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Bayesian uncertainty analysis with applications to turbulence modeling

机译：贝叶斯不确定性分析及其在湍流建模中的应用

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摘要

In this paper, we apply Bayesian uncertainty quantification techniques to the processes of calibrating complex mathematical models and predicting quantities of interest (Qol's) with such models. These techniques also enable the systematic comparison of competing model classes. The processes of calibration and comparison constitute the building blocks of a larger validation process, the goal of which is to accept or reject a given mathematical model for the prediction of a particular Qol for a particular scenario. In this work, we take the first step in this process by applying the methodology to the analysis of the Spalart-Allmaras turbulence model in the context of incompressible, boundary layer flows. Three competing model classes based on the Spalart-Allmaras model are formulated, calibrated against experimental data, and used to issue a prediction with quantified uncertainty. The model classes are compared in terms of their posterior probabilities and their prediction of Qol's. The model posterior probability represents the relative plausibility of a model class given the data. Thus, it incorporates the model's ability to fit experimental observations. Alternatively, comparing models using the predicted Qol connects the process to the needs of decision makers that use the results of the model. We show that by using both the model plausibility and predicted Qol, one has the opportunity to reject some model classes after calibration, before subjecting the remaining classes to additional validation challenges.
机译：在本文中，我们将贝叶斯不确定性量化技术应用于校准复杂数学模型并使用此类模型预测感兴趣量（Qol）的过程。这些技术还可以对竞争模型类进行系统比较。校准和比较过程构成了更大的验证过程的基础，验证过程的目标是接受或拒绝给定的数学模型，以预测特定场景下的特定Qol。在这项工作中，我们通过将方法论应用于在不可压缩边界层流的情况下对Spalart-Allmaras湍流模型的分析，迈出了这一过程的第一步。制定了基于Spalart-Allmaras模型的三个竞争模型类，并根据实验数据进行了校准，并用于发布具有不确定性的预测。比较模型类别的后验概率和对Qol的预测。模型后验概率表示给定数据的模型类别的相对合理性。因此，它结合了模型拟合实验观察结果的能力。另外，使用预测的Qol比较模型会将过程与使用模型结果的决策者的需求联系起来。我们表明，通过同时使用模型的真实性和预测的Qol，人们有机会在校准后拒绝某些模型类别，然后再对其余类别进行其他验证挑战。

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  • 来源
    《Reliability Engineering & System Safety》 |2011年第9期|p.1137-1149|共13页
  • 作者

    Sai Hung Cheung; Todd A. Oliver; Ernesto E. Prudencio; Serge Prudhomme; Robert D. Moser;

  • 作者单位

    Center for Predictive Engineering and Computational Sciences (PECOS), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin,1 University Station. C0200 Austin, TX 78712, USA;

    Center for Predictive Engineering and Computational Sciences (PECOS), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin,1 University Station. C0200 Austin, TX 78712, USA;

    Center for Predictive Engineering and Computational Sciences (PECOS), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin,1 University Station. C0200 Austin, TX 78712, USA;

    Center for Predictive Engineering and Computational Sciences (PECOS), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin,1 University Station. C0200 Austin, TX 78712, USA;

    Center for Predictive Engineering and Computational Sciences (PECOS), Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin,1 University Station. C0200 Austin, TX 78712, USA;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    model inadequacy representations; stochastic model classes; bayesian analysis; turbulence modeling; forward propagation of uncertainty; model validation under uncertainty;

    机译：模型不充分表示;随机模型类;贝叶斯分析;湍流建模;不确定性的正向传播;不确定性下的模型验证;

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