Locally Refined Adaptive Sparse Surrogate-Based Approach for Uncertainty Quantification

Abstract

Two novel surrogate-based approaches have been developed for uncertainty quantification of engineering systems. In doing so, two well-known techniques, namely, high dimensional model representation (HDMR) and Kriging, have been integrated. Specifically, the trend portion of Kriging has been replaced by HDMR such that the approximation accuracy may be enhanced. The improvement in accuracy is the result of the fact that the proposed hybrid surrogate model performs a two-tier approximation, first capturing the global variation in the functional space using a set of component functions by HDMR and subsequently interpolating the local fluctuations by Kriging. Additionally, to improve the computational cost of this proposed model, feature selection approaches, namely, least absolute shrinkage and selection operator and least angle regression have been employed. These efficient schemes utilized to determine the relevant unknown coefficients induces adaptive sparsity for the proposed surrogate models. The performance of the proposed approaches has been assessed by solving an analytical and practical engineering problem. The results illustrate excellent performance of the proposed approaches in terms of both approximation accuracy and computational effort.