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Effective Formulations of Optimization Under Uncertainty for Aerospace Design 10.17863/CAM.23427 Cook, Laurence William 0000000200331657 Jarrett, Jerome Peter Formulations of optimization under uncertainty (OUU) commonly used in aerospace design—those based on treating statistical moments of the quantity of interest (QOI) as separate objectives—can result in stochastically dominated designs. A stochastically dominated design is undesirable, because it is less likely than another design to achieve a QOI at least as good as a given value, for any given value. As a remedy to this limitation for the multi-objective formulation of moments, a novel OUU formulation is proposed—dominance optimization. This formulation seeks a set of solutions and makes use of global optimizers, so is useful for early stages of the design process when exploration of design space is important. Similarly, to address this limitation for the single-objective formulation of moments (combining moments via a weighted sum), a second novel formulation is proposed—horsetail matching. This formulation can make use of gradient- based local optimizers, so is useful for later stages of the design process when exploitation of a region of design space is important. Additionally, horsetail matching extends straightforwardly to different representations of uncertainty, and is flexible enough to emulate several existing OUU formulations. Existing multi-fidelity methods for OUU are not compatible with these novel formulations, so one such method—information reuse—is generalized to be compatible with these and other formulations. The proposed formulations, along with generalized information reuse, are compared to their most comparable equivalent in the current state-of-the-art on practical design problems: transonic aerofoil design, coupled aero-structural wing design, high-fidelity 3D wing design, and acoustic horn shape design. Finally, the two novel formulations are combined in a two-step design process, which is used to obtain a robust design in a challenging version of the acoustic horn design problem. Dominance optimization is given half the computational budget for exploration; then horsetail matching is given the other half for exploitation. Using exactly the same computational budget as a moment-based approach, the design obtained using the novel formulations is 95% more likely to achieve a better QOI than the best value achievable by the moment-based design. University of Cambridge 2018-07-20 Thesis Doctoral Doctor of Philosophy (PhD) en Funded by EPSRC under grant number EP/L504920/1 https://www.repository.cam.ac.uk/handle/1810/276146 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/26c11555-b68f-4414-a4c1-f82d840850fa/download cc59bced05fa572f735a0fd3ef0fbf17 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/e3342914-6a46-4cb8-b7e0-7a795a3e4f20/download 87eda9de84448d1f82354d60eee3eb5f https://creativecommons.org/licenses/by-sa/4.0/ Optimization Robust Optimization Optimization Under Uncertainty Design Design Optimization Aerospace Design Aerofoil Design Uncertainty Quantification Monte Carlo Multi-Fidelity Information Reuse Wing Design Aero-Structural Design