Random Fields and Uncertainty Quantification in Solid Mechanics of Continuum Media

Abstract

The statistical inverse problem for the experimental identification of a non-Gaussian matrix-valued random field that is the model parameter of a boundary value problem, using some partial and limited experimental data related to a model observation, is a very difficult and challenging problem. A complete advanced methodology is presented and is based on the use of all the developments presented in the previous chapters and in particular, the random matrix theory (Chapter 5 ), the stochastic solvers (Chapters 4 and 6 ), the statistical inverse methods (Chapter 7 ). However, we will start this chapter by presenting new mathematical results concerning the random fields and their polynomial chaos representations, which constitute the extension in infinite dimension of the tools presented in Sections 5.5 to 5.7 for the finite dimension, and which are necessary for solving the statistical inverse problems related to the non-Gaussian random fields.