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Model-reduction techniques for Bayesian finite element model updating using dynamic response data. (English) Zbl 1423.74893

Summary: This work presents a strategy for integrating a class of model reduction techniques into a finite element model updating formulation. In particular a Bayesian model updating approach based on a stochastic simulation method is considered in the present formulation. Stochastic simulation techniques require a large number of finite element model re-analyses to be performed over the space of model parameters during the updating process. Substructure coupling techniques for dynamic analysis are proposed to reduce the computational cost involved in the dynamic re-analyses. The effectiveness of the proposed strategy is demonstrated with identification and model updating applications for finite element building models using simulated seismic response data.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
90B25 Reliability, availability, maintenance, inspection in operations research
62F15 Bayesian inference
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[1] Zhao, Z.; Haldar, A.; Breen, F. L., Fatigue-reliability updating through inspection of steel bridges, J. Struct. Eng. ASCE, 120, 5, 1624-1641, (1994)
[2] Sindel, R.; Rackwitz, R., Problems and solution strategies in reliability updating, J. Offshore Mech. Arct. Eng., 120, 2, 109-114, (1998)
[3] Yao, J. T.P.; Natke, H. G., Damage detection and reliability evaluation of existing structures, Struct. Saf., 15, 3-16, (1994)
[4] Deodatis, G.; Asada, H.; Ito, S., Reliability of aircraft structures under nonperiodic inspection—a Bayesian approach, J. Eng. Fract. Mech., 53, 5, 789-805, (1996)
[5] Cremona, C., Reliability updating of welded joints damaged by fatigue, Int. J. Fatigue, 18, 567-575, (1996)
[6] Shoji, H.; Shinozuka, M.; Sampath, S., A Bayesian evaluation of simulation models of multiple-site fatigue crack, Probab. Eng. Mech., 16, 355-361, (2001)
[7] Beaurepaire, P.; Valdebenito, M. A.; Schuëller, G. I.; Jensen, H. A., Reliability-based optimization of maintenance scheduling of mechanical components under fatigue, Comput. Methods Appl. Mech. Engrg., 221-222, 24-40, (2012) · Zbl 1253.74074
[8] H.O. Madsen, Model updating in reliability theory, in: Proc. ICASP 5, Vancuver, Canada, 1987.
[9] Papadimitriou, C.; Beck, J. L.; Katafygiotis, L., Updating robust reliability using structural test data, Probab. Eng. Mech., 16, 103-113, (2001)
[10] Beck, J. L., Bayesian system identification based on probability logic, Struct. Control Health Monit., 17, 7, 825-847, (2010)
[11] Yuen, K. V., Bayesian methods for structural dynamics and civil engineering, (2010), John Wiley & Sons
[12] Bleistein, N.; Handelsman, R., Asymptotic expansions for integrals, (1986), Dover Publicactions, Inc. New York, NY
[13] Beck, J.; Katafygiotis, L., Updating models and their uncertainties. I: Bayesian statistical framework, J. Eng. Mech., 124, 4, 455-461, (1998)
[14] Katafygiotis, L.; Beck, J., Updating models and their uncertainties. II: model identifiability, J. Eng. Mech., 124, 4, 463-467, (1998)
[15] Duane, S.; Kennedy, A. D.; Pendleton, B. J.; Roweth, D., Hybrid Monte Carlo, Phys. Lett. B, 195, 2, 216-222, (1987)
[16] Beck, J. L.; Au, S. K., Bayesian updating of structural models and reliability using Markov chain Monte Carlo simulation, J. Eng. Mech., 128, 4, 380-391, (2002)
[17] Ching, J.; Chen, Y. C., Transitional Markov chain Monte Carlo method for Bayesian updating, model class selection, and model averaging, J. Eng. Mech., 133, 816-832, (2007)
[18] Cheung, S. H.; Beck, J. L., Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters, J. Eng. Mech., 1135, 4, 243-255, (2009)
[19] Yuen, K. V.; Kuok, S. C., Bayesian methods for updating dynamic models, Appl. Mech. Rev., 64, 1, (2011), 010802-1-010802-18
