Material Parameter Identification in Distributed Plasticity FE Models of Frame-Type Structures Using Nonlinear Stochastic Filtering
Publication: Journal of Engineering Mechanics
Volume 141, Issue 5
Abstract
This paper proposes a novel framework that combines high-fidelity mechanics-based nonlinear (hysteretic) finite-element (FE) models and a nonlinear stochastic filtering technique, referred to as the unscented Kalman filter, to estimate unknown material parameters in frame-type structures. The proposed identification framework updates nonlinear FE models using spatially limited noisy measurement data, and it can be further used for damage identification purposes. To validate its effectiveness, robustness, and accuracy, this framework is applied to a cantilever steel column representing a bridge pier and two-dimensional steel frame. Both structures are modeled using beam-column elements with distributed plasticity and are subjected to a suite of earthquake ground motions of varying intensity. The results indicate that the material parameters of the nonlinear FE models are accurately estimated provided that the loading intensity is sufficient to exercise the parts (branches) of the nonlinear material model, which are governed by the material parameters to be identified, and the measured response quantities are sufficiently sensitive to the material parameters to be identified, especially when a limited number of measurements are considered.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The first author acknowledges the support provided by the Fulbright-CONICYT Chile Equal Opportunities Scholarship. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect those of the sponsor.
References
AISC. (2010). Seismic provisions for structural steel buildings, Chicago.
Arulampalam, M. S., Maskell, S., Gordon, N., and Clapp, T. (2002). “A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking.” IEEE Trans. Signal Process., 50(2), 174–189.
ASTM. (2012). “Standard specification for carbon structural steel.” A36, West Conshohocken, PA.
Astroza, R., Ebrahimian, H., Conte, J. P., Restrepo, J., and Hutchinson, T. C. (2013). “Modal identification of 5-story RC building tested on NEES-UCSD shake table.” Proc., 31st Int. Modal Analysis Conf., Springer, New York, 109–117.
Ayoub, A., and Filippou, F. C. (2000). “Mixed formulation of nonlinear steel-concrete composite beam element.” J. Struct. Eng., 371–381.
Beck, J. L., and Katafygiotis, L. S. (1998). “Updating models and their uncertainties. I: Bayesian statistical framework.” J. Eng. Mech., 455–461.
Chassiakos, A. G., Masri, S. F., Smyth, A. W., and Caughey, T. K. (1998). “On-line identification of hysteretic systems.” J. Appl. Mech., 65(1), 194–203.
Chatzi, E. N., and Smyth, A. W. (2009). “The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non-collocated heterogeneous sensing.” Struct. Contr. Health Monit., 16(1), 99–123.
Ching, J., Beck, J. L., Porter, K. A., and Shaikhutdinov, R. (2006). “Bayesian state estimation method for nonlinear systems and its application to recorded seismic response.” J. Eng. Mech., 396–410.
Chopra, A. K. (2011). Dynamics of structures, 4th Ed., Prentice Hall, Englewood Cliffs, NJ.
Corigliano, A., and Mariani, S. (2004). “Parameter identification in explicit structural dynamics: Performance of the extended Kalman filter.” Comput. Methods Appl. Mech. Eng., 193(36–38), 3807–3835.
Deierlein, G. G., Reinhord, A. M., and Willford, M. R. (2010). “Nonlinear structural analysis for seismic design: A guide for practicing engineers.” NIST GCR 10-917-5, National Institute of Standards and Technology, Gaithersburg, MD.
Doebling, S. W., Farrar, C. R., Prime, M. B., and Shevit, D. W. (1996). “Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review.” Technical Rep. LA-13070-MS, Los Alamos National Laboratory, Los Alamos, NM.
Ebrahimian, H., Astroza, R., Conte, J. P., Restrepo, J. I., and Hutchinson, T. C. (2014). “Experimental validation of dynamic nonlinear FE model of full-scale five-story reinforced concrete building.” Proc., 9th Int. Conf. on Structural Dynamics (EURODYN 2014), European Association for Structural Dynamics (EASD), Volos, Greece, and Faculty of Engineering of the Univ. of Porto, Porto, Portugal, 337–344.
