Evidence-Based Identification of Weighting Factors in Bayesian Model Updating Using Modal Data
Publication: Journal of Engineering Mechanics
Volume 138, Issue 5
Abstract
In Bayesian model updating, parameter identification of structural systems using modal data can be based on the formulation of the likelihood function as a product of two probability density functions, one relating to modal frequencies and one to mode-shape components. The selection of the prior distribution of the prediction-error variances relating to these two types of data has to be performed carefully so that the relative contributions are weighted to give balanced results. A methodology is proposed in this paper to select these weights by performing Bayesian updating at the model class level, where the model classes differ by having different ratios of the two prediction-error variances. The most probable model class on the basis of the modal data then gives the best choice for this variance ratio. Two illustrative examples, one using simulated data and one using experimental data, point out the effect of the different relative contributions of the modal frequencies and mode-shape components to the total amount of information extracted from the modal data.
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Acknowledgments
This research was partially supported by the European Space Agency (ESA) under Project No. P8440-018-011, which is gratefully acknowledged by the authors. The first author is a recipient of a DOC-fForte-fellowship of the Austrian Academy of Science at the Institute of Engineering Mechanics (University of Innsbruck) and spent the Fall Term of 2008 as a Visiting Student Researcher at the California Institute of Technology.
References
Alvin, K. F. (1997). “Finite element model update via Bayesian estimation and minimization of dynamic residuals.” AIAA J.AIAJAH, 35(5), 879–886.
Beck, J. L. (1978). “Determining models of structures from earthquake records.” Technical Rep. EERL78-01, Earthquake Engineering Research Laboratory, CA Institute of Technology, Pasadena, CA.
Beck, J. L. (2010). “Bayesian system identification based on probability logic.” Struct. Control Health Monit., 17(7), 825–847.
Beck, J. L., Au, S. K., and Vanik, M. W. (2001). “Monitoring structural health using a probabilistic measure.” Comput.-Aided Civ. Infrastructural Eng.CCIEFR, 16(1), 1–11.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech.JENMDT, 124(4), 455–461.
Beck, J. L., and Yuen, K. V. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech.JENMDT, 130(2), 192–203.
Bernal, D., Dyke, S. J., Beck, J. L. and Lam, H. F. (2002). “Phase II of the ASCE benchmark study on structural health monitoring.” Proc., 15th Eng. Mech. Div. Conf. of the ASCE, ASCE, Reston, VA.
Bohle, K., and Fritzen, C.-P. (2003). “Results obtained by minimising natural frequency and MAC-value errors of a plate model.” Mech. Syst. Signal Process., 17(1), 55–64.
Calvi, A. (2005). “Uncertainty-based loads analysis for spacecraft: Finite element model validation and dynamic responses.” Comput. Struct.CMSTCJ, 83(14), 1103–1112.
Ching, J., and Beck, J. L. (2004). “Bayesian analysis of the Phase II IASC-ASCE structural health monitoring experimental benchmark data.” J. Eng. Mech.JENMDT, 130(10), 1233–1244.
Ching, J., and Chen, Y. C. (2007). “Transitional Markov Chain Monte Carlo method for Bayesian updating, model class selection, and model averaging.” J. Eng. Mech.JENMDT, 133(7), 816–832.
Christodoulou, K., Ntotsios, E., Papadimitriou, C., and Panetsos, P. (2008). “Structural model updating and prediction variability using Pareto optimal models.” Comput. Methods Appl. Mech. Eng.CMMECC, 198(1), 138–149.
Christodoulou, K., and Papadimitriou, C. (2007). “Structural identification based on optimally weighted modal residuals.” Mech. Syst. Signal Process., 21(1), 4–23.
Cox, R. T. (1946). “Probability, frequency and reasonable expectation.” Am. J. Phys.AJPIAS, 14(1), 1–13.
Datta, B. N. (2002). “Finite-element model updating, eigenstructure assignment and eigenvalue embedding techniques for vibrating systems.” Mech. Syst. Signal Process., 16(1), 83–96.
Dyke, S. J., Bernal, D., Beck, J. L., and Ventura, C. (2003). “Experimental Phase II of the Structural Health Monitoring Benchmark Problem.” Proc., 16th Eng. Mechanics Conf. of the ASCE, ASCE, Reston, VA.
Ewins, D. J. (2000). Modal testing: Theory, practice, and application, 2nd Ed., Research Studies, Baldock, UK.
Friswell, M. I., and Mottershead, J. E. (1995). “Finite element model updating in structural dynamics.” Kluwer Academic, Dordrecht, The Netherlands.
Haralampidis, Y., Papadimitriou, C., and Pavlidou, M. (2005). “Multi-objective framework for structural model identification.” Earthquake Eng. Struct. Dyn.IJEEBG, 34(6), 665–685.
Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” BiometrikaBIOKAX, 57(1), 97–109.
Hills, R. G. et al. (2008). “Validation challenge workshop.” Comput. Methods Appl. Mech. Eng.CMMECC, 197(29–32), 2375–2380.
Jaynes, E. T. (2003). Probability theory: The logic of science, Cambridge University, Cambridge, UK.
Katafygiotis, L. S., and Beck, J. L. (1998). “Updating models and their uncertainties. II: Model identifiability.” J. Eng. Mech.JENMDT, 124(4), 463–467.
Kullback, S., and Leibler, R. A. (1951). “On information and sufficiency.” Ann. Math. Stat.AASTAD, 22(1), 79–86.
Mackay, D. J. C. (1992). “Bayesian methods for adaptive models.” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Mares, C., Mottershead, J. E., and Friswell, M. I. (2003). “Results obtained by minimising natural frequency errors and using physical reasoning.” Mech. Syst. Signal Process., 17(1), 39–46.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equations of state calculations by fast computing machines.” J. Chem. Phys.JCPSA6, 21(6), 1087–1092.
Muto, M., and Beck, J. L. (2008). “Bayesian updating and model class selection using stochastic simulation.” J. Vib. ControlJVCOFX, 14(1–2), 7–34.
Oh, C. K., Beck, J. L., and Yamada, M. (2008). “Bayesian learning using automatic relevance determination prior with an application to earthquake early warning.” J. Eng. Mech.JENMDT, 134(12), 1013–1020.
Schedlinski, C. et al. (2005). “Test-based computational model updating of a car body in white.” Sound Vib.SOVIAJ, 39(9), 19–23.
Sivia, D. S. (1996). Data analysis. A Bayesian tutorial. Oxford University, Oxford, UK.
Vanik, M. W. (1997) “A Bayesian Probabilistic Approach to Structural Health Monitoring.” Ph.D. thesis, California Institute of Technology, Pasadena, CA.
Vanik, M. W, Beck, J. L., and Au, S. K. (2000). “Bayesian probabilistic approach to structural health monitoring.” J. Eng. Mech.JENMDT, 126(7), 738–745.
Werner, S. D., Beck, J. L., and Levine, M. B. (1987). “Seismic response evaluation of Meloland Road Overpass using 1979 Imperial valley earthquake records.” Earthquake Eng. Struct. Dyn.IJEEBG, 15(2), 249–274.
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Published In
Journal of Engineering Mechanics
Volume 138 • Issue 5 • May 2012
Pages: 430 - 440
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Aug 27, 2010
Accepted: Nov 8, 2011
Published online: Nov 10, 2011
Published in print: May 1, 2012
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