Sur la théorie des méconnaissances en mécanique des structures

International audienceToday, 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

Model validation in the presence of uncertain experimental data

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 Tarantula. 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.info:eu-repo/semantics/publishe

On a strategy for the reduction of the lack of knowledge (LOK) in model validation

International audienceToday, the quantification of the quality of a dynamic structural model remains a major issue, and the number of methods being devised in order to validate a model by comparison with an experimental reference keeps increasing. This paper presents a theory based on the concept of lack of knowledge, which consists in globalizing the various sources of errors on the substructure level by means of a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. These intervals, which are defined for each substructure, are then propagated rigorously throughout the mechanical model in order to determine intervals with stochastic bounds within which lies a given quantity of interest defined over the whole structure. Then, a general strategy for the reduction of the lack of knowledge is discussed and applied to academic examples as well as industrial cases

Lack of knowledge in structural model validation

International audienceThis paper deals with the structural modeling of a family of similar, actual structures taking into account uncertainties and modeling errors. Only errors of the “structural stiffness” type are considered. We develop a new theory in which what we call the lack of knowledge (LOK) is defined through an internal variable, whose upper and lower bounds are stochastic, associated with each substructure. Two main questions are discussed: the impact of the basic LOKs on the predicted structural response and the reduction of the basic LOKs through the use of additional information

Theory of the Lack of Knowledge : basic aspects and applications

International audienceThe concept of Lack Of Knowledge (LOK) was first introduced in [1, 2]. The basic principle consists in globalizing the various sources of errors on the substructure level using a scalar internal variable, called the LOK variable, defined over an interval whose upper and lower bounds follow probabilistic laws. The question of the impact of the structural model with LOKs on the prediction of the structural response can then be addressed. By a rigorous propagation of the intervals and the probability laws associated to the bounds, the envelope of the possible actual responses is defined, resulting in an interval with stochastic bounds including the structural response of interest. The comparison between these intervals and the experimental values available results in a reduction process of the basic LOKs, which considers the experimental data as additional information. In [3], we presented the first results of this strategy of reduction, starting from an initial overestimated LOK level, given by experience or a priori knowledge. This paper is focused on the reduction of the LOKs of a actual, industrial structure from the EADS Space Transportation division; this real-case study shows the effectiveness of the strategy of reduction used

Sur une théorie des méconnaissances en calcul des structures

The quantification of the quality of a structural mechanical model remains a major issue today, with the use of an increasing number of methods in order to validate a model in comparison with an experimental reference. This paper presents a new theory based on the concept of Lack of Knowledge combining convex uncertainty models with probabilistic features by introducing for each substructure two bounds of the strain energy as stochastic variables. A general strategy of reduction of the lack of knowledge is discussed and applied to academic as well as industrial cases.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Sur la théorie des méconnaissances en élasticité anisotrope

International audienceAs an extension of safety factors, the Lack-Of-Knowledge theory is an answer to model validation problems in structural mechanics. We introduce a LOK operator for orthotropic elasticity problems. This refined model is illustrated on academic and industrial examples.La théorie des méconnaissances répond au problème de la validation des modèles en mécanique des structures en étendant le concept de coefficient de sécurité. Dans cet article, nous introduisons une description par opérateur de méconnaissances pour traiter des problèmes d'élasticité anisotrope

Validation of structural dynamics models containing uncertainties

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