Fat Latin hypercube sampling and efficient sparse polynomial chaos expansion for uncertainty propagation on finite precision models: Application to 2D deep drawing process

In the context of uncertainty propagation, the variation range of random variables may be many oder of magnitude smaller than their nominal values. When evaluating the non-linear Finite Element Model (FEM), simulations involving contact/ friction and material non linearity on such small perturbations of the input data, a numerical noise alters the output data and distorts the statistical quantities and potentially inhibit the training of Uncertainty Quantification (UQ) models. In this paper, a particular attention is given to the definition of adapted Design of Experiment (DoE) taking into account the model sensitivity with respect to infinitesimal numerical perturbations. The samples are chosen using an adaptation of the Latin Hypercube Sampling (Fat-LHS) and are required to be sufficiently spaced away to filter the discretization and other numerical errors limiting the number of possible numerical experiments. In order to build an acceptable Polynomial Chaos Expansion with such sparse data, we implement a hybrid LARS+Q-norm approach. We showcase the proposed approach with UQ of springback effect for deep drawing process of metal sheet, considering up to 8 random variables.SCOPUS: cp.k