Model validation in the presence of uncertain experimental data
Tóm tắt
In this paper, we discuss the application of the constitutive relation error (CRE) to model updating and validation in the context of uncertain measurements. First, a parallel is drawn between the CRE method and a general theory for inverse problems proposed by Tarantola. Then, an extension of the classical CRE method considering uncertain measurements is proposed. It is shown that the proposed mechanics‐based approach for model validation is very effective in filtering noise in the experimental data. The method is applied to an industrial structure, the SYLDA5, which is a satellite support for Ariane5. The results demonstrate the robustness of the method in actual industrial situations.
Tài liệu tham khảo
Ahmadian, H., Mottershead, J. and Friswell, M. (1998), “Regularisation methods for finite element model updating”, Mechanical Systems and Signal Processing, Vol. 12 No. 1, pp. 47‐64.
Balmès, E. (2000), “Review and evaluation of shape expansion methods”, Proc. IMAC XVIII, S.E.M., San Antonio, TX.
Barthe, D., Deraemaeker, A., Ladevèze, P. and Loch, S.Le (2004), “Validation and updating of models of industrial structures based on the constitutive relation error”, AIAA Journal, Vol. 42 No. 7, pp. 1427‐34.
Baruch, M. (1982), “Optimal correction of mass and stiffness matrices using measured modes”, AIAA Journal, Vol. 20 No. 11, pp. 1623‐6.
Berger, H., Ohayon, R., Quetin, L., Barthe, L., Ladèveze, P. and Reynier, M. (1991), “Méthodes de recalage de modèles de structures en dynamique”, La Recherche Aérospatiale, Vol. 5, pp. 9‐20.
Berman, A. and Nagy, E.J. (1983), “Improvement of a large analytical model using test data”, AIAA Journal, Vol. 21 No. 8, pp. 1168‐73.
Bonnet, M. and Abdallah, J.B. (1994), “Structural parameter identification using non linear Gaussian inversion”, in Bui, H.D., Tanaka, M., et al. (Eds), Inverse Problems in Engineering, 1st ed., Balkema, Rotterdam, pp. 235‐42.
Chouaki, A., Ladevèze, P. and Proslier, L. (1998), “Updating structural dynamic models with emphasis on the damping properties”, AIAA Journal, Vol. 36 No. 6, pp. 1094‐9.
Chouaki, A., Deraemaeker, A., Ladevèze, P. and Le Loch, S. (2000), “Model updating using the error in the constitutive relation: Real case study”, Proc. IMAC XVIII, S.E.M., San Antonio, TX, pp. 140‐6.
Deraemaeker, A. and Ladevèze, P. (2001), “Effect of the finite element discretisation on the dynamic model updating process”, Proc. IMAC XIX, S.E.M., Kissimmee, Florida.
Doebling, S., Hemez, F., Shultze, J. and Chundy, A. (2002), “A metamodel‐based approach to model validation of nonlinear finite element simulations”, Proc. IMAC XX, S.E.M., Los Angeles, CA.
Drucker, D. (1964), “On the postulate of stability of material in the mechanics of continua”, Journal de Mécanique, Vol. 3 No. 2, pp. 235‐49.
Farhat, C. and Hemez, F. (1993), “Updating finite element dynamic models using an element‐by‐element sensitivity methodology”, AIAA Journal, Vol. 31 No. 9, pp. 1702‐11.
Hemez, F. and Doebling, S. (1999), “Test‐analysis correlation and finite element model updating for nonlinear, transient dynamics”, Proc. IMAC XVII, Kissimmee, FL, pp. 1501‐10.
Kaouk, M. and Zimmerman, D. (1994), “Structural damage assessment using a generalized minimum rank perturbation”, AIAA Journal, Vol. 32 No. 4, pp. 836‐42.
Ladevèze, P. (1983), “Updating of complex structures models”, Technical Report 33.11.01.4, Aérospatiale, Les Mureaux.
Ladevèze, P. (1993), “Error on the constitutive relation in dynamics: theory and application to model updating in structural dynamics”, Internal Report 150, L.M.T., Cachan.
Ladevèze, P. and Chouaki, A. (1999), “Application of a posteriori error estimation for structural model updating”, Inverse Problems, Vol. 15, pp. 49‐58.
Ladevèze, P. and Leguillon, D. (1983), “Error estimate procedure in the finite element method and application”, SIAM J. Num. Anal., Vol. 20 No. 3, pp. 485‐509.
Ladevèze, P. and Pelle, J. (2001), Mastering Computations in Linear and Non‐linear Mechanics, Hermes (in French).
Ladevèze, P. and Reynier, M. (1989), “A localization method of stiffness errors for the adjustment of F.E. models”, Vibrations Analysis Techniques and Applications, chapter F.E. Modeling and Analysis, A.S.M.E. Publishers, New York, NY, pp. 355‐61.
Ladevèze, P., Reynier, M. and Maia, N. (1994), “Error on the constitutive relation in dynamics”, in Bui, H.D., Tanaka, M., et al. (Eds), Inverse Problems in Engineering, 1st ed., Balkema, Rotterdam, pp. 251‐6.
Lammens, S., Brughmans, M., Leuridan, J., Heylen, W. and Sas, P. (1995), “Application of a FRF based model updating technique for the validation of a finite element models of components of the automotive industry”, Proc. Design Engineering Technical Conferences, A.S.M.E. Conferences, Boston, pp. 1191‐200.
Mottershead, J. and Friswell, M. (1993), “Model updating in structural dynamics: a survey”, Journal of Sound and Vibration, Vol. 167 No. 2, pp. 347‐75.
Pascual, R., Golinval, J. and Razeto, M. (1998), “On the reliability of error localization indicators”, Proc. ISMA 23, Leuven, Belgium.
Piranda, J., Lallement, G. and Cogan, S. (1991), “Parametric correction of finite element models by minimization of an output residual: Improvement of the sensitivity method”, S.E.M., (ed.), Proc. IMAC IX, Firenze, pp. 363‐8.
Shinn, R., Hemez, F. and Doebling, S. (2003), “Estimating the error in simulation prediction over the design space”, 44th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Norfolk, VA.
Tarantola, A. (1987), Inverse Problem Theory, Elsevier, Amsterdam.
Zimmerman, D. and Kaouk, M. (1992), “Eingenstructure assignment approach for structural damage detection”, AIAA Journal, Vol. 30 No. 7, pp. 1848‐55.