A multi-fidelity approach for possibilistic uncertainty analysis

Possibilisitic uncertainty representation can be used to model a system in case of sparse data or incomplete information. This, however, comes along with a large number of deterministic model evaluations, which in case of a complex, large-scale model results in tremendous computational effort. Hence, special techniques should be applied to reduce the computational cost by simplification or model-order reduction techniques, or by building a computationally less expensive surrogate model. In this paper, a novel approach is introduced which combines the analyses of the expensive, high-fidelity model and the approximated, low-fidelity model in a multi-fidelity approach. For this purpose, a possibilistic correlation analysis is applied to estimate the conditional possibility of the high-fidelity output given the low-fidelity output. In this way, the possibilistically quantified uncertainty of the high-fidelity model output can be estimated using only a low number of expensive model evaluations.