Abstract:  High-dimensional uncertainty propagation currently faced the curse of dimensionality, which made it difficult to utilize the limited sampling resources to obtain high-precision uncertainty analysis results. To address this problem, a high-dimensional uncertainty propagation method was proposed based on supervised dimension reduction and adaptive Kriging modeling. The high-dimensional inputs were projected into the low-dimensional space using the improved sufficient dimension reduction method, and the dimensionality of the low-dimensional space was determined by using the Ladle estimator. The projection matrix was embedded into the Kriging kernel function to reduce the number of hyperparameters to be estimated and improve the modeling accuracy and efficiency. Finally, the leave-one-out cross-validation error of the projection matrix was innovatively defined and the corresponding Kriging adaptive sampling strategy was proposed, which might effectively avoid large fluctuations of model accuracy in the adaptive sampling processes. The results of numerical and engineering examples show that, compared with the existing methods, the proposed method may obtain high-precision uncertainty propagation results with fewer sample points, which may provide references for the uncertainty analysis and design of complex structures. 

Key words: high-dimensional uncertainty propagation, supervised dimension reduction, Kriging model, adaptive sampling

摘要： 高维不确定性传播目前面临维度灾难和小样本的问题，难以利用有限的样本资源获得高精度的分析结果，针对此问题，提出了一种基于监督降维和自适应Kriging模型的高维不确定性传播方法。利用改进充分降维方法将高维输入投影到低维空间中，并利用Ladle估计器确定低维空间的维度。将降维投影矩阵嵌入Kriging核函数中以减少待估计超参数的数量，提高建模精度和效率。最后，创新性地定义了投影矩阵留一交叉验证误差，并基于此提出了相应的Kriging自适应采样策略，可以有效避免模型精度在自适应采样过程中发生较大波动。数值算例与工程案例的结果表明，相比现有方法，所提方法能够以较少的样本点获得高精度不确定性传播结果，对复杂装备结构的不确定性分析和设计具有一定参考作用。

关键词: 高维不确定性传播, 监督降维, Kriging模型, 自适应采样