FEMA. (2000). “State-of-the-art report on systems performance of steel moment frames subjected to earthquake ground shaking.” FEMA 355C, Washington, DC.
Filippou, F. C., and Fenves, G. L. (2004). “Methods of analysis for earthquake-resistant structures.” Chapter 6, Earthquake engineering: From engineering seismology to performance-based engineering, CRC Press, Boca Raton, FL.
Filippou, F. C., Popov, E. P., and Bertero, V. V. (1983). “Effects of bond deterioration on hysteretic behavior of reinforced concrete joints.” Rep. No. EERC 83–19, Earthquake Engineering Research Center, Univ. of California, Berkeley, CA.
Friswell, M. I., and Mottershead, J. E. (1995). Finite element model updating in structural dynamics, Kluwer, Boston.
Giagopoulos, D., Papadioti, D.-C., Papadimitriou, C., and Natsiavas, S. (2013). “Bayesian uncertainty quantification and propagation in nonlinear structural dynamics.” Proc., 31st Int. Modal Analysis Conf. (IMAC XXXI), Springer, New York, 33–41.
Gupta, A., and Krawinkler, H. (2000). “Behavior of ductile SMRFs at various seismic hazard levels.” J. Struct. Eng., 98–107.
Haug, A. J. (2005). “A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non-Gaussian processes.” Technical Rep. MTR 05W0000004, MITRE, McLean, VA.
Haykin, S., ed. (2001). Kalman filtering and neural networks, Wiley, New York.
Housner, G. W., et al. (1997). “Structural control: Past, present, and future.” J. Eng. Mech., 897–971.
Huang, H., Yang, J. N., and Zhou, L. (2010). “Adaptive quadratic sum-squares error with unknown inputs for damage identification of structures.” Struct. Contr. Health Monit., 17(4), 404–426.
Imai, H., Yun, C. B., Maruyama, O., and Shinozuka, M. (1989). “Fundamentals of system identification in structural dynamics.” Probab. Eng. Mech., 4(4), 162–173.
International Conference of Building Officials (ICBO). (1994). Uniform building code, Whittier, CA.
Ismail, M., Ikhouane, F., and Rodellar, J. (2009). “The hysteresis Bouc-Wen model, a survey.” Arch. Comput. Meth. Eng., 16(2), 161–188.
Ji, X., Fenves, G. L., Kajiwara, K., and Nakashima, M. (2011). “Seismic damage detection of a full-scale shaking table test structure.” J. Struct. Eng., 14–21.
Julier, S. J., and Uhlmann, J. K. (1997). “A new extension of the Kalman filter to nonlinear systems.” Proc., 11th Int. Symp. on Aerospace/Defense Sensing, Simulation and Controls, Society of Photo-optical Instrumentation Engineers (SPIE), Bellingham, WA, 182–193.
Kalman, R. E. (1960). “A new approach to linear filtering and prediction problems.” J. Fluids Eng., 82(1), 35–45.
Kalman, R. E., and Bucy, R. (1961). “New results in linear filtering and prediction theory.” J. Fluids Eng., 83(1), 95–107.
Kerschen, G., Worden, K., Vakakis, A. F., and Golinval, J.-C. (2006). “Past, present and future of nonlinear system identification in structural dynamics.” Mech. Syst. Signal Process., 20(3), 505–592.
Koutromanos, I., Stavridis, A., Shing, P. B., and Willam, K. (2011). “Numerical modeling of masonry-infilled RC frames subjected to seismic loads.” Comput. Struct., 89(11–12), 1026–1037.
Lee, D.-J. (2005). “Nonlinear Bayesian filtering with applications to estimation and navigation.” Ph.D. thesis, Dept. of Aerospace Engineering, Texas A&M Univ., College Station, TX.
Martinelli, P., and Filippou, F. C. (2009). “Simulation of the shaking table test of a seven-story shear wall building.” Earthquake Eng. Struct. Dyn., 38(5), 587–607.
