M. Wyrozębski, Efficient Usage of 2nd Order Sensitivity for Uncertainty Quantification

We propose a method based on nodal representation of continuous geometrical uncertainty field. Such discretization leads to a large set of correlated uncertainties. Number of resultant uncertainties is too big to be analyzed with existing methods in reasonable time.
The proposed approach is based on the idea of reducing the number of analyzed uncertainties, maintaining at the same time high approximation accuracy. In order to do this one needs to compute directional 2nd order derivatives. This derivatives can be easily calculated with algorithms like tangent-on-reverse. The proposed approach allowed for a significant reduction in computational time.

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