Hierarchical surrogate model with dimensionality reduction technique for high‐dimensional uncertainty propagation

Abstract

Summary In this article, hierarchical surrogate model combined with dimensionality reduction technique is investigated for uncertainty propagation of high‐dimensional problems. In the proposed method, a low‐fidelity sparse polynomial chaos expansion model is first constructed to capture the global trend of model response and exploit a low‐dimensional active subspace (AS). Then a high‐fidelity (HF) stochastic Kriging model is built on the reduced space by mapping the original high‐dimensional input onto the identified AS. The effective dimensionality of the AS is estimated by maximum likelihood estimation technique. Finally, an accurate HF surrogate model is obtained for uncertainty propagation of high‐dimensional stochastic problems. The proposed method is validated by two challenging high‐dimensional stochastic examples, and the results demonstrate that our method is effective for high‐dimensional uncertainty propagation.

Global sensitivity analysis of structural models by active subspace and neural network

“…The relative mean square error (RMSE) and relative maximum absolute error (RMAE) (Cheng and Lu, 2020) are used to verify the accuracy of numerical examples bywhere fi is model response, gi is predicted response value of surrogate model and f‾i is the average value of fi.…”

“…The relative mean square error (RMSE) and relative maximum absolute error (RMAE) (Cheng and Lu, 2020) are used to verify the accuracy of numerical examples by…”

“…With the rapid increase of structural complexity, there may be many uncertain factors considered in structural models. For the high-dimensional uncertainty propagation, the number of training samples and computational resources required for constructing surrogate models usually increase exponentially (Cheng and Lu, 2020). This phenomenon is called “curse of dimensionality” (Constantine and Diaz, 2017).…”