Efficient Possibilistic Uncertainty Analysis of a Car Crash Scenario Using a Multifidelity Approach

The early design stage of mechanical structures is often characterized by unknown or only partially known boundary conditions and environmental influences. Particularly, in the case of safety-relevant components, such as the crumple zone structure of a car, those uncertainties must be appropriately quantified and accounted for in the design process. For this purpose, possibility theory provides a suitable tool for the modeling of incomplete information and uncertainty propagation. However, the numerical propagation of uncertainty described by possibility theory is accompanied by high computational costs. The necessarily repeated model evaluations render the uncertainty analysis challenging to be realized if a model is complex and of large scale. Oftentimes, simplified and idealized models are used for the uncertainty analysis to speed up the simulation while accepting a loss of accuracy. The proposed multifidelity scheme for possibilistic uncertainty analysis, instead, takes advantage of the low costs of an inaccurate low-fidelity model and the accuracy of an expensive high-fidelity model. For this purpose, the functional dependency between the high- and low-fidelity model is exploited and captured in a possibilistic way. This results in a significant speedup for the uncertainty analysis while ensuring accuracy by using only a low number of expensive high-fidelity model evaluations. The proposed approach is applied to an automotive car crash scenario in order to emphasize its versatility and applicability.