数据驱动的Turbulence模型预测置信度的先验评估
A Priori Assessment of Prediction Confidence for Data-Driven Turbulence Modeling
摘要：
尽管雷诺平均纳维尔-斯托克斯（RANS）方程仍然是工程设计和涉及湍流的分析应用的主要工具，但已知标准RANS模型在许多与工程相关的流动中是不可靠的，包括具有分离、强压力梯度或平均流动曲率的流动。随着大涡模拟（LES）和直接数值模拟（DNS）等方法获得的大量三维实验数据和高精度模拟数据的不断增加，数据驱动的湍流模型已成为提高RANS模拟预测能力的一种很有前途的方法。最近，已经提出了通过机器学习的数据驱动的湍流建模方法，以基于来自密切相关的流的高保真数据来预测给定流的雷诺应力各向异性。在这项工作中，不同的流量的接近程度进行了调查，以评估预测的信心先验。具体而言，Mahalanobis距离和核密度估计（KDE）技术被用作度量，以量化特征空间中的流数据集之间的距离。以Re=10595的周期性山丘上的流动作为测试集，以7种不同构型的流动作为训练集。结果表明，雷诺应力各向异性的预测误差与Mahalanobis距离和KDE距离呈正相关，表明两种外推度量均可用于先验地估计预测置信度。使用相关系数的定量比较表明，Mahalanobis距离在估计预测置信度方面不如KDE距离准确。在这项工作中引入的外推度量和相应的分析提供了一种方法，以帮助选择的数据源，并评估数据驱动的湍流建模的预测置信度。
英文摘要：
Although Reynolds-Averaged Navier-Stokes (RANS) equations are still the dominant tool for engineering design and analysis applications involving turbulent flows, standard RANS models are known to be unreliable in many flows of engineering relevance, including flows with separation, strong pressure gradients or mean flow curvature. With increasing amounts of 3-dimensional experimental data and high fidelity simulation data from Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS), data-driven turbulence modeling has become a promising approach to increase the predictive capability of RANS simulations. Recently, a data-driven turbulence modeling approach via machine learning has been proposed to predict the Reynolds stress anisotropy of a given flow based on high fidelity data from closely related flows. In this work, the closeness of different flows is investigated to assess the prediction confidence a priori. Specifically, the Mahalanobis distance and the kernel density estimation (KDE) technique are used as metrics to quantify the distance between flow data sets in feature space. The flow over periodic hills at Re=10595 is used as the test set and seven flows with different configurations are individually used as training set. The results show that the prediction error of the Reynolds stress anisotropy is positively correlated with Mahalanobis distance and KDE distance, demonstrating that both extrapolation metrics can be used to estimate the prediction confidence a priori. A quantitative comparison using correlation coefficients shows that the Mahalanobis distance is less accurate in estimating the prediction confidence than KDE distance. The extrapolation metrics introduced in this work and the corresponding analysis provide an approach to aid in the choice of the data source and to assess the prediction confidence for data-driven turbulence modeling.
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