Validation of structural dynamics models containing uncertainties. (English) Zbl 1193.74049

Summary: This paper deals with model validation in structural dynamics for a family of quasi-identical structures in the context of uncertain measurements. The crucial point is for the engineer to be able to quantify the quality of the model, which is probabilistic with respect to a set of measurements from which a probability density function can be extracted. Our approach is based on the “mechanical concept” of constitutive relation error estimator (CRE), which was introduced initially in order to quantify the quality of finite element analyses, then developed in the deterministic context. Our extended CRE estimator enables us to quantify the quality of a given probabilistic model and, thus, to update and validate the model. Several examples are given, including an industrial case.


74H15 Numerical approximation of solutions of dynamical problems in solid mechanics
74K99 Thin bodies, structures
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[1] Ladevèze, P., A modelling error estimator for dynamic structural model updating, (), 135-154
[2] P. Ladevèze, J.-P. Pelle, Mastering Calculations in Linear and Nonlinear Mechanics, Springer, in press.
[3] Babuska, I.; Strouboulis, T., The finite element method and its reliability, (2001), Oxford Science · Zbl 0997.74069
[4] P. Ladevèze, Validation and verification of stochastic models in uncertain environment through the constitutive relation error method, Internal Report 258, LMT-Cachan, June 2003 (in French).
[5] Mottershead, J.; Friswell, M., Model updating in structural dynamics: a survey, J. sound vib., 167, 2, 347-375, (1993) · Zbl 0967.74525
[6] Ibrahim, S.R., Analytical dynamic model updating: the challenge for the nineties, Trans. inst. eng. aust., 16, 1, 17, (1991)
[7] Baruch, M., Optimal correction of mass and stiffness matrices using measured modes, Aiaa j., 20, 11, 1623-1626, (1982)
[8] Berman, A.; Nagy, E.J., Improvement of a large analytical model using test data, Aiaa j., 21, 8, 1168-1173, (1983)
[9] Kaouk, M.; Zimmerman, D., Structural damage assessment using a generalized minimum rank perturbation, Aiaa j., 32, 4, 836-842, (1994) · Zbl 0802.73059
[10] Zimmerman, D.; Kaouk, M., Eigenstructure assignment approach for structural damage detection, Aiaa j., 30, 7, 1848-1855, (1992)
[11] Berger, H.; Ohayon, R.; Quetin, L.; Barthe, L.; Ladèveze, P.; Reynier, M., Updating methods for structural dynamics models, La recherche Aérospatiale, 5, 9-20, (1991), (in French)
[12] Farhat, C.; Hemez, F., Updating finite element dynamic models using an element-by-element sensitivity methodology, Aiaa j., 31, 9, 1702-1711, (1993) · Zbl 0783.73068
[13] J. Piranda, G. Lallement, S. Cogan, Parametric correction of finite element models by minimization of an output residual: improvement of the sensitivity method, in: Proc. IMAC IX, Firenze, Italy, 1991, pp. 363-368.
[14] S. Lammens, M. Brughmans, J. Leuridan, W. Heylen, P. Sas, Application of a FRF based model updating technique for the validation of a finite element models of components of the automotive industry, in: Proc. Design Engineering Technical Conferences, A.S.M.E. Conferences, Boston, 1995, pp. 1191-1200.
[15] F. Hemez, S. Doebling, Test-analysis correlation and finite element model updating for nonlinear, transient dynamics, in: Proc. IMAC XVIII, Kissimmee, FL, 1999, pp. 1501-1510.
[16] S. Doebling, F. Hemez, J. Schulze, A. Gundy, A metamodel-based approach to model validation of nonlinear finite element simulations, in: Proc. IMAC XX, Los Angeles, CA, 2002.
[17] R. Shinn, F. Hemez, S. Doebling, Estimating the error in simulation prediction over the design space, in: 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, VA, 2003.
[18] P. Ladevèze, Updating of complex structures models, Tech. Rep., Aérospatiale, Les Mureaux, in French (1983).
