概率盒全局灵敏度和活跃子空间跨层降维

航空航天仿真系统中的不确定性通常是多源的、混合的，并且系统参数的维数众多。针对高维混合不确定性量化问题，提出一种结合概率盒全局灵敏度和活跃子空间的跨层降维方法。在随机和认知不确定的概率盒表征基础上，使用不确定性缩减法分析参数的全局灵敏度继而进行参数筛选；基于输出梯度协方差矩阵的特征分解，使用活跃子空间法对参数进行降维；构造出一种概率盒表征下的参数筛选和跨层降维方法。最后以NASA多学科不确定性量化挑战问题为例，通过概率盒全局灵敏度分析进行第1层次的参数筛选，原有的21维输入参数减为13维；随后采用活跃子空间进行第2层次的参数降维，维数进一步降至一维。研究结果表明，所提出的方法能够对混合不确定性参数进行灵敏度排序，还能够有效降低模型输入参数的维度，为高维系统混合不确定性量化和进一步的优化工作奠定了基础。

Cross-layer dimension reduction based on probability box global sensitivity analysis and active subspace method

Uncertainties in aerospace simulation systems are usually multi-sourced and mixed, with a high dimension of system parameters. To address the problem of mixed uncertainty quantification of high-dimension parameters, a cross-layer dimension reduction method combining the global sensitivity analysis of the probability box and the active subspace method is proposed. Based on the probability box characterization for aleatory and epistemic uncertainties, the pinching method is used to analyze the global sensitivity of parameters for parameter selection. The active subspace method is adopted for dimension reduction according to the eigen-decomposition of the output gradient covariance matrix. A cross-layer method based on the parameter selection and dimension reduction with the probability box analysis is then constructed. Finally, the NASA multidisciplinary uncertainty quantification challenge problem is taken as an example. The first-level parameter selection is performed through the global sensitivity analysis of the probability box, and the dimension of the input parameters is reduced from the original 21 to 13. Then the active subspace method is used for the second-level dimension reduction, with the dimension of parameters further reduced to one. The results demonstrate that the proposed method can perform sensitivity ranking for parameters with mixed uncertainties and effectively reduce the dimension of the model input parameters, laying a foundation for further mixed uncertainty quantification and optimization of high-dimension systems.