High Dimensional Constrained Bayesian Optimization Applied to Aircraft Design ; Optimisation bayésienne sous contraintes et en grande dimension appliquée à la conception avion avant projet

Nowadays, the preliminary design in aeronautics is based mainly on numerical models bringing together many disciplines aimed at evaluating the performance of the aircraft.These disciplines, such as aerodynamics, structure and propulsion, are interconnected in order to take into account their interactions.This produces a computationally expensive aircraft performance evaluation process.Indeed, an evaluation can take from thirty seconds for low fidelity models to several weeks for higher fidelity models.In addition, because of the multi-disciplinarity of the process and the diversity of the calculation tools, we do not always have access to the properties or the gradient of this performance function.In addition, each discipline uses its own design variables and must respect equality or inequality constraints which are often numerous and multi-modal.We ultimately seek to find the best possible configuration in a given design space.This research can be mathematically translated to a black-box optimization problem under inequality and equality constraints, also known as mixted constraints, depending on a large number of design variables.Moreover, the constraints and the objective function are expensive to evaluate and their regularity is not known.This is why we are interested in derivative-free optimization methods and more specifically the ones based on surrogate models.Bayesian optimization methods, using Gaussian processes, are more particularly studied because they have shown rapid convergence on multimodal problems.Indeed, the use of evolutionary optimization algorithms or other gradient-based methods is not possible because of the computational cost that this implies: too many calls to generate populations of points, or to approach the gradient by finite difference.However, the Bayesian optimization method is conventionally used for optimization problems without constraints and of small dimension.Extensions have been proposed to partially take this lock into account.On the one hand, optimization methods have ...