We formulate and solve data-driven aerodynamic shape design problems with distributionally robust optimization (DRO) approaches. DRO aims to minimize the worst-case expected performance in a set of distributions that is informed by observed data with uncertainties. Building on the findings of the work Gotoh, et al. (2018), we study the connections between a class of DRO and robust design optimization, which is classically based on the mean–variance (standard deviation) optimization formulation pioneered by Taguchi. Our results provide a new perspective to the understanding and formulation of robust design optimization problems. It enables data-driven and statistically principled approaches to quantify the trade-offs between robustness and performance, in contrast to the classical robust design formulation that captures uncertainty only qualitatively. Our preliminary computational experiments on aerodynamic shape optimization in transonic turbulent flow show promising design results.

中文翻译：

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数据驱动的空气动力学形状设计，具有分布稳健的优化方法


我们采用分布稳健优化 (DRO) 方法来制定和解决数据驱动的空气动力学形状设计问题。 DRO 旨在最大限度地减少一组分布中最坏情况的预期性能，这些分布是由具有不确定性的观测数据提供的。以 Gotoh 等人的工作结果为基础。 （2018），我们研究了一类 DRO 和鲁棒设计优化之间的联系，这通常基于田口开创的均值-方差（标准差）优化公式。我们的结果为理解和制定鲁棒设计优化问题提供了新的视角。它使数据驱动和统计原则的方法能够量化稳健性和性能之间的权衡，这与仅定性捕获不确定性的经典稳健设计公式形成鲜明对比。我们关于跨音速湍流空气动力学形状优化的初步计算实验显示了有希望的设计结果。