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In this contribution, the extended Optimal Uncertainty Quantification framework is integrated within the context of reliability‐based design optimizations (RBDO). By that, all advantages the extended Optimal Uncertainty Quantification framework offers for the polymorphic uncertainty quantification, such as the ability to incorporate exact or bounded moment information on epistemic uncertainties without...
The determination of the sharpest bounds on the probability of failure (PoF) based on the Optimal Uncertainty Quantification (OUQ) framework relies on the solution of non‐convex global optimization problems. These problems are subjected to non‐linear constraints to reflect moment constraints from available data, which impedes the numerical efficiency of the method. A different parameterization approach...
This contribution focuses on the combination of the Optimal Uncertainty Quantification framework with fuzzy numbers for a polymorphic uncertainty quantification. The combination allows an integrated approach for the investigation and comparison of different combinations of intervals, which are used as input quantity for the OUQ framework.
For the modeling of micro‐heterogeneous materials, the effective macroscopic response can be determined by means of computational homogenization. The complex morphology of the microstructure needs to be discretized efficiently for numerical simulations. To reduce the effort arising from the generation of a conforming finite element mesh the finite cell method is applied. In this contribution, we focus...
In this contribution, the Optimal Uncertainty Quantification framework is extended to account for aleatory uncertainties, such that both epistemic and aleatory uncertainties can be quantified. The extended framework is demonstrated for an example of a forming process of a Dual‐Phase steel sheet, for which optimal bounds on the probability of failure are computed under polymorphic uncertainties.
A method to quantify uncertain macroscopic material properties resulting from variations of a material’s microstructure morphology is proposed. Basis is the computational homogenization of virtual experiments as part of a Monte-Carlo simulation to obtain the associated uncertain macroscopic material properties. A new general approach is presented to construct a set of artificial microstructures, which...
Multiscale analyses require to consider the scale bridging influences of uncertain parameters. In this paper, approaches for polymorphic uncertainty quantification at different length scales are presented. Especially, the effect of uncertain material parameters computed at lower structural scales is investigated with respect to the resulting macroscopic structural behavior. Also the dependencies of...
The macroscopic behavior of many materials is dependent from their microstructure morphology. As the morphology is often random, the macroscopic response of the material is uncertain. In this paper we propose a method to capture the statistics of the variability of the morphology of the real material, transfer this variability to artificial microstructures and perform virtual tests to quantify the...
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