基于稀疏多项式混沌方法的不确定性量化分析

Uncertainty quantification analysis with sparse polynomial chaos method

在工程复杂外形的数值模拟过程中存在着多种来源的不确定性输入。量化模拟结果的不确定性对于工程外形的性能评估和优化设计非常重要。在多变量不确定性量化问题中,传统的分析方法需要大量的样本点,计算开销巨大,因此急需发展更加高效的工具。本文发展了非嵌入式稀疏多项式混沌方法,研究了湍流模型系数的不确定性对RAE2822翼型跨声速绕流模拟的影响和材料物性参数的不确定性对烧蚀热响应预测的影响。通过求解P1优化问题,在样本点数目小于展开多项式自由度的情况下,能够比较准确地还原量级较大的若干个自由度,捕捉到输出的主要特征,也能够合理预测输出的统计信息,包括平均值、方差和每个输入变量的全局敏感性指标等。这为工程中多变量不确定性量化问题提供了很好的解决方案。

Various sources of uncertainty exist in numerical simulations of industry relevant geometries.Uncertainty quantification plays an important role during the design and assessment process.The computational cost increases dramatically with the number of stochastic input variables.Therefore,more efficient approaches are necessary.This paper develops a nonintrusive sparse polynomial chaos method and investigates the effects of uncertainty in turbulence model closure coefficients on the simulation of flow over RAE2822airfoil and the effects of uncertainty in material properties on the prediction of charring ablator thermal response are investigated.It is proved that the method is capable of recovering the freedoms of several most important bases under the condition of under-determined system by solving P1programming problem.The prediction of system response,including mean value,variance,and the relative contribution of each closure coefficient to the variation of the output quantities,is reasonable compared with full polynomial chaos.The method provides an efficient solution to the uncertainty quantification problems in industry applications.