Multifidelity multiobjective trust-region-based optimisation for high-lift devices.

This thesis addresses the maximum lift prediction early in the design stage. To do so, the wing high-lift element positions is optimised to estimate the maximum achievable lift. Aircraft design is currently done in at least two main stages: a first high-level design work is undertaken using fast but not very reliable tools which is then improved in a subsequent loop using more accurate tools but requiring more computational time. The present work uses synergies between those models to quickly estimate the maximum lift capabilities of an aerofoil with the use of a derivative-free method along with a trust region framework to perform the multiobjective optimisation while ensuring the convergence towards the most accurate tool optima. The method is first applied on a single-objective formulation and shows significant time saving when the aerodynamic problem is simple. A decrease in benefits is observed when applied to the high-lift devices optimisation because of the increased differences between the low- and the high-fidelity models and a decrease in the tools robustness. A co-Kriging model instead of the additive correction is shown to be beneficial for the accuracy without reducing time saving. Two trust region definitions are compared and shown not to be equivalent: the Euclidean trust region is more accurate but usually more expensive whereas the step-based one uses a more approximated solution of the subproblem which decreases the cost. It is also shown, in accordance with literature, that the multifidelity method increases the variability in convergence because it exacerbates the suboptimiser stochastic characteristics. The main contribution to knowledge is the extension to multiobjective problems. Because of the low correlation between the low- and high-fidelity tools, the method with an additive correction is shown to be dominated by the high-fidelity-only optimiser, albeit the multifidelity is more diversified. The use of a co-Kriging model shows a significant improvement of the Pareto front optimality and extent. Single-fidelity Surrogate Based Optimisation however may provide similar benefits. A novel visualisation approach to compare two models of different fidelity is introduced and a qualitative analysis of the low-fidelity accuracy effect on the multifidelity convergence is done: the most sensitive variables should be correctly captured by the lower fidelity model whereas the less sensitive ones will be corrected by the model correction.