Abstract
A Bayesian probabilistic methodology is presented for structural model updating using incomplete measured modal data which also takes into account different types of errors such as modelling errors due to the approximation of actual complex structure, uncertainties introduced by variation in material and geometric properties, measurement errors due to the noises in the signal and the data processing. The present work uses Linear Optimization Problems (LOP) to compute the probability that continually updated the model parameters. A real life rail-cum-roadway long steel truss bridge (Saraighat bridge) is considered in the present study, where identified modal data are available from measured acceleration responses due to ambient vibration. The main contributions of this paper are: (1) the introduction of sufficient number of model parameters at the element property level in order to capture any variations in the sectional properties; (2) the development of an accurate baseline model by utilizing limited sensor data; (3) the implementation of a probabilistic damage detection approach that utilizes updated model parameters from the undamaged state and possibly damaged state of the structure.
Similar content being viewed by others
References
Baruch, M. (1982). “Optimal correction of mass and stiffness matrices using measured modes.” Journal of American Institute of Aeronautics and Astronautics, 20(11), pp. 1623–1626.
Beck, J. L. and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” Journal of Engineering Mechanics, ASCE, 124(4), pp. 455–461.
Beck, J. L., Au, S. K., and Vanik, M. W. (2001). “Monitoring structural health using a probabilistic measure.” Computer-Aided Civil and Infrastructure Engineering, 16(1), pp. 1–11.
Beck, J. L. and Au, S. K. (2002). “Bayesian updating of structural models and reliability using Markov Chain Monte Carlo simulation.” Journal of Engineering Mechanics, ASCE, 128(4), pp. 380–391.
Berman, A. (2000). “Inherently incomplete finite element model and its effects on model updating.” Journal of American Institute of Aeronautics and Astronautics, 38(11), pp. 2142–2146.
Caesar, B. (1987). “Updating system matrices using modal testing data.” Proc. Fifth IMAC, pp. 453–459.
Caicedo, J., Dyke, S., and Johnson, E. (2004). “Natural excitation technique and eigensystem realization algorithm for phase I of the IASC-ASCE benchmark problem: simulated data.” Journal of Engineering Mechanics, 130(1), pp. 49–60.
Carvalho, J., Datta, B. N., Lin, W., and Wang, C. (2006). “Symmetry preserving eigenvalue embedding in finite element model updating of vibration structures.” Journal of Sound and Vibration, 290, pp. 839–864.
Chen, H. P. (2006). “Efficient methods for determining modal parameters of dynamic structures with large modifications.” Journal of Sound and Vibration, 298, pp. 462–470.
Ching, J. and Chen, Y. C. (2007). “Transitional Markov Chain Monte Carlo method for Bayesian updating, model class selection, and model averaging.” Journal of Engineering Mechanics, 133, pp. 816–832.
Collins, J. D., Hart, G. C., Hasselman, T. K., and Kennedy, B. (1974). “Statistical identification of structures.” Journal of American Institute of Aeronautics and Astronautics, 12, pp. 185–190.
CSI Computer & Structures Inc. (2009). Three dimentional static and dynamic finite element analysis and design of structures. SAP2000, Computer & Structures, Inc., Berkeley, CA.
Debnath, N., Dutta, A., and Deb, S. K. (2012). “Placement of sensors in operational modal analysis for truss bridges.” Mechanical Systems and Signal Processing, 31, pp. 196–216.
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 vibrations characteristics: A literature review. Technical Report LA-13070-MS, Los Alamos National Laboratory, Los Alamos, NM.
Ewins, D. J. (2000). Modal testing: Theory, practice, and application, 2nd Ed., Research Studies, Baldock, UK.
Feng, M. Q., Kim, J. M., and Xue, H. (1998). “Identification of a dynamic system using ambient vibration measurements.” Journal of Applied Mechanics, ASME, 65, pp. 1010–1021.
Friswell, M. I. and Mottershead, J. E. (1995). Finite element model updating in structural dynamics. Kluwer Academic, Dordrecht, The Netherlands.
Goller, B., Beck, J. L., and Schueller, G. I. (2012). “Evidence-based identification of weighting factors in Bayesian model updating using modal data.” Journal of Engineering Mechanics, 138, pp. 430–440.
Haario, H., Laine, M., Mira, A., and Saksman, E. (2006). “DRAM: efficient adaptive MCMC.” Journal of Statistics and Computing, 16, pp. 339–354.
