NESTED OPTIMAL UNCERTAINTY QUANTIFICATION FOR AN EFFICIENT INCORPORATION OF RANDOM FIELDS-APPLICATION TO SHEET METAL FORMING

Abstract

In this work, a new method is presented to quantify the sharpest bounds on the probability of failure while including local variations of properties in terms of random fields. The method is based on the extended optimal uncertainty quantification (OUQ) for polymorphic uncertainties. Therein, a special focus is on the incorporation of aleatory as well as epistemic uncertainties without the requirement of making unjustified assumptions regarding stochastic distribution functions for the epistemic uncertainties. Two approaches are proposed to incorporate the information gained from random field simulations in uncertainty quantifications in this paper: the first approach is based on a nested OUQ scheme to account for the potentially limited data, whereas the second approach focuses on artificial neural networks to build a surrogate model directly from the random field result data. The proposed approaches are numerically analyzed in detail by considering a sheet metal forming process as an engineering application example.