Comparison and Implementation of Multiple Model Structural Identification Methods
Publication: Journal of Structural Engineering
Volume 141, Issue 11
Abstract
Although multiple-model structural identification (MM ST-ID) approaches appear to offer clear, conceptual benefits over single-model approaches, they have not yet been employed within a transparent scenario that will allow quantitative comparison, critique, and refinement. To fill this gap, the research reported in this paper aimed to (1) implement and compare current MM ST-ID approaches on a physical laboratory model to establish their accuracy and identify their merits and shortcomings, and (2) identify the ability to refine MM ST-ID methods by weighing observations based on their correlation with the desired predictions. The scenario implemented used modal parameters as the observations, and static displacements and strains as the desired predictions. The various MM ST-ID methods were evaluated based on how their prediction distributions agreed with the actual responses of the physical model. The results indicated that while all methods were successful in bounding the actual responses, the Bayesian updating approach proved to be the most efficient in terms of required number of simulations, and was able to produce prediction distributions with the smallest bounds (while still incorporating all measured responses). In addition, the mean of the MM ST-ID prediction distributions did not coincide with the model that had the largest weight (i.e., the highest likelihood), which indicates that single model approaches not only are unable to provide estimates of variability, but may produce biased predictions. Finally, through a second set of scenarios, the research reported in this paper showed how prediction distributions may be improved by weighing observations based on their correlation with the desired predictions.
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Acknowledgments
The research reported in this paper was supported by the National Science Foundation under Grant No. CMMI-0846591. In addition, the writers would like to acknowledge Drs. Emin Aktan, Jeffrey Weidner, John Prader, and John Devitis for their support and guidance throughout the research reported in this paper.
References
AISC (American Institute of Steel Construction). (2005). Steel construction manual, 13th Ed., Chicago.
Aktan, A., et al. (1997). “Structural identification for condition assessment: Experimental arts.” J. Struct. Eng., 1674–1684.
Aktan, A., and Brownjohn, J. (2013). “Structural identification: Opportunities and challenges.” J. Struct. Eng., 1639–1647.
Allemang, R. J. (1999). Vibrations: Experimental modal analysis, Structural Dynamics Research Laboratory (SDRL), Univ. of Cincinnati, Cincinnati.
Antony, J. (2003). Design of experiments for engineers and scientists, Elsevier, London.
Aoki, T., and Sabia, D. (2005). “Structural identification and seismic performance of brick chimneys, Tokoname, Japan.” Struct. Eng. Mech., 21(5), 553–570.
ASCE Structural Engineering Institute (SEI) Committee on Structural Identification of Constructed Systems. (2011). “Structural identification (St-Id) of constructed facilities.” Approaches, methods and technologies for effective practice of St-Id, F. Catbas, T. Kijewski-Correa, and A. Aktan, eds., Reston, VA.
Beck, J., and Yuen, K. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 192–203.
Beck, J. L., and Au, S.-K. (2002). “Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation.” J. Eng. Mech., 380–391.
Beck, J. L., and Jennings, P. C. (1980). “Structural identification using linear models and earthquake records.” Earthquake Eng. Struct. Dyn., 8(2), 145–160.
Beck, J. L., and Katafygiotis, L. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Brownjohn, J. M. W., Moyo, P., Omenzetter, P., and Lu, Y. (2003). “Assessment of highway bridge upgrading by dynamic testing and finite-element model updating.” J. Bridge Eng., 162–172.
Catbas, F. N., Brown, D. L., and Aktan, A. E. (2004). “Parameter estimation for multiple-input multiple-output modal analysis of large structures.” J. Eng. Mech., 921–930.
Catbas, F. N., Ciloglu, S., Hasancebi, O., Grimmelsman, K., and Aktan, A. (2007). “Limitations in structural identification of large constructed structures.” J. Struct. Eng., 1051–1066.
Chen, J., and Garba, J. (1979). “Analytical model improvement using modal test results.” AIAA, 18(6), 684–690.
Chen, M.-H., Shao, Q.-M., and Ibrahim, J. G. (2000). Monte Carlo methods in Bayesian computation, Springer, New York.
Cheung, S., and Beck, J. (2009). “Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters.” J. Eng. Mech., 243–255.
Ching, J., and Chen, Y. (2007). “Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging.” J. Eng. Mech., 816–832.
Deblauwe, F., Brown, D. L., and Allemang, R. J. (1987). “Polyreference time domain technique.” Proc., Int. Modal Analysis Conf. V, 832–845.
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.”, Los Alamos, NM.
Dubbs, N. C. (2012). “Development, validation, and assessment of a multiple model structural identification method.” Ph.D. thesis, Dept. of Civil, Architectural, and Environmental Engineering, Drexel Univ., Philadelphia.
Galambos, T. V., and Ravindra, M. K. (1978). “Properties of steel for use in LRFD.” J. Struct. Div., 104(9), 1459–1468.
Gelman, A., Roberts, G. O., and Gilks, W. R. (1996). “Efficient Metropolis jumping rules.” Bayesian Statistics, J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, eds., Vol. 5, Oxford University Press, 599–608.
Gentile, C. (2006). “Modal and structural identification of a RC arch bridge.” Struct. Eng. Mech., 22(1), 53–70.
Geyer, C. (1992). “Practical Markov chain Monte Carlo.” Stat. Sci., 7(4), 473–483.
Glaser, R., Lee, C., Nitao, J., Hickling, T., and Hanley, W. (2007). “Markov chain Monte Carlo-based method for flaw detection in beams.” J. Eng. Mech., 1258–1267.
Gokce, H., Catbas, F., Gul, M., and Frangopol, D. (2013). “Structural identification for performance prediction considering uncertainties: Case study of a movable bridge.” J. Struct. Eng., 1703–1715.