[20] Nichols, J. M.; Moore, E. Z.; Murphy, K. D., Bayesian identification of a cracked plate using a population-based Markov chain Monte Carlo method, Comput. Struct., 89, 1323-1332, (2011)
[21] Jensen, H. A.; Vergara, C.; Papadimitriou, C.; Millas, E., The use of updated robust reliability measures in stochastic dynamical systems, Comput. Methods Appl. Mech. Engrg., 267, 293-317, (2013) · Zbl 1286.62086
[22] Craig, R. R, Structural dynamics, an introduction to computer methods, (1981), John Wiley & Sons New York
[23] Papadimitriou, C.; Papadioti, D. Ch., Component mode synthesis techniques for finite element model updating, Comput. Struct., 126, 15-28, (2013)
[24] Jeffreys, H., Theory of probability, (1961), Oxford University Press USA · Zbl 0116.34904
[25] Beck, J. L.; Yuen, K. V., Model selection using response measurements: Bayesian probabilistic approach, J. Eng. Mech., 130, 2, 192-203, (2004)
[26] Jaynes, E., Probability theory: the logic of science, (2003), Cambridge University Press · Zbl 1045.62001
[27] Simoen, E.; Papadimitriou, C.; Lombaert, G., On prediction error correlation in Bayesian model updating, J. Sound Vib., 332, 18, 4136-4152, (2013)
[28] Katafygiotis, L. S.; Papadimitriou, C.; Lam, H. F., A probabilistic approach to structural model updating, J. Soil Dyn. Earthq. Eng., 17, 495-507, (1998)
[29] Katafygiotis, L. S.; Lam, H. F.; Papadimitriou, C., Treatment of unidentifiability in structural model updating, Adv. Struct. Eng., 3, 1, 19-39, (2000)
[30] B. Goller, J.L. Beck, G.I. Schuëller, Evidence-based identification of weighting factors in Bayesian model updating using modal data, in: ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, Rhodes, Greece, 2009.
[31] Goller, B.; Broggi, M.; Calvi, A.; Schuëller, G. I., A stochastic model updating technique for complex aerospace structures, Finite Elem. Anal. Des., 47, 739-752, (2011)
[32] Angelikopoulos, P.; Papadimitriou, C.; Koumoutsakos, P., Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework, J. Chem. Phys., 137, (2012), 1441103-1-1441103-19
[33] Metropolis, N.; Resenbluth, A.; Resenbluth, M.; Teller, A.; Teller, E., Equations of state calculations by fast computing machines, J. Chem. Phys., 21, 6, 1087-1092, (1953) · Zbl 1431.65006
[34] Hastings, W., Monte Carlo sampling methods using Markov chains and their applications, Biometrika, 57, 1, 97-109, (1970) · Zbl 0219.65008
[35] Craig, R. R; Bampton, M. C.C., Coupling of substructures for dynamic analysis, AIAA J., 6, 5, 678-685, (1965)
[36] Castanier, M. P.; Tan, Y. C.; Pierre, C., Characteristic constraint modes for component mode synthesis, AIAA J., 39, 6, 1182-1187, (2001)
[37] Bathe, J., Finite element procedures, (2006), Prentice Hall
[38] Sepulveda, A. E.; Thomas, H. L., Improved transient response approximation for general damped systems, AIAA J., 34, 6, 1261-1269, (1996) · Zbl 0894.73075
[39] Jensen, H. A.; Sepulveda, A. E., Design sensitivity metric for structural dynamic response, AIAA J., 35, 9, 1286-1693, (1998)
[40] Gull, S. F., Bayesian inductive inference and maximun entropy, (Skilling, J., Maximum Entropy and Bayesian Methods, (1989), Kluwer Dordrecht, Boston, MA, USA)
[41] Minewaki, S.; Yamamoto, M.; Higashino, M.; Hamaguchi, H.; Kyuke, H.; Sone, T.; Yoneda, H., Performance tests of full size isolators for super high-rise isolated buildings, J. Struct. Eng. AIJ, 55(B), 469-477, (2009)
[42] Yamamoto, M.; Minewaki, S.; Yoneda, H.; Higashimo, M., Nonlinear behavior of high-damping rubber bearings under horizontal bidirectional loading: full-scale tests and analytical modeling, Earthq. Eng. Struct. Dyn., 41, 13, 1845-1860, (2012)
[43] H.A. Jensen, D.S Kusanovic, M. Papadrakakis, Reliability-based characterization of base-isolated structural systems, in: European Congress on Computational Methods in Applied Sciences and Engineering, Vienna, Austria, 2012.
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