Technical Papers
May 15, 2014

Investigation of Uncertainty Changes in Model Outputs for Finite-Element Model Updating Using Structural Health Monitoring Data

Publication: Journal of Structural Engineering
Volume 140, Issue 11

Abstract

This article aims to investigate the effect of uncertainties on the predicted response of structures using updated finite-element models (FEMs). Modeling uncertainties are quantified by fuzzy numbers and are incorporated into the fuzzy FEM updating procedure. The impact of the amount and types of data used on the performance of the updated model is investigated. In order to perform the complex FEM updating calculations, which generally take too much time for complex models, a Gaussian process (GP) is used as a surrogate model. The central composite design (CCD) method is used to sample the input parameter space for more accurate GP models. Genetic algorithms (GA) are employed to solve the inverse fuzzy model updating problem. Additional constraints are presented to capture the variation space of the uncertain response parameters. The University of Central Florida benchmark test structure, which is designed to represent short-span to medium-span bridges, is used in the scope of uncertainty quantification study. Static and dynamic experimental test data obtained from the benchmark structure under different loadings and conditions are used for the demonstration. A damage case, in which the stiffness reduction in boundaries is simulated by using flexible pads, is considered. The results show that appropriate data sets, which contain the least uncertainty, should be generated instead of involving the entire set of measurements obtained from different tests. Nevertheless, uncertainty quantification should be employed to find the variation range of uncertain responses predicted by simplified FEM models.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

In the present study, the parallel computations are carried out in the framework of the project supported by Istanbul Technical University (ITU) National Center for High Performance Computing with Grant Number: 20682009. ITU also supported the first author during his studies at the University of Central Florida. The third author appreciates the support provided by Federal Highway Administration (FHWA) Cooperative Agreement Award DTFH61-07-H-00040 as part of the Exploratory Advanced Research Program. The opinions, findings, and conclusions expressed in this publication are those of the authors and do not necessarily reflect the views of the sponsoring organizations.

