Adaptive surrogate models for reliability analysis and reliability-based design optimization

Abstract

This thesis is a contribution to the resolution of the reliability-based design optimization problem. This probabilistic design approach is aimed at considering the uncertainty attached to the system of interest in order to provide optimal and safe solutions. The safety level is quantified in the form of a probability of failure. Then, the optimization problem consists in ensuring that this failure probability remains less than a threshold specified by the stakeholders. The resolution of this problem requires a high number of calls to the limit-state design function underlying the reliability analysis. Hence it becomes cumbersome when the limit-state function involves an expensive-to-evaluate numerical model (e.g. a finite element model). In this context, this manuscript proposes a surrogate-based strategy where the limit-state function is progressively replaced by a Kriging meta-model. A special interest has been given to quantifying, reducing and eventually eliminating the error introduced by the use of this meta-model instead of the original model. The proposed methodology is applied to the design of geometrically imperfect shells prone to buckling.

Keywords

adaptive surrogate modelling - kriging - Gaussian processes for regression and probabilistic classification reliability analysis - rare event probabilities - importance sampling - reliability-based design optimization - probabilistic buckling - geometrically imperfect shells

BibTeX cite

@PHDTHESIS{DubourgThesis,
  author = {Dubourg, V.},
  title = {Adaptive surrogate models for reliability analysis and reliability-based
    design optimization},
  school = {Universit\'e Blaise Pascal, Clermont-Ferrand, France},
  year = {2011}
}