Goulet, J., Kripakaran, P., and Smith, I. (2010). “Multimodel structural performance monitoring.” J. Struct. Eng., 1309–1318.
Goulet, J., and Smith, I. (2013). “Predicting the usefulness of monitoring for identifying the behavior of structures.” J. Struct. Eng., 1716–1727.
Goulet, J., Texier, M., Michel, C., Smith, I., and Chouinard, L. (2014). “Quantifying the effects of modeling simplifications for structural identification of bridges.” J. Bridge Eng., 59–71.
Green, P. (2003). “Trans-dimensional Markov chain Monte Carlo.” Highly structured stochastic systems, Oxford University Press.
Haario, H., Laine, M., Mira, A., and Saksman, E. (2006). “DRAM: Efficient adaptive MCMC.” Stat. Comput., 16(4), 339–354.
Hart, G. C., and Yao, J. T. P. (1977). “System identification in structural dynamics.” J. Eng. Mech. Div., 103(6), 1089–1104.
Hastings, W. K. (1970). “Monte Carlo sampling methods using Markov chains and their applications.” Biometrika, 57(1), 97–109.
He, X., Moaveni, B., Conte, J., Elgamal, A., and Masri, S. (2009). “System identification of Alfred Zampa Memorial Bridge using dynamic field test data.” J. Struct. Eng., 54–66.
Hjelmstad, K., Wood, S., and Clark, S. (1992). “Mutual residual energy method for parameter estimation in structures.” J. Struct. Eng., 223–242.
Imregun, M., and Visser, W. J. (1991). “A review of model updating techniques.” Shock Vib. Digest, 23(1), 9–20.
Katafygiotis, L., and Beck, J. (1998). “Updating models and their uncertainties. II: Model identifiability.” J. Eng. Mech., 463–467.
Kripakaran, P., and Smith, I. F. C. (2008). “Damage identification in truss bridges using multiple models.” 15th EG-ICE Workshop on Intelligent Computing in Engineering (ICE08), Plymouth, U.K.
Liu, H., Yang, Z. H., and Gaulke, M. S. (2005). “Structural identification and finite element modeling of a 14-story office building using recorded data.” Eng. Struct., 27(3), 463–473.
Liu, S. C., and Yao, J. T. P. (1978). “Structural identification concept.” J. Struct. Div., 104(12), 1845–1858.
Mares, C., Mottershead, J. E., and Friswell, M. I. (2000). “Selection and updating of parameters for the GARTEUR SM-AG19 testbed.” Proc., Int. Conf. for Noise and Vibration Engineering (ISMA), 25th Int. Seminar on Modal Analysis, 635–640.
MATLAB version R2010b [Computer software]. Natick, MA, Mathworks.
McKay, M. D., Beckman, R. J., and Conover, W. J. (1979). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2), 239–245.
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). “Equation of state calculations by fast computing machines.” J. Chem. Phys., 21(6), 1087–1092.
Monforton, G. R., and Wu, T. S. (1963). “Matrix analysis of semi-rigidly connected frames.” J. Struct. Div., 89(ST6), 13–42.
Moon, F., and Aktan, A. E. (2006). “Impacts of epistemic uncertainty on structural identification of constructed systems.” Shock Vib. Digest, 38(5), 399–420.
Morassi, A., and Stefano, T. (2008). “Dynamic testing for structural identification of a bridge.” J. Bridge Eng., 573–585.
Mottershead, J. E., and Friswell, M. I. (1993). “Model updating in structural dynamics: A survey.” J. Sound Vib., 167(2), 347–375.
Pan, Q., Grimmelsman, K., Moon, F., and Aktan, E. (2011). “Mitigating epistemic uncertainty in structural identification: Case study for a long-span steel arch bridge.” J. Struct. Eng., 1–13.
Robert-Nicoud, Y., Raphael, B., Burdet, O., and Smith, I. F. C. (2005a). “Model identification of bridges using measurement data.” Comput.-Aided Civ. Infrastruct. Eng., 20(2), 118–131.
Robert-Nicoud, Y., Raphael, B., and Smith, I. (2005b). “System identification through model composition and stochastic search.” J. Comput. Civ. Eng., 239–247.
Sanayei, M., McClain, J., Wadia-Fascetti, S., and Santini, E. (1999). “Parameter estimation incorporating modal data and boundary conditions.” J. Struct. Eng., 1048–1055.
Smith, I., and Saitta, S. (2006). “Multiple-model updating to improve knowledge of structural system behavior.” Proc., Structures Congress, ASCE, Reston, VA, 1–10.
Smith, I., and Saitta, S. (2008). “Improving knowledge of structural system behavior through multiple models.” J. Struct. Eng., 553–561.
Soize, C. (2013). “Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances.” J. Sound Vib., 332(10), 2379–2395.
Stein, M. (1987). “Large sample properties of simulations using Latin hypercube sampling.” Technometrics, 29(2), 143–151.
Strand7 [Computer software]. Sydney, Australia, Strand7.
Toksoy, T., and Aktan, A. E. (1994). “Bridge condition assessment by modal flexibility.” J. Exp. Mech., 34(3), 271–278.
Worden, K., and Hensman, J. J. (2012). “Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference.” Mech. Syst. Signal Process., 32, 153–169.
Zhao, J., and DeWolf, J. (1999). “Sensitivity study for vibrational parameters used in damage detection.” J. Struct. Eng., 410–416.
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© 2015 American Society of Civil Engineers.
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Received: Dec 20, 2013
Accepted: Jan 12, 2015
Published online: Mar 9, 2015
Discussion open until: Aug 9, 2015
Published in print: Nov 1, 2015
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