Risk-based functional black-box optimization: Contribution to the NASA Langley UQ challenge on optimization under uncertainty

This paper presents an approach to solve the 2019/2020 NASA Langley UQ challenge problem on optimization under uncertainty. We define an uncertainty model (UM) as a pair fa|e,E, where fa|e is a probability density over a for each e∈E, and proceed to infer fa|e in a Bayesian fashion. Special attention is given to dimensionality reduction of the functional (time-series) data, to obtain a finite dimensional representation suitable for robust Bayesian inversion. Reliability analysis is performed using fa|e, whereas for design optimization we approximate fa|e using truncated Gaussians and a Gaussian copula. We apply an unscented transform (UT) in the standard normal space to estimate moments of the limit state, which is numerically very efficient. Design optimization is performed with this procedure to obtain negligible failure probability in g1 and g3 and acceptable failure probability and severity in g2.