Construction of a probabilistic model for impedance matrices

R. Cottereau (1) , Didier Clouteau (1) , Christian Soize (2)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
2 LaM - Laboratoire de Mécanique

Impedance matrices allow for the coupling of domains with very different properties, and possibly modeled with different methods. This paper presents the construction of a probabilistic model for such matrices, using a nonparametric method that allows for the consideration of data errors as well as model errors. To enable the application of this method in the case of a domain for which no Finite Element model is available, the identification of a "hidden state variables model" - from the knowledge of the impedance matrix at a discrete set of frequencies - is also described. Finally the construction of the probabilistic model of the impedance of a pile foundation on a layered unbounded soil illustrates the capabilities of the method.

Mots clés: model uncertainties; nonparametric probabilistic method; unbounded domains; uncertainty quantification; computational stochastic mechanics; impedance matrix; random matrix; modeling errors

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

R. Cottereau, Didier Clouteau, Christian Soize. Construction of a probabilistic model for impedance matrices. Computer Methods in Applied Mechanics and Engineering, 2007, 196 (17-20), pp.2252-2268. ⟨10.1016/j.cma.2006.12.001⟩. ⟨hal-00686151⟩