Abstract
This chapter presents a framework for the identification of nonlinear finite element (FE) structural models using Bayesian inference methods. Using the input-output dynamic data recorded during an earthquake event, batch and recursive Bayesian estimation methods are employed to update a mechanics-based nonlinear FE model of the structure of interest (building, bridge, dam, etc.). Unknown parameters of the nonlinear FE model characterizing material constitutive models, inertia, geometric, and/or constraint properties of the structure can be estimated using limited response data recorded through accelerometers or heterogeneous sensor arrays. The updated nonlinear FE model can be used to identify the damage in the structure following a damage-inducing event. This framework, therefore, can provide an advanced tool for post-disaster damage identification and structural health monitoring. The batch estimation method is based on a maximum a posteriori estimation (MAP) approach, where the time history of the input and output measurements are used as a single batch of data for estimating the FE model parameters. This method results in a nonlinear optimization problem that can be solved using gradient-based and non-gradient-based optimization algorithms. In contrast, the recursive Bayesian estimation method processes the information from the measured data recursively, and updates the estimation of the FE model parameters progressively over the time history of the event. The recursive Bayesian estimation method results in a nonlinear Kalman filtering approach. The Extended Kalman filter (EKF) and Unscented Kalman filter (UKF) are employed as recursive Bayesian estimation methods herein. For those estimation methods that require the computation of structural FE response sensitivities (total partial derivatives) with respect to the unknown FE model parameters, the direct differentiation method (DDM) is used. Response data numerically simulated from a nonlinear FE model (with unknown material model parameters) of a five-story two-by-one bay reinforced concrete frame building subjected to bi-directional horizontal seismic excitation are used to illustrate the performance of the proposed framework.
References
Astroza R, Ebrahimian E, Conte JP (2015) Material parameter identification in distributed plasticity FE models of frame-type structures using nonlinear stochastic filtering. ASCE J Eng Mech 141(5):04014149
Balan TA, Spacone E, Kwon M (2001) A 3D hypoplastic model for cyclic analysis of concrete structures. Eng Struct 23(4):333–342
Byrd RH, Hribar ME, Nocedal J (1999) An interior point algorithm for large-scale nonlinear programming. SIAM J Optim 9(4):877–900
Ching J, Beck JL, Porter KA, Shaikhutdinov R (2006) Bayesian state estimation method for nonlinear systems and its application to recorded seismic response. ASCE J Eng Mech 132(4):396–410
Cosenza E, Manfredi G, Ramasco R (1993) The use of damage functionals in earthquake engineering: A comparison between different methods. Earthquake Eng Struct Dynam 22(10):855–868
Distefano N, Pena-Pardo B (1976) System identification of frames under seismic loads. J Eng Mech Division 102(EM2):313–330
Distefano N, Rath A (1975a) System identification in nonlinear structural seismic dynamics. Comput Methods Appl Mech Eng 5:353–372
Distefano N, Rath A (1975b) Sequential identification of hysteretic and viscous models in structural seismic dynamics. Comput Methods Appl Mech Eng 6:219–232
Ebrahimian H, Astroza R, Conte JP (2015) Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method. Earthquake Eng Struct Dynam 44(10):1495–1522
Ebrahimian H, Astroza R, Conte JP, de Callafon RA (2016) Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation. Mech Syst Signal Process 84(B):194–222. doi:10.1016/j.ymssp.2016.02.002
Filippou FC, Popov EP, Bertero VV (1983) Effects of bond deterioration on hysteretic behavior of reinforced concrete joints. UCB/EERC-83/19. EERC Report 83-19, Earthquake Engineering Research Center, Berkeley, CA
Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht, The Netherlands
Gill PE, Murray W, Wright MH (1981) Practical optimization. Academic Press, London, England
Haukaas T, Gardoni P (2011) Model Uncertainty in Finite-Element Analysis: Bayesian Finite Elements. ASCE J Eng Mech 137(8):519–526
Huang Q, Gardoni P, Hurlebaus S (2015) Adaptive reliability analysis of reinforced concrete bridges using nondestructive testing. ASCE-ASME J Risk Uncertain Anal 1(4):04015014
International Code Council (ICC) (2012) International Building Code. Falls Church, VA
Julier SJ, Uhlmann JK (1997) A new extension of the Kalman filter to nonlinear systems. In: 11th international symposium on aerospace/defense sensing, simulation and controls, Orlando, FL
Kleiber M, Antunez H, Hien TD, Kowalczyk P (1997) Parameter sensitivity in nonlinear mechanics: theory and finite element computations. Wiley, England
Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice Hall, Upper Saddle River
Mander JB, Priestley MJN, Park R (1988) Theoretical stress-strain model for confined concrete. ASCE J Struct Eng 114(8):1804–1826
OpenSees—Open system for earthquake engineering simulation. http://opensees.berkeley.edu/. Accessed Nov 2015
Park YJ, Ang AH, Wen YK (1985) Seismic damage analysis of reinforced concrete buildings. ASCE J Struct Eng 111(4):740–757
Popovics S (1973) A numerical approach to the complete stress–strain curve of concrete. Cement Concrete Res 3(5):583–599
Saenz IP (1964) Discussion of ‘Equation for the stress–strain curve of concrete, by Desay P, Krishan S. American Concrete Institute (ACI) J 61(9):1229–1235
Scott BD, Park R, Priestley MJN (1982) Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates. American Concrete Inst (ACI) J 79(1):13–27
Shahidi S, Pakzad S (2014) Generalized response surface model updating using time domain data. ASCE J Struct Eng 140:A4014001
Simoen E, De Roeck G, Lombaert G (2015) Dealing with uncertainty in model updating for damage assessment: a review. Mech Syst Signal Process 56–57:123–149
Simon D (2006) Optimal state estimation: Kalman, H infinity, and nonlinear approaches. Wiley, Hoboken
Song W, Dyke SJ (2014) Real-time dynamic model updating of a hysteretic structural system. ASCE J Struct Eng 140(3):04013082
Taucer FF, Spacone E, Filippou FC (1991) A fiber beam-column element for seismic response analysis of reinforced concrete structures. Report 91/17, EERC, Earthquake Engineering Research Center (EERC), University of California, Berkeley
Tsay JJ, Arora JS (1990) Nonlinear structural design sensitivity analysis for path dependent problems. Part 1: general theory. Comput Methods Appl Mech Eng 81(2):183–208
Van Trees HL (2002) Optimum array processing, Part IV of detection, estimation, and modulation theory. Wiley, New York
Wan EA, van der Merwe R (2000) The unscented Kalman filter for nonlinear estimation. In: IEEE 2000 adaptive systems for signal processing, communications, and control symposium, Lake Louise, AB, Canada
Yang J, Xia Y, Loh CH (2014) Damage detection of hysteretic structures with pinching effect. ASCE J Eng Mech 140(3):462–472
Zhang Y, Der Kiureghian A (1993) Dynamic response sensitivity of inelastic structures. Comput Methods Appl Mech Eng 108(1–2):23–36
Acknowledgements
Partial support of this research by the UCSD Academic Senate under Research Grant RN091G − CONTE is gratefully acknowledged. 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 study are those of the authors and do not necessarily reflect those of the sponsors.
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Astroza, R., Ebrahimian, H., Conte, J.P. (2017). Batch and Recursive Bayesian Estimation Methods for Nonlinear Structural System Identification. In: Gardoni, P. (eds) Risk and Reliability Analysis: Theory and Applications. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-52425-2_15
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