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Efficient uncertainty quantification of CFD problems by combination of proper orthogonal decomposition and compressed sensing

机译：通过适当的正交分解和压缩传感的组合有效地不确定量化CFD问题

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摘要

In the current paper, an efficient surrogate model based on combination of Proper Orthogonal Decomposition (POD) and compressed sensing is developed for affordable representation of high dimensional stochastic fields. In the developed method, instead of the full (or classical) Polynomial Chaos Expansion (PCE), the ℓ_1-minimization approach is utilized to reduce the computational work-load of the low-fidelity calculations. To assess the model capability in the real engineering problems, two challenging high-dimensional CFD test cases namely; ⅰ) turbulent transonic flow around RAE2822 airfoil with 18 geometrical uncertainties and ⅱ) turbulent transonic flow around NASA Rotor 37 with 3 operational and 21 geometrical uncertainties are considered. Results of Uncertainty Quantification (UQ) analysis in both test cases showed that the proposed multi-fidelity approach is able to reproduce the statistics of quantities of interest with much lower computational cost than the classical regression-based PCE method. It is shown that the combination of the POD with the compressed sensing in RAE2822 and Rotor 37 test cases gives respectively computational gains between 1.26-7.72 and 1.79-9.05 times greater than the combination of the POD with the full PCE.
机译：在目前的纸张中，基于适当正交分解（POD）和压缩感测的基于适当的正交分解（POD）和压缩感测的高效代理模型用于高尺寸随机区域的实惠表示。在开发方法中，代替全（或经典）多项式混沌扩展（PCE），利用χ_1-最小化方法来减少低保真计算的计算工作负载。为了评估实际工程问题中的模型能力，两个具有挑战性的高维CFD测试用例。 Ⅰ）湍流延长横向于RAE2822翼型的翼型流动，具有18个几何不确定性和Ⅱ），NASA转子37周围的湍流延时流动，具有3个操作和21个几何不确定因素。两个测试用例的不确定度量（UQ）分析结果表明，所提出的多维保险费方法能够以比基于经典回归的PCE方法更低的计算成本来再现利息数量统计数据。结果表明，荚与RAE2822和转子37的压缩检测的组合分别在1.26-7.72和1.79-9.05倍之间的计算增益大于POD与完整PCE的组合。

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