Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often introduce significant uncertainties due to deficiencies in the mathematical models employed. In this paper, we discuss two recent improvements in the quantification and combination of uncertainties from multiple sources that can help generate probabilistic aerodynamic databases for use in aerospace engineering problems. We first discuss the eigenspace perturbation methodology to estimate model-form uncertainties stemming from inadequacies in the turbulence models used in Reynolds-Averaged Navier-Stokes Computational Fluid Dynamics (RANS CFD) simulations. We then present a multi-fidelity Gaussian Process framework that can incorporate noisy observations to generate integrated surrogate models that provide mean as well as variance information for Quantities of Interest (QoIs). The process noise is varied spatially across the domain and across fidelity levels. Both these methodologies are demonstrated through their application to a full configuration aircraft example, the NASA Common Research Model (CRM) in transonic conditions. First, model-form uncertainties associated with RANS CFD simulations are estimated. Then, data from different sources is used to generate multi-fidelity probabilistic aerodynamic databases for the NASA CRM. We discuss the transformative effect that affordable and early treatment of uncertainties can have in traditional aerospace engineering practices. The results are presented and compared to those from a Gaussian Process regression performed on a single data source.

中文翻译：

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用于航空航天工程的概率空气动力学数据库的多保真建模

工程模拟中不确定性的显式量化越来越多地用于为稳健可靠的设计实践提供信息。在航空航天工业中，由于采用的数学模型存在缺陷，用于设计优化目的的计算可行分析通常会引入重大的不确定性。在本文中，我们讨论了最近在量化和组合来自多个来源的不确定性方面的两项改进，这些改进可以帮助生成用于航空航天工程问题的概率空气动力学数据库。我们首先讨论特征空间扰动方法来估计由雷诺平均纳维-斯托克斯计算流体动力学 (RANS CFD) 模拟中使用的湍流模型的不足引起的模型形式不确定性。然后，我们提出了一个多保真高斯过程框架，该框架可以结合嘈杂的观察来生成集成的替代模型，该模型为感兴趣的数量 (QoI) 提供均值和方差信息。过程噪声在整个域和保真度级别上在空间上变化。这两种方法都通过将它们应用于全配置飞机示例，即跨音速条件下的 NASA 通用研究模型 (CRM) 来演示。首先，估计与 RANS CFD 模拟相关的模型形式的不确定性。然后，来自不同来源的数据用于为 NASA CRM 生成多保真概率空气动力学数据库。我们讨论了在传统航空航天工程实践中对不确定性进行负担得起的早期处理可能产生的变革性影响。