Identification of random shapes from images through polynomial chaos expansion of random level-set functions

Ioannis Stefanou (1) , Anthony Nouy (1) , Alexandre Clément (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

In this paper, an efficient method is proposed for the identification of random shapes in a form suitable for numerical simulation within the eXtended Stochastic Finite Element Method (X-SFEM). The method starts from a collection of images representing different outcomes of the random shape to identify. The key-point of the method is to represent the random geometry in an implicit manner using the level-set technique. In this context, the problem of random geometry identification is equivalent to the identification of a random level-set function, which is a random field. This random field is represented on a polynomial chaos basis and various efficient numerical strategies are proposed in order to identify the coefficients of its polynomial chaos decomposition. The performance of these strategies is evaluated through some "manufactured" problems and useful conclusions are provided. The propagation of geometrical uncertainties in structural analysis using the X-SFEM is finally examined.

Mots clés: Random geometry; Level-set method; Probabilistic identification; Polynomial chaos; Maximum likelihood; Extended stochastic finite element method

Domaines: Analyse numérique [math.NA]; Mécanique [physics.med-ph]

Ioannis Stefanou, Anthony Nouy, Alexandre Clément. Identification of random shapes from images through polynomial chaos expansion of random level-set functions. International Journal for Numerical Methods in Engineering, 2009, 79 (2), pp.127-155. ⟨10.1002/nme.2546⟩. ⟨hal-00366640⟩