On the lack-of-knowledge theory for low and high values of uncertainties

Sami Daouk (1) , François Louf (2) , Olivier Dorival (1, 3) , Laurent Champaney (2)

1 LMT - Laboratoire de Mécanique et Technologie
2 LMT - Laboratoire de Mécanique et Technologie
3 ICA - Institut Clément Ader

Model validation of real structures remains a major issue, not only because of their complexity but also due to their uncertain behavior. Over the past decades, the development of computational tools improved the modeling of the behavior of these structures, in statics and dynamics, at low cost. Thus, in order to build accurate models and take uncertainties into account, many numerical stochastic and non-stochastic methods have been developed. This paper deals with the Lack-Of-Knowledge (LOK) theory, that intends to model "the unknown" in a conservative way. Data uncertainties and modeling errors are taken into account through a scalar internal variable, defined on the substructure level and located in a stochastic interval. The first part of this article presents a description of the mathematical background of the theory in the case of low and high values of uncertainties. A simple academic model is used to validate the implementation of the method through a comparison with the results obtained by Monte Carlo simulation. The study of a case representative of a complex industrial structure shows the ability of the LOK theory to evaluate the propagation of numerous large uncertainties through numerical models.

Mots clés: Uncertainty propagation; Structural dynamics; Lack of knowledge; Large uncertainties; Vibrations

Domaines: Mécanique [physics]

Sami Daouk, François Louf, Olivier Dorival, Laurent Champaney. On the lack-of-knowledge theory for low and high values of uncertainties. 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling, Uncertainties 2014, 2014, Rouen, France. pp.1. ⟨hal-01023550⟩