Marwala, T. (2010). Finite element model updating using computational intelligence techniques: Applications to structural dynamics, Springer-Verlag, London.
Masri, S. F., and Caughey, T. K. (1979). “A nonparametric identification technique for nonlinear dynamic problems.” J. Appl. Mech., 46(2), 433–447.
MATLAB 8.2 [Computer software]. Natick, MA, MathWorks.
Menegotto, M., and Pinto, E. (1973). “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” Proc., IABSE Symp. on Resistance and Ultimate Deformability of Structures Acted on by Well-Defined Repeated Loads, International Association for Bridge and Structural Engineering, Zurich, Switzerland, 15–21.
Moaveni, B., He, X., Conte, J. P., and Restrepo, J. I. (2010). “Damage identification study of a seven-story full-scale building slice tested on the UCSD-NEES shake table.” Struct. Saf., 32(5), 347–356.
Moaveni, B., He, X., Conte, J. P., Restrepo, J. I., and Panagiotou, M. (2011). “System identification study of a 7-story full-scale building slice tested on the UCSD-NEES shake table.” J. Struct. Eng., 705–717.
Muto, M., and Beck, J. L. (2008). “Bayesian updating and model class selection using stochastic simulation.” J. Vib. Control, 14(1–2), 7–34.
Nasrellah, H. A., and Manohar, C. S. (2011). “Finite element method based Monte Carlo filters for structural system identification.” Probab. Eng. Mech., 26(2), 294–307.
OpenSees 2.4.2 [Computer software]. Berkeley, CA, Pacific Earthquake Engineering Research Center, Univ. of California at Berkeley.
Ristic, B., Arumpalam, S., and Gordon, N. (2004). Beyond the Kalman filter—Particle filters for tracking applications, Artech House, Boston.
Simoen, E., Moaveni, B., Conte, J. P., and Lombaert, G. (2013). “Uncertainty quantification in the assessment of progressive damage in a 7-story full-scale building slice.” J. Eng. Mech., 1818–1830.
Simon, D. (2006). Optimal state estimation, Wiley, New York.
Taucer, F. F., Spacone, E., and Filippou, F. C. (1991). “A fiber beam-column element for seismic response analysis of reinforced concrete structures.” Rep. 91/17, Earthquake Engineering Research Center (EERC), Univ. of California, Berkeley, CA.
Uriz, P., Filippou, F. C., and Mahin, S. A. (2008). “Model for cyclic inelastic buckling of steel braces.” J. Struct. Eng., 619–628.
van der Merwe, R., Wan, E. A., and Julier, S. (2004). “Sigma-point Kalman filters nonlinear estimation and sensor fusion—Applications in integrated navigation.” Proc., AIAA Guidance Navigation and Controls Conf., American Institute of Aeronautics and Astronautics, Reston, VA, 1735–1764.
Wan, E. A., and van der Merwe, R. (2000). “The unscented Kalman filter for nonlinear estimation.” Proc., IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symp., IEEE, New York.
Wu, M., and Smyth, A. W. (2007). “Application of the unscented Kalman filter for real-time nonlinear structural system identification.” Struct. Contr. Health Monit., 14(7), 971–990.
Yang, J. N., and Lin, S. (2004). “On-line identification of non-linear hysteretic structures using an adaptive tracking technique.” Int. J. Non Linear Mech., 39(9), 1481–1491.
Yang, J. N., Xia, Y., and Loh, C.-H. (2014). “Damage detection of hysteretic structures with a pinching effect.” J. Eng. Mech., 462–472.
Yuen, K.-V., and Kuok, S.-C. (2011). “Bayesian methods for updating dynamic models.” Appl. Mech. Rev., 64(1), 010802.
Yun, C.-B., and Shinozuka, M. (1980). “Identification of nonlinear structural dynamic systems.” J. Struct. Mech., 8(2), 187–203.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 141 • Issue 5 • May 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 24, 2013
Accepted: Jul 21, 2014
Published online: Sep 19, 2014
Published in print: May 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.