Parameter Selection in Finite-Element-Model Updating by Global Sensitivity Analysis Using Gaussian Process Metamodel
Publication: Journal of Structural Engineering
Volume 141, Issue 6
Abstract
Parameter selection is a key step in finite-element-model updating (FEMU) because it determines whether the task of FEMU is successful or not. The as-built engineering structures are inevitably subject to many sources of uncertainty such as geometric dimension variability due to manufacture process, inherent random variation of materials, and imprecisely known boundary conditions. Uncertainty involving parameters challenges the task of parameter selection in FEMU. In this paper, the powerful global sensitivity analysis (GSA) is proposed to perform parameter selection in FEMU when uncertainty exists. The Monte Carlo simulation (MCS) method is extensively adopted to perform GSA. However, the brute-force MCS method is likely to be unaffordable and impractical because it entails a large number of model evaluations due to its slow convergence. Therefore, the Gaussian process metamodel is used as the surrogate model of the time-consuming finite-element model to ease the heavy computational burden. Gaussian process metamodel is favored here because of its probabilistic, nonparametric features and high capability of modeling a complex physical system. The space-filling Sobol sequence sampling method is utilized to generate the informative training data for establishing the Gaussian process metamodel. Finally, two study cases of the simple flat steel plate and full-scale arch bridge are presented to detail the procedure of employing the proposed GSA method to select parameters for FEMU.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
Financial support from the Natural Science Foundation of China (NSFC) under grant numbers 51078357 and 51278163 is acknowledged.
References
Abu Husain, N., Haddad Khodaparast, H., and Ouyang, H. (2012). “Parameter selection and stochastic model updating using perturbation methods with parameter weighting matrix assignment.” Mech. Syst. Signal Process., 32, 135–152.
ANSYS [Computer software]. Houston, TX, Swanson Analysis System.
Antonov, I. A., and Saleev, V. M. (1979). “An economic method of computing -sequences.” USSR Comput. Math. Math. Phys., 19(1), 252–256.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Becker, W., Oakley, J. E., Surace, C., Gili, P., Rowson, J., and Worden, K. (2012). “Bayesian sensitivity analysis of a nonlinear finite element model.” Mech. Syst. Signal Process., 32, 18–31.
Bratley, P., and Fox, B. L. (1988). “Algorithm 659: Implementing Sobol’s quasirandom sequence generator.” ACM Trans. Math. Software, 14(1), 88–100.
Brownjohn, J., and Xia, P. (2000). “Dynamic assessment of curved cable-stayed bridge by model updating.” J. Struct. Eng., 252–260.
Cheng, J., and Druzdzel, M. J. (2000). “Computational investigation of low-discrepancy sequences in simulation algorithms for Bayesian networks.” Proc., 16th Conf. on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers, Standard, CA, 72–81.
Efron, B., and Stein, C. (1981). “The jackknife estimate of variance.” Ann. Stat., 9(3), 586–596.
Fang, S. E., and Perera, R. (2011). “Damage identification by response surface based model updating using D-optimal design.” Mech. Syst. Signal Process., 25(2), 717–733.
Fang, S. E., Ren, W. X., and Perera, R. (2012). “A stochastic model updating method for parameter variability quantification based on response surface models and Monte Carlo simulation.” Mech. Syst. Signal Process., 33, 83–96.
Friswell, M. I., and Mottershead, J. E. (1995). Finite element model updating in structural dynamics, Kluwer Academic Publishers, Dordrecht, Netherlands.
Govers, Y., and Link, M. (2010). “Stochastic model updating-Covariance matrix adjustment from uncertain experimental modal data.” Mech. Syst. Signal Process., 24(3), 696–706.
Halton, J. H. (1960). “On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals.” Numerische Mathematik, 2(1), 84–90.
Helton, J. C., Johnson, J. D., Sallaberry, C. J., and Storlie, C. B. (2006). “Survey of sampling-based methods for uncertainty and sensitivity analysis.” Reliab. Eng. Syst. Saf., 91(10–11), 1175–1209.
Jäckel, P. (2002). Monte Carlo methods in finance, Wiley, Chichester, West Sussex, U.K.
Jaishi, B., and Ren, W. X. (2005). “Structural finite element model updating using ambient vibration test results.” J. Struct. Eng., 617–628.
Kala, Z. (2009). “Sensitivity assessment of steel members under compression.” Eng. Struct., 31(6), 1344–1348.
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.
Khodaparast, H. H., Mottershead, J. E., 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.
Lemieux, C., Cieslak, M., and Luttmer, K. (2002). “RandQMC user’s guide: A package for randomized quasi-Monte Carlo methods in C.” Technical Rep. 2002-712-15, Dept. of Computer Science, Univ. of Calgary, Canada.
Li, L., Lu, Z., Feng, J., and Wang, B. (2012). “Moment-independent importance measure of basic variable and its state dependent parameter solution.” Struct. Saf., 38, 40–47.
Likar, B., and Kocijan, J. (2007). “Predictive control of a gas–liquid separation plant based on a Gaussian process model.” Comput. Chem. Eng., 31(3), 142–152.
