A High-dimensional Uncertainty Propagation Method Based on Supervised Dimension Reduction and Adaptive Kriging Modeling

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. © 2024 Chinese Mechanical Engineering Society. All rights reserved.