Aircraft design requires extensive aerodynamic data to characterize various flight conditions throughout the aircraft’s flight envelope. Typically, the aerodynamic data is acquired through wind tunnel testing or numerical analysis, which are costly and inevitably entails multiple sources of uncertainty. In the present work, we propose a multi-fidelity Bayesian neural network (MFBNN) framework for multi-source aerodynamic data fusion with heterogeneous uncertainties. We first employ mean-field variational inference (VI) to maximize the evidence lower bound (ELBO), yielding informative priors for BNN hyperparameters. Then, the stochastic Hamiltonian Monte Carlo (HMC) method is adopted to estimate their posteriors. Notably, we introduce mini-batch learning to address a key constraint of traditional HMC methods, particularly in the aerodynamic modeling scenarios involving large sample sizes, where the computation of required gradients for simulation of the Hamiltonian dynamical system is impractical. The proposed MFBNN framework is applied in three cases, including the RAE2822 airfoil, the ONERA M6 wing and the NASA Common Research Model. The results demonstrate that the proposed MFBNN framework can remarkably improve accuracy and outperform the multi-fidelity Gaussian process regression model.

中文翻译：

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多保真贝叶斯神经网络，用于异构不确定性的空气动力学数据融合


飞机设计需要大量的空气动力学数据来描述整个飞机飞行包线中的各种飞行条件。通常，空气动力学数据是通过风洞测试或数值分析获得的，这成本高昂，并且不可避免地会带来多个不确定性来源。在本工作中，我们提出了一个多保真贝叶斯神经网络 （MFBNN） 框架，用于具有异构不确定性的多源空气动力学数据融合。我们首先采用平均场变分推断 （VI） 来最大化证据下限 （ELBO），为 BNN 超参数产生信息丰富的先验。然后，采用随机哈密顿蒙特卡洛 （HMC） 方法估计它们的后验。值得注意的是，我们引入了小批量学习来解决传统 HMC 方法的一个关键约束，特别是在涉及大样本量的空气动力学建模场景中，其中计算模拟哈密顿动力学系统所需的梯度是不切实际的。所提出的 MFBNN 框架应用于三种情况，包括 RAE2822 翼型、ONERA M6 机翼和 NASA 通用研究模型。结果表明，所提出的 MFBNN 框架可以显著提高准确性并优于多保真度高斯过程回归模型。