Uncertainty quantification and management in multidisciplinary design optimisation.

We analyse the uncertainty present at the structural-sizing stage of aircraft design due to interactions between aeroelastic loading and incomplete structural definition. In particular, we look at critical load case identification: the process of identifying the flight conditions at which the maximum loading conditions occur from sparse, expensive to obtain data. To address this challenge, we investigate the construction of robust emulators: probabilistic models of computer code outputs, which explicitly and reliably model their predictive uncertainty. Using Gaussian process regression, we show how such models can be derived from simple and intuitive considerations about the interactions between parameter inference and data, and via state-of-the- art statistical software, develop a generally applicable and easy to use method for constructing them. The effectiveness of these models is demonstrated on a range of synthetic and engineering test functions. We then use them to approach two facets of critical load case identification: sample efficient searching for the critical cases via Bayesian optimisation, and probabilistic assessment of possible locations for the critical cases from a given sample; the latter facilitating quantitative downselection of candidate load cases by ruling out regions of the search space with a low probability of containing the critical cases, potentially saving a designer many hours of simulation time. Finally, we show how the presence of design variability in the loads analysis implies a stochastic process, and attempt to construct a model for this by parametrisation of its marginal distributions.