Decomposition-based Evolutionary Aerodynamic Robust Optimization with Multi-fidelity Point Collocation Non-intrusive Polynomial Chaos
Decomposition-based Evolutionary Aerodynamic Robust Optimization with Multi-fidelity Point Collocation Non-intrusive Polynomial Chaos
复制标题
基于分解的多保真点配置非侵入多项式混沌的进化气动鲁棒优化
DOI：
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发表时间：
2015
期刊：
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通讯作者：
G. Parks
中科院分区：
文献类型：
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作者：
P. Palar;T. Tsuchiya;G. Parks
© 2015 美国航空航天学会有限公司。保留所有权利。进化算法是强大的优化器，通常用于探索鲁棒优化中性能和鲁棒性之间的权衡。评估鲁棒性时不确定性量化（UQ）的一种流行方法是使用多项式混沌（PC）展开。为了充分利用可用的计算预算，需要提高优化器和 UQ 方法的性能。在本文中，我们提出了一种空气动力学鲁棒优化方法，该方法由基于分解的优化器（MOEA/D）和多保真度点搭配非侵入式 PC 组成。基于分解的优化器产生的继承多样性对于多目标鲁棒优化应用程序来说是一个有益的特征。在我们的昆士兰大学方法中，多保真度模拟的可用性被纳入点配置 PC 中，以允许灵活的样本数量并有效地计算不确定性的影响。 MOEA/D 和 NSGA-II 之间的比较是针对亚音速应用进行的。这表明基于分解的优化器能够找到更加多样化的帕累托前沿。然后在跨音速翼型鲁棒优化应用上演示了多保真鲁棒优化框架，其目标是最大化升阻比 (L/D)，同时最小化对偶然不确定性的敏感性。多保真点配置非侵入式PC方法能够减少UQ所需的计算时间。在跨音速情况下，具有最大 L/D 平均值的解决方案优于其他翼型，即使它伴随着 L/D 的高标准偏差。随机响应面表明，其L/D在响应面上的最小值仍然高于标准差最小的翼型。这表明在得出结论和做出决策之前检查随机响应面的趋势非常重要。
© 2015 American Institute of Aeronautics and Astronautics Inc. All rights reserved. Evolutionary algorithms are powerful optimizers often used to explore the trade-off between performance and robustness in robust optimization. A popular methodology for un- certainty quantiffication (UQ) in evaluating robustness is through use of a polynomial chaos (PC) expansion. To make best use of the available computational budget, improvements in the performance of both optimizer and UQ method are desired. In this paper we present an approach for aerodynamic robust optimization which consists of a decomposition-based optimizer (MOEA/D) and multi-ffidelity point collocation non-intrusive PC. The inherited diversity that a decomposition-based optimizer produces is a benefficial trait for multi-objective robust optimization applications. In our UQ approach, the availability of the multi-ffidelity simulations is incorporated within the point collocation PC to allow exible numbers of samples and calculate the effiect of uncertainty efficiently. A comparison between MOEA/D and NSGA-II is performed for a subsonic application. This shows that the decomposition-based optimizer is able to find a more diverse Pareto front. The multi-ffidelity robust optimization framework is then demonstrated on a transonic airfoil robust optimization application with the goals of maximizing lift-to-drag ratio (L/D) while minimizing the sensitivity to aleatory uncertainties. The multi-ffidelity point collocation non-intrusive PC approach is able reduce the computational time needed for UQ. In the transonic case, the solution with the maximum mean of L/D is preferred over the other airfoils even though it is accompanied by a high standard deviation in L/D. The stochastic response surface shows that its minimum value of L/D over the response surface is still higher than that of the airfoil with the minimum standard deviation. This shows that it is important to examine the trend of the stochastic response surface before conclusions are drawn and decisions made.