考虑随机和认知混合不确定性的航空发动机燃烧效率灵敏度分析

Sensitivity Analysis of Aeroengine Combustion Efficiency Considering Hybrid Aleatory and Epistemic Uncertainties

关键词:  航空发动机  全局灵敏度  燃烧效率  概率盒  不确定性  Sobol指标

Key words:  Aeroengine  Global sensitivity  Combustion efficiency  Probability box  Uncertainty  Sobol’ indices

摘要:

针对燃烧室初步设计阶段输入参数存在混合不确定性的特点，提出一种概率盒框架下的全局灵敏度分析方法。简单介绍了航空发动机燃烧效率的一维计算方法；在随机和认知混合不确定性的概率盒表征基础上，使用Sobol指标的上下限表征概率盒中随机与认知混合不确定性对响应的贡献程度；最后基于双层嵌套蒙特卡洛/非嵌入式多项式混沌展开（Monte Carlo Simulation/Non-intrusive Polynomial Chaos Expansion，MCS/NIPCE）方法对概率盒灵敏度指标进行求解，筛选出重要变量和次要变量，实现模型的降维。通过某航空发动机燃烧效率的全局灵敏度分析对所提出的方法进行了验证。研究结果表明，Sobol指标的上下限可以显著表征概率盒灵敏度指标，在保证计算精度的前提下，双层MCS/NIPCE方法的计算效率要远远高于传统双层蒙特卡洛（Monte Carlo Simulation， MCS/MCS）方法，可获得考虑随机和认知混合不确定性情况下燃烧效率输入参数的重要性排序。

Abstract:

Uncertainties in combustion systems are usually multi-source and mixed. To discuss both aleatory and epistemic uncertainties of input parameters in the preliminary design stage of the combustion chamber， a global sensitivity analysis method was proposed under the framework of probability box. The one-dimensional calculation method of aeroengine combustion efficiency was briefly introduced. Based on the probability box representation of both aleatory and epistemic uncertainties， the upper and lower bounds of the Sobol’ indices were used to characterize the contribution of both aleatory and epistemic uncertainties in the probability box to the response. Finally， the probability box sensitivity index was solved based on the double-nested Monte Carlo Simulation（MCS） and the Non-intrusive Polynomial Chaos Expansion （NIPCE） method， which was also known as the double-loop MCS/NIPCE method. The important variables and secondary variables were screened to reduce the dimension of the model. The proposed method was validated by global sensitivity analysis of the combustion efficiency of an aeroengine. The result shows that the probability box sensitivity can be significantly characterized by the upper and lower bounds of the Sobol’ indices. Under the premise of ensuring the calculation accuracy， the computational efficiency of the double-layer MCS/NIPCE method is much higher than that of the traditional double-loop MCS/MCS method and the importance ranking of input parameters for combustion efficiency can be obtained considering both aleatory and epistemic uncertainties.