Uncertainty Quantification and Global Sensitivity Analysis in Computational Mechanics

This thesis provides insight on Uncertainty Quantification (UQ) and Global Sensitivity Analysis (GSA) processes and explores in detail those aspects of metamodels which make them suitable for real applications. For this purpose, UQ, GSA, and the construction of well-designed meta-models, instrumental to complete both processes, are revisited by providing a balance between a rigorous mathematical approach and practical guidelines needed in an industrial environment. This work is motivated by the advantages that derive, at the industrial level, from the adoption of an effective UQ/GSA framework: a one-time process of product development with increases reliability and durability and the opportunity to provide more credible and realistic simulations. The required additional efforts, essentially an investment in people skills and some extra time in the design and engineering phases of the project, have a clear return of investment in the midand long-term. For the reasons outlined, large companies such as AIRBUS are investing large amounts of funds in the development of rigorous, yet practical, UQ/GSA frameworks that are tightly coupled with their simulation workflows. In this thesis, a clear description and an exhaustive literature review on UQ and GSA processes are provided. A new perspective is provided for Sobol’s sensitivity indices and Saltelli’s resampling approach, the technique usually employed to estimate them. This is done first in light of an experimental campaign. Also, a novel link with the coefficients of approximation in regression is identified. Building well-design metamodels is instrumental to complete UQ and GSA processes. Because of that, a rigorous framework for metamodels evaluation and selection is provided and a novel methodology to systematically construct quasioptimal metamodels is proposed. Specifically, a link between anisotropic metrics and Sobol’s sensitivities is explored and quantified using GSA. As an example of the usefulness of well-designed metamodels, some analytical functions and two industrial applications are studied. In particular, the sensitivities are calculated for the material model of Johnson and Cook, illustrating, for the first time, the use of UQ/GSA to guide the parameter fitting of complex constitutive models. The ideas are, however, general and can be used to steer the formulation of effective meta-models in other complex experimental setups. Finally, an application to a real aeronautical structure is considered. The novelty of this thesis is in the incorporation in the UQ process of a nonlinear Order Reduction Method (ROM). Combining ROM with meta-models is shown to be a suitable and pragmatic approach proving that the methodology presented in this thesis can be extended to computational models where the uncertainties can be localized at lumped parameters