Global sensitivity analysis for nested and multiscale models

Abstract

This thesis is a contribution to the nested modelling of complex systems. A global methodology to quantify uncertainties and their origins in a workflow composed of several models that can be intricately linked is proposed. This work is organized along three axes. First, the dependence structure of the model parameters induced by the nested modelling is rigorously described thanks to the copula theory. Then, two sensitivity analysis methods for models with correlated inputs are presented: one is based on the analysis of the model response distribution and the other one is based on the decomposition of the covariance. Finally, a framework inspired by the graph theory is proposed for the description of the imbrication of the models. The proposed methodology is applied to different industrial applications: a multiscale modelling of the mechanical properties of concrete by homogenization method and a multiphysics approach of the damage on the cylinder head of a diesel engine. The obtained results provide the practitioner with essential informations for a significant improvement of the performance of the structure.

Keywords

Global sensitivity analysis, correlation, copula theory, graph theory, nested modelling, multiscale modelling.

BibTeX cite

@PHDTHESIS{CaniouThesis,
  author = {Caniou, Y.},
  title = {Global sensitivity analysis for nested and multiscale models},
  school = {Universit\'e Blaise Pascal, Clermont-Ferrand, France},
  year = {2012}
}