基于稀疏自回归贝叶斯批量主动学习的CFD综合不确定性量化方法

Comprehensive Uncertainty Quantification Method for CFD Based on Sparse Autoregressive Bayesian Batch Active Learning

  • 摘要: 随着航空航天、船舶等领域对CFD数值模拟可信度要求的提升,量化试验数据、模型参数及模型选择等多源不确定性对模拟结果的影响成为关键挑战。现有CFD不确定性量化(UQ)方法往往仅针对单一或少数不确定性类型,且忽视耦合效应,导致工程应用受限;同时量化多源不确定性又面临计算成本激增的难题。本文基于贝叶斯统计理论,提出一种基于稀疏自回归贝叶斯批量主动学习的综合UQ框架,涵盖模型参数估计、预测不确定性建模及模型选择不确定性量化。为降低计算量,该框架引入多可信度深度贝叶斯自回归神经网络构建CFD代理模型,提出基于信息先验与参数稀疏化的两阶段训练策略提升网络训练效率,并设计融合空间填充性加权最大互信息与行列式点过程的批量主动学习策略,优化样本信息价值与空间多样性。经数学算例及MD30P30N翼型气动分析验证,所提方法相比现有方法可显著提高网络训练速度、降低代理模型构建的综合成本,高效实现了多源不确定性综合量化,为CFD工程决策提供可靠置信度评估。

     

    Abstract:   
      With the increasing demand for CFD simulation credibility in aerospace, marine, and related fields, quantifying the impact of multi-source uncertainties—including experimental data, model parameters, and model selection—on simulation results has become a critical challenge. Existing CFD uncertainty quantification (UQ) methods typically address only single or limited uncertainty types while neglecting coupling effects, thereby restricting their engineering applicability. Moreover, quantifying multi-source uncertainties simultaneously poses significant computational challenges. This paper proposes a comprehensive UQ framework based on Bayesian statistical theory, utilizing sparse autoregressive Bayesian batch active learning. The framework encompasses model parameter estimation, predictive uncertainty modeling, and model selection uncertainty quantification. To reduce computational costs, the framework introduces a multi-fidelity deep Bayesian autoregressive neural network for constructing CFD surrogate models, develops a two-stage training strategy based on informative priors and parameter sparsification to enhance network training efficiency, and designs a batch active learning strategy that integrates space-filling weighted maximum mutual information with determinantal point processes to optimize sample information value and spatial diversity. Validation through mathematical examples and aerodynamic analysis of the MD30P30N airfoil demonstrates that the proposed method significantly improves network training speed and reduces the overall cost of surrogate model construction compared to existing approaches, thereby efficiently achieving comprehensive multi-source uncertainty quantification and providing reliable confidence assessment for CFD engineering decisions.
      With the increasing demand for CFD simulation credibility in aerospace, marine, and related fields, quantifying the impact of multi-source uncertainties—including experimental data, model parameters, and model selection—on simulation results has become a critical challenge. Existing CFD uncertainty quantification (UQ) methods typically address only single or limited uncertainty types while neglecting coupling effects, thereby restricting their engineering applicability. Moreover, quantifying multi-source uncertainties simultaneously poses significant computational challenges. This paper proposes a comprehensive UQ framework based on Bayesian statistical theory, utilizing sparse autoregressive Bayesian batch active learning. The framework encompasses model parameter estimation, predictive uncertainty modeling, and model selection uncertainty quantification. To reduce computational costs, the framework introduces a multi-fidelity deep Bayesian autoregressive neural network for constructing CFD surrogate models, develops a two-stage training strategy based on informative priors and parameter sparsification to enhance network training efficiency, and designs a batch active learning strategy that integrates space-filling weighted maximum mutual information with determinantal point processes to optimize sample information value and spatial diversity. Validation through mathematical examples and aerodynamic analysis of the MD30P30N airfoil demonstrates that the proposed method significantly improves network training speed and reduces the overall cost of surrogate model construction compared to existing approaches, thereby efficiently achieving comprehensive multi-source uncertainty quantification and providing reliable confidence assessment for CFD engineering decisions.

     

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