Ling, Y., and Mahadevan, S. (2012). “Integration of structural health monitoring and fatigue damage prognosis.” Mech. Syst. Signal Process., 28, 89–104.
Mackay, D. J. C. (1998). “Introduction to Gaussian processes.” NATO ASI series F computer and systems sciences, Vol. 168, 133–166.
Mares, C., Mottershead, J. E., and Friswell, M. I. (2006). “Stochastic model updating: Part 1—Theory and simulated example.” Mech. Syst. Signal Process., 20(7), 1674–1695.
Marino, S., Hogue, I. B., Ray, C. J., and Kirschner, D. E. (2008). “A methodology for performing global uncertainty and sensitivity analysis in systems biology.” J. Theor. Biol., 254(1), 178–196.
Mottershead, J. E., and Friswell, M. I. (1993). “Model updating in structural dynamics: A survey.” J. Sound Vib., 167(2), 347–375.
Mottershead, J. E., Mares, C., James, S., and Friswell, M. I. (2006). “Stochastic model updating: Part 2—Application to a set of physical structures.” Mech. Syst. Signal Process., 20(8), 2171–2185.
Myers, R. H., Montgomery, D. C., and Anderson-Cook, C. M. (2009). Response surface methodology: Process and product optimization using designed experiments, 3rd Ed., Wiley, Hoboken, NJ.
Neal, R. M. (1999). “Regression and classification using Gaussian process priors.” Proc., Bayesian Statistics 6: Proc., 6th Valencia Int. Meeting, Oxford University Press, 476–501.
Oakley, J., and O’Hagan, A. (2002). “Bayesian inference for the uncertainty distribution of computer model outputs.” Biometrika, 89(4), 769–784.
O’Hagan, A. (2006). “Bayesian analysis of computer code outputs: A tutorial.” Reliab. Eng. Syst. Saf., 91(10–11), 1290–1300.
Paskov, S. H. (1994). “Computing high dimensional integrals with applications to finance.” Dept. of Computer Science, Columbia Univ., New York.
Rasmussen, C. E., and Williams, C. K. I. (2006). Gaussian processes for machine learning, MIT Press, Cambridge, MA.
Ren, W. X., and Chen, H. B. (2010). “Finite element model updating in structural dynamics by using the response surface method.” Eng. Struct., 32(8), 2455–2465.
Rohmer, J., and Foerster, E. (2011). “Global sensitivity analysis of large-scale numerical landslide models based on Gaussian-process meta-modeling.” Comput. Geosci., 37(7), 917–927.
Sacks, J., Welch, W. J., Mitchell, T. J., and Wynn, H. P. (1989). “Design and analysis of computer experiments.” Stat. Sci., 4(4), 409–423.
Saltelli, A. (2002). “Making best use of model evaluations to compute sensitivity indices.” Comput. Phys. Commun., 145(2), 280–297.
Saltelli, A., Chan, K., and Scott, M. (2000). Sensitivity analysis, Wiley, New York.
Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F. (2001a). “Kriging models for global approximation in simulation-based multidisciplinary design optimization.” AIAA J., 39(12), 2233–2241.
Simpson, T. W., Poplinski, J. D., Koch, P. N., and Allen, J. K. (2001b). “Metamodels for computer-based engineering design: Survey and recommendations.” Eng. Comput., 17(2), 129–150.
Sobol, I. M. (1967). “On the distribution of points in a cube and the approximate evaluation of integrals.” USSR Comput. Math. Math. Phys., 7(4), 86–112.
Sobol, I. M. (1993). “Sensitivity analysis for non-linear mathematical models.” Math. Model. Comput., 1, 407–414.
Steenackers, G., and Guillaume, P. (2006). “Finite element model updating taking into account the uncertainty on the modal parameters estimates.” J. Sound Vib., 296(4–5), 919–934.
Tang, Q. H., Lau, Y. B., Hu, S. Q., Yan, W. J., Yang, Y. H., and Chen, T. (2010). “Response surface methodology using Gaussian processes: Towards optimizing the trans-stilbene epoxidation over Co2+-NaX catalysts.” Chem. Eng. J., 156(2), 423–431.
Yan, W. J., Hu, S. Q., Yang, Y. H., Gao, F. R., and Chen, T. (2011). “Bayesian migration of Gaussian process regression for rapid process modeling and optimization.” Chem. Eng. J., 166(3), 1095–1103.
Yuan, J., Wang, K. S., Yu, T., and Fang, M. (2008). “Reliable multi-objective optimization of highspeed WEDM process based on Gaussian process regression.” Int. J. Mach. Tools Manuf., 48(1), 47–60.
Zong, Z. H., Jaishi, B., Ge, J. P., and Ren, W. X. (2005). “Dynamic analysis of a half-through concrete-filled steel tubular arch bridge.” Eng. Struct., 27(1), 3–15.
Information & Authors
Information
Published In
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 21, 2012
Accepted: May 6, 2014
Published online: Aug 7, 2014
Discussion open until: Jan 7, 2015
Published in print: Jun 1, 2015
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.