[论文解读] A Multi-Model Approach for Uncertainty Propagation and Model Calibration in CFD Applications

Jianxun Wang, Christopher J. Roy+1 more|arXiv (Cornell University)|Jan 13, 2015

Probabilistic and Robust Engineering Design参考文献 26被引用 3

一句话总结

本文提出一种多保真度贝叶斯方法，通过结合高保真度和低保真度的CFD模型，量化并减少不确定性传播中的模型差异。通过使用高斯过程回归推断差异函数，并利用贝叶斯推断估计未测试参数区域中的不确定性，该方法在预测精度上超越了单一模型所能达到的水平。

ABSTRACT

Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for CFD applications. A particular obstacle for uncertainty quantifications in CFD problems is the large model discrepancies associated with the CFD models used for uncertainty propagation. Neglecting or improperly representing the model discrepancies leads to inaccurate and distorted uncertainty distribution for the Quantities of Interest. High-fidelity models, being accurate yet expensive, can accommodate only a small ensemble of simulations and thus lead to large interpolation errors and/or sampling errors; low-fidelity models can propagate a large ensemble, but can introduce large modeling errors. In this work, we propose a multi-model strategy to account for the influences of model discrepancies in uncertainty propagation and to reduce their impact on the predictions. Specifically, we take advantage of CFD models of multiple fidelities to estimate the model discrepancies associated with the lower-fidelity model in the parameter space. A Gaussian process is adopted to construct the model discrepancy function, and a Bayesian approach is used to infer the discrepancies and corresponding uncertainties in the regions of the parameter space where the high-fidelity simulations are not performed. The proposed multi-model strategy combines information from models with different fidelities and computational costs, and is of particular relevance for CFD applications, where a hierarchy of models with a wide range of complexities exists. Several examples of relevance to CFD applications are performed to demonstrate the merits of the proposed strategy. Simulation results suggest that, by combining low- and high-fidelity models, the proposed approach produces better results than what either model can achieve individually.

研究动机与目标

• 解决CFD模拟中的模型差异问题，该问题在高保真度模型因计算成本过高而难以进行大规模采样时，会扭曲不确定性传播。
• 通过整合低成本但不准确的低保真度模型与高成本但准确的高保真度模型，克服计算成本与精度之间的权衡。
• 开发一种统计框架，以估计在高保真度模拟不可用的参数空间区域中的模型差异及其不确定性。
• 通过融合不同保真度的多模型信息，提高CFD应用中的预测精度和可靠性。

提出的方法

• 使用具有不同保真度的CFD模型层级——高保真度用于精度，低保真度用于计算效率。
• 将低保真度与高保真度模型之间的差异建模为参数空间上的高斯过程函数。
• 应用贝叶斯推断以估计差异函数，并量化参数空间中未测试区域的不确定性。
• 利用稀疏的高保真度模拟数据训练差异模型，并将预测结果扩展至整个参数域。
• 将低保真度模型的预测结果与推断出的差异相结合，生成经过校正的高精度预测，并附带不确定性量化。
• 利用完整的后验分布传播不确定性，确保预测结果的鲁棒性和可靠性。

实验结果

研究问题

• RQ1 如何在不确定性分析中有效量化和传播低保真度与高保真度CFD模型之间的模型差异？
• RQ2 当高保真度模拟数量有限时，贝叶斯高斯过程模型在多大程度上能改善不确定性量化？
• RQ3 与使用单一模型相比，整合多种不同保真度的模型是否能降低整体预测误差？
• RQ4 所提出的方法在捕捉CFD应用中关键量真实不确定性分布方面表现如何？

主要发现

• 所提出的多模型策略显著降低了与单独使用低保真度或高保真度模型相比的预测误差。
• 贝叶斯高斯过程模型即使在缺乏高保真度数据的区域，也能有效捕捉参数空间中的模型差异。
• 与单模型方法相比，该方法为关键量提供了更准确、更可靠的不确定性分布。
• 通过结合稀疏的高保真度数据与差异模型，该方法在降低计算成本的同时实现了高精度。
• 结果表明，该方法在不确定性传播中表现出更高的鲁棒性和保真度，特别是在高保真度模拟覆盖有限的区域中。