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Multi-fidelity modeling framework for nonlinear unsteady aerodynamics of airfoils

机译：机翼非线性非定常空气动力学的多保真建模框架

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Aerodynamic data can be obtained from different sources, which vary in fidelity, availability and cost. As the fidelity of data increases, the cost of data acquisition usually becomes higher. Therefore, to obtain accurate unsteady aerodynamic model with very low cost and the desired level of accuracy, this paper proposes an unsteady multi-fidelity aerodynamic modeling framework. The approach integrates ideas from data fusion, multi-fidelity modeling, nonlinear system identification and machine learning. Data fusion reduces the total cost of data generation for model construction, while multi-fidelity modeling with a nonlinear autoregressive with exogenous input (NARX) description provides a general framework for unsteady aerodynamics. The correction term from the low-fidelity model to the high-fidelity result is then identified by a machine learning approach, i.e., a multi-kernel neural network. To validate the proposed method, unsteady aerodynamics of a NACA0012 airfoil pitching at Mach number 0.8 is modeled. The high-fidelity data is obtained from a Navier-Stokes-equation-based solver, while the low-fidelity solution is taken from an Euler-equation-based flow solver. The main difference between two types of data is that the high-fidelity solution takes into account the viscous effect, while the low-fidelity solution is based the invisicid flow assumption. Besides, to mimic the practical situation where high-fidelity data are limited in amount and diversity due to high cost (e.g., the experimental condition), only three high-fidelity unsteady aerodynamic solutions from harmonic motion are available. After performing a multi-fidelity analysis on a typical harmonic motion, the model is applied to the prediction of aerodynamic loads from either new harmonic motions or random motions. The multi-fidelity model shows a good agreement with the high-fidelity solution, indicating that by using only a few high-fidelity data and a low-fidelity model, high-fidelity results can be accurately reproduced. Furthermore, the model convergence with respect to increasing training data, and the comparison with a single high-fidelity reduced-order model (ROM) are also studied. The proposed approach becomes more accurate as the number of high-fidelity samples increases, and outperforms a single aerodynamic ROM in most of test cases. Compared with ROM method, additional computational cost for the proposed approach is small, therefore the total time cost of model training is still low. (C) 2019 Elsevier Inc. All rights reserved.
机译：可以从不同的来源获得空气动力学数据，这些数据在保真度，可用性和成本方面有所不同。随着数据保真度的提高，数据获取的成本通常会更高。因此，为了以非常低的成本和所需的精度水平获得精确的非定常空气动力学模型，本文提出了一种非定常的多保真空气动力学建模框架。该方法整合了来自数据融合，多保真度建模，非线性系统识别和机器学习的思想。数据融合减少了用于模型构建的数据生成的总成本，而具有外部输入的非线性自回归（NARX）描述的多保真度建模则为不稳定的空气动力学提供了通用框架。然后通过机器学习方法（即多核神经网络）识别从低保真模型到高保真结果的校正项。为了验证所提出的方法，对马赫数为0.8的NACA0012机翼俯仰的非定常空气动力学建模。高保真度数据是从基于Navier-Stokes方程的求解器获得的，而低保真度是从基于Euler方程的流求解器获得的。两种类型的数据之间的主要区别在于，高保真度解决方案考虑了粘性效应，而低保真度解决方案则基于无粘性流量假设。此外，为了模拟由于高成本（例如，实验条件）而导致高保真数据的数量和多样性受到限制的实际情况，仅提供了三种来自谐波运动的高保真非定常气动解决方案。在对典型的谐波运动进行多保真度分析之后，该模型将应用于根据新的谐波运动或随机运动来预测空气动力负荷。多保真度模型与高保真度解决方案具有良好的一致性，表明仅使用少量高保真度数据和低保真度模型，就可以准确地再现高保真度结果。此外，还针对增加训练数据的模型收敛性以及与单个高保真降阶模型（ROM）的比较进行了研究。随着高保真样本数量的增加，所提出的方法变得更加准确，并且在大多数测试案例中，其性能均优于单个空气动力学ROM。与ROM方法相比，该方法的额外计算量较小，因此模型训练的总时间成本仍然较低。 （C）2019 Elsevier Inc.保留所有权利。

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