Robust Analysis with Respect to the Uncertainties for Analysis, Updating, Optimization, and Design

Abstract

The objective of this chapter is to present some applications in different areas in order to show the importance to perform robust computation with respect to the uncertainties that exist in the computational models. The developments given in this chapter use all the tools and methods 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), and the parametric probabilistic approach of model-parameter uncertainties, the nonparametric probabilistic approach of both the model-parameter uncertainties and the model uncertainties induced by the modeling errors, and the generalized probabilistic approaches of uncertainties, that have been presented in Chapter 8.