UQ Case Study

Surrogate modelling for uncertainty propagation, sensitivity analysis and rare events estimation
B. Sudret, S. Marelli, Chair of Risk, Safety and Uncertainty Quantification, ETH Zurich

In industrial applications, engineers are used to develop their simulation models with in-house or commercial codes following established workflows. Uncertainty quantification (UQ) or sensitivity analysis (SA) questions shall be addressed using these pre-existing models. This calls for methods which can handle those models as “black boxes”, which provide a vector of output quantities of interest for each run with given input parameters.
In a first lecture we introduce sparse polynomial chaos expansions based on penalized least-squares analysis as a tool for UQ (computation of outputs PDF, moments, quantiles, etc.). Global sensitivity analysis will then be introduced, more specifically functional ANOVA, the Sobol’ indices and their estimation through sparse PCE. A third lecture will be devoted to rare events simulation (estimation of so-called probabilities of failure in the engineering wording), which will cover classical approaches as well as recent methods based on Gaussian process modelling and active learning. Finally, a tutorial using the Matlab-based general-purpose software UQLab (external pagewww.uqlab.comcall_made) will exemplify the various lectures.