References

Adhikari, S., and Friswell, M. I. (2007). “Random matrix eigenvalue problems in structural dynamics.” Int. J. Numer. Methods Eng., 69(3), 562–591.
Arendt, P. D., Apley, D. W., and Chen, W. (2012). “Quantification of model uncertainty: Calibration, model discrepancy and identifiability.” J. Mech. Des., 134(10), 100908.
ASME. (2006). Guide for verification and validation in computational solid mechanics, New York.
Bakir, P. G. (2011). “Automation of the stabilization diagrams for subspace based system identification.” Expert Syst. Appl., 38(12), 14,390–14,397.
Bakir, P. G., Reynders, E., and De Roeck, G. (2007). “Sensitivity-based finite element model updating using constrained optimization with a trust region algorithm.” J. Sound Vib., 305(1–2), 211–225.
Bakir, P. G., Reynders, E., and De Roeck, G. (2008). “An improved finite element model updating method by the global optimization technique ‘Coupled Local Minimizers’.” Compt. Struct., 86(11–12), 1339–1352.
Beck, J., and Katafygiotis, L. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Beck, J. L., and Yuen, K. V. (2004). “Model selection using response measurements: Bayesian probabilistic approach.” J. Eng. Mech., 192–203.
Bell, S. E., Sanayei, M., Javdekar, C. N., and Slavsky, E. (2007). “Multiresponse parameter estimation for finite element model updating using nondestructive test data.” J. Struct. Eng., 1067–1079.
Box, G. E. P., and Wilson, K. B. (1951). “On the experimental attainment of optimum conditions (with discussion).” J. Roy. Stat. Soc. B, 13(1), 1–45.
Buezas, F. S., Rosales, M. B., and Filipich, C. P. (2011). “Damage detection with genetic algorithms taking into account a crack contact model.” Eng. Fract. Mech., 78(4), 695–712.
Catbas, F. N., Aktan, A. E., and Brown, D. L. (2004). “Parameter estimation for multiple input multiple output analysis of large structures.” J. Eng. Mech., 921–930.
Catbas, F. N., Brown, D. L., and Aktan, A. E. (2006). “Use of modal flexibility for damage detection and condition assessment: Case studies and demonstrations on large structures.” J. Struct. Eng., 1699–1712.
Catbas, F. N., Gokce, H. B., and Frangopol, D. M. (2012a). “Predictive analysis by incorporating uncertainty through a family of models calibrated with structural health monitoring data.” J. Eng. Mech., 712–723.
Catbas, F. N., Gul, M., and Burkett, J. (2008). “Damage assessment using flexibility and flexibility-based curvature for structural health monitoring.” Smart Mater. Struct., 17(1), 15–24.
Catbas, F. N., Kijewski-Correa, T. L., and Aktan, A. E., eds. (2012b). “Structural identification of constructed systems: Approaches, methods and technologies for effective practice of st-id.”.
Cheng, J., and Li, Q. S. (2012). “Artificial neural network-based response surface methods for reliability analysis of pre-stressed concrete bridges.” Struct. Infrastruct. Eng., 8(2), 171–184.
Degrauwe, D., De Roeck, G., and Lombaert, G. (2009). “Uncertainty quantification in the damage assessment of a cable-stayed bridge by means of fuzzy numbers.” Compt. Struct., 87(17–18), 1077–1084.
Degrauwe, D., Lombaert, G., and De Roeck, G. (2010). “Improving interval analysis in finite element calculations by means of affine arithmetic.” Compt. Struct., 88(3–4), 247–254.
Erdogan, Y. S., and Bakir, P. G. (2013). “Inverse propagation of uncertainties in finite element model updating problem through use of fuzzy arithmetic.” Eng. Appl. Artif. Intell., 26(1) 357–367.
Esfandiari, A., Bakhtiari-Nejad, F., Sanayei, M., and Rahai, A. (2010). “Structural finite element model updating using transfer function data.” Compt. Struct., 88(1–2), 54–64.
Fonseca, J. R., Friswell, M. I., Mottershead, J. E., and Lees, A. W. (2005). “Uncertainty identification by the maximum likelihood method.” J. Sound Vib., 288(3), 587–599.
Gokce, H. B., Catbas, F. N., Gul, M., and Frangopol, D. M. (2012). “Structural identification for performance prediction considering uncertainties: A case study of a movable bridge.” J. Struct. Eng., 1703–1715.
Goller, B., and Schueller, G. I. (2011). “Investigation of model uncertainties in Bayesian structural model updating.” J. Sound Vib., 330(25), 6122–6136.
Haag, T., Herrmann, J., and Hanss, M. (2010). “Identification procedure for epistemic uncertainties using inverse fuzzy arithmetic.” Mech. Syst. Signal Process., 24(7), 2021–2034.
Hanss, M. (2005). Applied Fuzzy Arithmetic—An Introduction with Engineering Applications, Springer, Berlin.
Hua, X., Ni, Y., Chen, Z., and Ko, J. (2008). “An improved perturbation method for stochastic finite element model updating.” Int. J. Numer. Methods Eng., 73(13), 1845–1864.
Hua, X. G., Ni, Y. Q., and Ko, J. M. (2009). “Adaptive regularization parameter optimization in output-error-based finite element model updating.” Mech. Syst. Signal Process., 23(3), 563–579.
Khodaparast, H., Mottershead, J., and Friswell, M. I. (2008). “Perturbation methods for the estimation of parameter variability in stochastic model updating.” Mech. Syst. Signal Process., 22(8), 1751–1773.
