Phys., 21, 1087–1092.
Mosegaard, K. (1998). “Resolution analysis of general inverse problems through inverse Monte Carlo sampling.” Inverse Probl., 14, 405–426.
Newmark, R., et al. (2001). “Stochastic engine: Direct incorporation of measurements into predictive simulations.” Rep. No. UCRL-JC-145116, Lawrence Livermore National Laboratory, Livermore, Calif.
Ramirez, A. J., et al. (2005). “Stochastic inversion of electrical resistivity changes using a Markov chain Monte Carlo approach.” J. Geophys. Res., 110, B02101.
Sohn, H., and Law, K. H. (1997). “A Bayesian probabilistic approach for structure damage detection.” Earthquake Eng. Struct. Dyn., 26, 1259–1281.
Vanik, M. W., Beck, J. L., and Au, S. K. (2000). “Bayesian probabilistic approach to structural health monitoring.” J. Eng. Mech., 126(7), 738–745.
Yuen., K.-V., and Katafygiotis, L. S. (2002). “Bayesian model updating using complete input and incomplete response noisy measurements.” J. Eng. Mech., 128(3), 340–350.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 12 • December 2007
Pages: 1258 - 1267
Copyright
© 2007 ASCE.
History
Received: Oct 24, 2005
Accepted: Apr 23, 2007
Published online: Dec 1, 2007
Published in print: Dec 2007
Notes
Note. Associate Editor: Arvid Naess
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.