Robust optimisation of wing aerostructural response

Abstract

The life cycle of an aeronautical product is characterised by an increasing design certainty and a decreasing in design freedom over time. The uncertainty in the design and in the manufacturing process may be quantified to assess its impact on the aircraft performance and on the likelihood of meeting the performance requirements, given the design margins and constraints. One of the major challenges in this process is the so-called curse of dimensionality, where the associated computational cost grows exponentially as a function of the number of random variables and intractable integrals. This challenge is addressed by exploring how recent advances in numerical methods and in machine learning might be used in uncertainty quantification and in robust optimisation. This work investigates how to solve the following industrially relevant aeronautical problem: How to perform the robust optimisation of wing twist (jig shape) to balance aerodynamic performance and risk of exceeding the design loads margins in the presence of structural uncertainties? To address this problem, this thesis presents theoretical and algorithmic advances in probabilistic regression, uncertainty quantification and Bayesian optimisation, demonstrating and expanding its engineering applications. The primary aim is to formulate and solve the robust optimisation challenge using Gaussian processes and Bayesian optimisation of a wing subject to structural uncertainties and design load constraints. The problem is formulated as the evaluation of the impact of the wing jig shape twist angles, bending and torsional stiffness uncertainties on the overall lift-to-drag ratio, shear, moment and torque loads across the wingspan for different load cases and considering design load constraints. As secondary aim, a variational approach for inference is investigated since the required mathematical machinery is rarely tractable. It is concluded that probabilistic methods greatly expand the ability to learn and infer from data yielded by highly complex simulations.