Khodaparast, H. H., Mottershead, J. E., and Badcock, K. J. (2011). “Interval model updating with irreducible uncertainty using the Kriging predictor.” Mech. Syst. Signal Process., 25(4), 1204–1226.
Li, X. Y., and Law, S. S. (2010). “Consistent regularization for damage detection with noise and model errors.” AIAA J., 48(4), 777–787.
Linderholt, A., and Abrahamsson, T. (2003). “Parameter identifiability in finite element model error localization.” Mech. Syst. Signal Process., 17(3), 579–588.
Massa, F., Ruffin, K., Tison, T., and Lallemand, B. (2005). “A complete method for efficient fuzzy modal analysis.” J. Sound Vib., 309(1–2), 63–85.
Meruane, V., and Heylen, W. (2011). “An hybrid real genetic algorithm to detect structural damage using modal properties.” Mech. Syst. Signal Process., 25(5), 1559–1573.
Mottershead, J. E., Michael, L., and Friswell, M. I. (2011). “The sensitivity method in finite element model updating: A tutorial.” Mech. Syst. Signal Process., 25(7), 2275–2296.
Mthembu, L., Marwala, T., Friswell, M. I., and Adhikari, S. (2011). “Model selection in finite element model updating using the Bayesian evidence statistic.” Mech. Syst. Signal Process., 25(7), 2399–2412.
Myers, R. H., and Montgomery, D. C. (2002). Response surface methodology; Process and product optimisation using designed experiments, John Wiley and Sons, New York.
Nicolai, B. N., Egea, J. A., Scheerlinck, N., Banga, J. R., and Datta, A. K. (2011). “Fuzzy finite element analysis of heat conduction problems with uncertain parameters.” J. Food Eng., 103(1), 38–46.
O’Hagan, A. (2006). “Bayesian analysis of computer code outputs: A tutorial.” Reliability Eng. Syst. Safety, 91(10–11), 1290–1300.
Perera, R., Fang, S. E., and Ruiz, A. (2010). “Application of particle swarm optimization and genetic algorithms to multiobjective damage identification inverse problems with modelling errors.” Meccanica, 45(5), 723–734.
Ren, W. X., Fang, S. E., and Deng, M. Y. (2011). “Response surface-based finite-element-model updating using structural static responses.” J. Eng. Mech., 248–257.
Reynders, E., Teughels, A., and De Roeck, G. (2010). “Finite element model updating and structural damage identification using OMAX data.” Mech. Syst. Signal Process., 24(5), 1306–1323.
Sankararaman, S., and Mahadevan, S. (2013). “Bayesian methodology for diagnosis uncertainty quantification and health monitoring.” Struct. Contr. Health Monit., 20(1), 88–106.
Schmidt, A. M., Conceição, M. F. G., and Moreira, G. A. (2008). “Investigating the sensitivity of Gaussian processes to the choice of their correlation function and prior specifications.” J. Stat. Comput. Simulat., 78(8), 681–699.
Simoen, E., Moaveni, B., Conte, J., and Lombaert, G. (2013). “Uncertainty quantification in the assessment of progressive damage in a seven-story full-scale building slice.” J. Eng. Mech., 1818–1830.
Titurus, B., and Friswell, M. I. (2008). “Regularization in model updating.” Int. J. Numer. Methods Eng., 75(4), 440–478.
Waisman, H., Chatzi, E., and Smyth, A. W. (2010). “Detection and quantification of flaws in structures by the extended finite element method and genetic algorithms.” Int. J. Numer. Methods Eng., 82(3), 303–328.
Xiong, Y., Chen, W., Tsui, K. L., and Apley, D. W. (2009). “A better understanding of model updating strategies in validating engineering models.” Comput. Meth. Appl. Mech. Eng., 198(15–16), 1327–1337.
Xu, B., He, J., Rovekamp, R., and Dyke, S. J. (2012). “Structural parameters and dynamic loading identification from incomplete measurements: Approach and validation.” Mech. Syst. Signal Process., 28, 244–257.
Zadeh, L. A. (1965). “Fuzzy sets.” Infect. Contr., 8(3), 338–353.
Zhang, E. L., Feissel, P., and Antoni, J. A. (2011). “Comprehensive Bayesian approach for model updating and quantification of modeling errors.” Probabilist. Eng. Mech., 26(4), 550–560.
Zhang, G. W., Tang, B. P., and Tang, G. W. (2012). “An improved stochastic subspace identification for operational modal analysis.” Measurement, 45(5), 1246–1256.

Information & Authors

Information

Published In

Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 140Issue 11November 2014

History

Received: Sep 10, 2012
Accepted: Nov 13, 2013
Published online: May 15, 2014
Discussion open until: Oct 15, 2014
Published in print: Nov 1, 2014

Permissions

Request permissions for this article.

Authors

Affiliations

Yildirim Serhat Erdogan [email protected]
Dept. of Civil Engineering, Istanbul Technical Univ., Maslak, Istanbul 34469, Turkey. E-mail: [email protected]
Mustafa Gul [email protected]
Assistant Professor, Dept. of Civil and Environmental Engineering, Univ. of Alberta, Edmonton, AB, Canada T6G 2W2. E-mail: [email protected]
F. Necati Catbas [email protected]
M.ASCE
Professor, Dept. of Civil, Environmental and Construction Engineering, Univ. of Central Florida, Orlando, FL 32816-2450 (corresponding author). E-mail: [email protected]
Pelin Gundes Bakir [email protected]
M.ASCE
Professor, Dept. of Civil Engineering, Istanbul Technical Univ., Maslak, Istanbul 34469, Turkey. E-mail: [email protected]

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.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share