Today, the validation of complex structural models – i.e. the assessment of their quality compared to an experimental reference – remains a major issue. Strictly speaking, the validation problem consists in comparing the response of the numerical model (whether deterministic or stochastic) with complete reality. A first answer to this problem, using Lack-Of-Knowledge (LOK) theory, was introduced at LMT-Cachan. This theory is an attempt to “model the unknown” by taking all the sources of uncertainties, including modeling errors, into account through the concept of basic LOKs. In this article, we introduce basic LOKs associated with both the amplitudes and directions of excitations. These basic LOKs are propagated rigorously throughout the mechanical model in order to determine intervals (with stochastic bounds) within which lies a given quantity of interest (stress or displacement). Then, we introduce a strategy for the reduction of lack of knowledge, which we illustrate through an academic example.
La validation de modèles structuraux complexes – c'est-à-dire la vérification de leur qualité vis-à-vis d'une référence expérimentale – demeure un verrou scientifique fort. Le véritable problème de validation consiste à comparer la réponse du modèle numérique, qu'il soit déterministe ou pas, avec la réponse de toutes les structures réelles, dans tous les environnements possible. Un premier élément de réponse à ce problème a été introduit via la théorie des méconnaissances au LMT-Cachan. Afin de « modéliser l'inconnu », cette théorie prend en compte toutes les incertitudes, en incluant les erreurs de modèles, à travers le concept de méconnaissances de base. Dans le cet article, on introduit des méconnaissances de base sur les excitations (amplitude et direction). Ces méconnaissances de base sont ensuite propagées à travers le modèle mécanique afin de déterminer des intervalles dont les bornes sont probabilistes, contenant une quantité d'intérêt (contrainte ou déplacement). Ensuite une stratégie de réduction des méconnaissances de base par apport d'information expérimentale est présentée sur un exemple académique.
Mots-clés : Méconnaissances, Validation, Incertitudes, Problèmes inverses
François Louf 1; Paul Enjalbert 1; Pierre Ladevèze 1; Thierry Romeuf 2
@article{CRMECA_2010__338_7-8_424_0, author = {Fran\c{c}ois Louf and Paul Enjalbert and Pierre Ladev\`eze and Thierry Romeuf}, title = {On lack-of-knowledge theory in structural mechanics}, journal = {Comptes Rendus. M\'ecanique}, pages = {424--433}, publisher = {Elsevier}, volume = {338}, number = {7-8}, year = {2010}, doi = {10.1016/j.crme.2010.07.012}, language = {en}, }
TY - JOUR AU - François Louf AU - Paul Enjalbert AU - Pierre Ladevèze AU - Thierry Romeuf TI - On lack-of-knowledge theory in structural mechanics JO - Comptes Rendus. Mécanique PY - 2010 SP - 424 EP - 433 VL - 338 IS - 7-8 PB - Elsevier DO - 10.1016/j.crme.2010.07.012 LA - en ID - CRMECA_2010__338_7-8_424_0 ER -
François Louf; Paul Enjalbert; Pierre Ladevèze; Thierry Romeuf. On lack-of-knowledge theory in structural mechanics. Comptes Rendus. Mécanique, Inverse problems, Volume 338 (2010) no. 7-8, pp. 424-433. doi : 10.1016/j.crme.2010.07.012. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.012/
[1] The Logic of Scientific Discovery, Routledge Classics, Taylor and Francis, 2003
[2] Research directions in computational mechanics, Computer Methods in Applied Mechanics and Engineering, Volume 192 (2003), pp. 913-922
[3] A brief tutorial on verification and validation, Proceedings of the 22nd International Modal Analysis Conference (IMAC-XXII), Dearborn, Michigan, January 26–29, 2004
[4] W. Oberkampf, T. Trucano, C. Hirsh, Verification, validation and predictive capability in computational engineering and physics, Technical report, Sandia Report 2003-3769, 2003.
[5] Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, John Wiley and Sons, 2004
[6] Updating methods for structural dynamics models, La Recherche Aérospatiale, Volume 5 (1991), pp. 9-20 (in French)
[7] Updating finite element dynamics models using an element-by-element sensitivity methodology, AIAA Journal, Volume 31 (1993) no. 9, pp. 1702-1711
[8] J. Piranda, G. Lallement, S. Cogan, Parametric correction of finite element modes by minimization of an output residual: improvement of the sensitivity method, in: Proc. IMAC IX, Firenze, Italy, 1991, pp. 363–368.
[9] 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 model of components of the automotive industry, in: ASME Conference, Boston, 1995, pp. 1191–1200.
[10] FE modeling and analysis: a localization method of stiffness errors and adjustments of FE models, Vibrations Analysis Techniques and Application, ASME Publishers, 1989, pp. 355-361
[11] Validation of stochastic linear structural dynamics models, Computers and Structures, Volume 87 (2009) no. 13–14, pp. 829-837
[12] P. Ladevèze, On a theory of the lack of knowledge in structural computation, Technical Note SY/XS 136 127, EADS Launch Vehicles, April 2002 (in French).
[13] P. Ladevèze, Model validation or how can one describe the lack of knowledge, IACM Expressions, 2005.
[14] Computational stochastic mechanics – recent advances, Computers and Structures, Volume 79 (2001), pp. 2225-2234
[15] Information-Gap Decision Theory, Academic Press, London, 2001
[16] Generalized information theory, Fuzzy Sets and Systems, Volume 40 (1991), pp. 127-142
[17] Statistical Reasoning with Imprecise Probabilities, Chapman and Hall, 1990
[18] Methods and Applications of Interval Analysis, Studies in Applied Mathematics (SIAM), 1979
[19] Lack of knowledge in structural model validation, Computer Methods in Applied Mechanics and Engineering, Volume 195 ( July 2006 ), pp. 4697-4710
[20] Reduction of the lack of knowledge of an industrial structural dynamics model, 8th US National Congress on Computational Mechanics, Austin, Texas, July 25–27, 2005
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