Katafygiotis, L. S. and Beck, J. L. (1998). “Updating models and their uncertainties. II: Model identifiability.” Journal of Engineering Mechanics, ASCE, 124(4), pp. 463–467.
Katafygiotis, L. S. and Yuen, K. V. (2001). “Bayesian spectral density approach for modal updating using ambient data.” Earthquake Engineering and Structural Dynamics, 30(8), pp. 1103–1123.
Kinemetrics Inc. (2008a). “EpiSensor ES-U2, Uni-axial force balance accelerometers.” <http://www.kinemetrics. com/p-86-EpiSensor-ES-U2.aspx>, retrieved April 2, 2015.
Kinemetrics Inc. (2008b). “EpiSensor ES-T, Tri-axial force balance accelerometers.” <http://www.kinemetrics.com/ p-87-EpiSensor-ES-T.aspx>, retrieved April 2, 2015.
Marwala, T. (2010). Finite element model updating using computational intelligence techniques: applications to structural dynamics. Springer.
Masri, S. F., Nakamura. M., Chassiakos, A. G., and Caughey, T. K. (1996). “Neural network approach to the detection of changes in structural parameters.” Journal of Engineering Mechanics, 122(4), pp. 350–360.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equation of state calculations by fast computing machines.” Journal of Chemical Physics, 21, pp. 1087–1092.
Mottershead, J. E. and Friswell, M. I. (1993). “Model updating in structural dynamics: A survey.” Journal of Sound and Vibration, 167, pp. 347–375.
Nakamura, M., Masri, S. F., Chassiakos, A. G., and Caughey, T. K. (1998). “A method for non-parametric damage detection through the use of neural networks.” Earthquake Engineering and Structural Dynamics, 27(9), pp. 997–1010.
Papadimitriou, C., Beck. J. L., and Katafygiotis, L. S. (1997). “Asymptotic expansions for reliability and moments of uncertain systems.” Journal of Engineering Mechanics, ASCE, 123(12), pp. 1219–1229.
Salawu, O. S. (1997). “Detection of structural damage through changes in frequency: a review.” Engineering Structures, 19(9), pp. 718–723.
Sohn, H., Farrar, C. R., Hemez, F. M, Shunk, D. D, Stinemates, D. W., and Nadler, B. R. (2003). A review of structural health monitoring literature: 1996-2001. Technical Report LA-13976-MS, Los Alamos National Laboratory, Los Alamos, NM.
Vanik, M. W., Beck, J. L., and Au, S. K. (2000). “Bayesian probabilistic approach to structural health monitoring.” Journal of Engineering Mechanics, ASCE, 126(7), pp. 738–745.
Van Overschee, P. and De Moor, B. (1993). “Subspace algorithm for the stochastic identification problem.” Automatica, 29(3), pp. 649–660.
Wu, S. R. (2006). “Lumped mass matrix in explicit finite element method for transient dynamics of elasticity”. Journal of Computer Methods in Applied Mechanics and Engineering, 195(44), pp. 5983–5994.
Yang, Y. B. and Chen, Y. J. (2009). “A new direct method for updating structural models based on measured modal data.” Journal of Engineering Structures, 31, pp. 32–42.
Yuen, K. V. and Katafygiotis, L. S. (2002). “Bayesian modal updating using complete input and incomplete response noisy measurements.” Journal of Engineering Mechanics, ASCE, 128(3), pp. 340–350.
Yuen, K. V., Beck, J. L., and Katafygiotis, L. S. (2006). “Efficient model updating and monitoring methodology using incomplete modal data without mode matching.” Journal of Structural Control and Health Monitoring, 13(1), pp. 91–107.
Yuen, K. V. (2010). Bayesian methods for structural dynamics and civil engineering. John Wiley & Sons (Asia) Pte Ltd.
Zhang, L., Wang, T., and Tamura, Y. (2010). “A frequencyspatial domain decomposition (FSDD) method for operational modal analysis.” Mechanical Systems and Signal Processing, 24(5), pp. 227–1239.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mustafa, S., Debnath, N. & Dutta, A. Bayesian probabilistic approach for model updating and damage detection for a large truss bridge. Int J Steel Struct 15, 473–485 (2015). https://doi.org/10.1007/s13296-015-6016-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13296-015-6016-3