[19] Ladevèze, P.; Reynier, M., FE modeling and analysis: a localization method of stiffness errors for the adjustments of FE models, (), 355-361
[20] P. Ladevèze, Error on the constitutive relation in dynamics: theory and application to model updating in structural dynamics, Internal Report 150, LMT-Cachan, 1993 (in French).
[21] Chouaki, A.; Ladevèze, P.; Proslier, L., Updating structural dynamic models with emphasis on the damping properties, Aiaa j., 36, 6, 1094-1099, (1998)
[22] Ladevèze, P.; Chouaki, A., Application of a posteriori error estimation for structural model updating, Inverse prob., 15, 49-58, (1999) · Zbl 0928.74039
[23] Ladevèze, P., Nonlinear computational structural mechanics, (1999), Springer New York
[24] A. Chouaki, A. Deraemaeker, P. Ladevèze, S. Le Loch, Model updating using the error in the constitutive relation: real case study, in: Proc. IMAC XVIII, San Antonio, TX, 2000, pp. 140-146.
[25] E. Balmès, Review and evaluation of shape expansion methods, in: Proc. IMAC XVIII, San Antonio, TX, 2000.
[26] P. Moine, L. Billet, D. Aubry, Updating a non conservative finite element model: two modal methods, in: Proc. Design Engineering Technical Conference No. 3, Boston, USA, 1995, pp. 1302-1310.
[27] R. Pascual, J. Golinval, M. Razeto, On the reliability of error localization indicators, in: Proc. ISMA 23, Leuven, Belgium, 1998.
[28] Barthe, D.; Deraemaeker, A.; Ladevèze, P.; Le Loch, S., Validation and updating of models of industrial structures based on the constitutive relation error, Aiaa j., 42, 7, 1427-1434, (2004)
[29] Ghanem, R.; Spanos, P., Stochastic finite elements: a spectral approach, (1991), Springer Berlin · Zbl 0722.73080
[30] A. Keese, H. Matthies, Numerical methods and smolyak quadrature for nonlinear stochastic partial differential equations, SIAM J. Sci. Comput., in press. · Zbl 1088.65002
[31] Schueller, G., A state-of-the-art report on computational stochastic mechanics, Probabilist. engrg. mech., 12, 4, 197-321, (1997)
[32] R. Ghanem, M. Pelissetti, A method for the validation of predictive computations using a stochastic approach, in: Proc. of OMAE’02, Oslo, Norway, 2002.
[33] R. Ghanem, M. Pelissetti, Error estimation for the validation of model-based predictions, in: Proc. of 5th World Congress on Computational Mechanics, Vienna, Austria, 2002.
[34] Tarantola, A., Inverse problem theory, (1987), Elsevier
[35] Menke, W., Geophysical data analysis: discrete inverse theory, (1984), Academic Press
[36] Bonnet, M.; Abdallah, J.B., Structural parameter identification using nonlinear Gaussian inversion, (), 235-242
[37] A. Chouaki, Updating of structural dynamical models with damping, Ph.D. thesis, LMT-Cachan, ENS Cachan—Paris 6 University, 1997.
[38] Deraemaeker, A.; Ladevèze, P.; Romeuf, T., Model validation in the presence of uncertain experimental data, Engrg. comput., 21, 8, 808-833, (2004) · Zbl 1134.65304
[39] Deraemaeker, A.; Ladevèze, P.; Leconte, P., Reduced bases for model updating in structural dynamics based on constitutive relation error, Comput. methods appl. mech. engrg., 191, 21-22, 2427-2444, (2002) · Zbl 1131.74310
[40] J.C. Golinval, P. Collignon, Comparison of model updating methods adapted to local error detection, in: Proc. ISMA 21, Leuven, Belgium, 1996.
[41] A. Deraemaeker, P. Ladevèze, Effect of the finite element discretisation on the dynamic model updating process, in: Proc. IMAC XIX, Kissimmee, FL, 2001.
[42] P. Ladevèze, G. Puel, T. Romeuf, On a strategy reduction of the lack of knowledge (LOK) of a structural dynamics model, in: Proc. IMAC XXII, Dearborn, MI, 2004.
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