Sparse polynomial chaos expansion for universal stochastic kriging

Abstract

Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering applications and decision-making, the incorporation of uncertainty quantification into meta-models remains a challenging open area of research. To address this issue, this paper presents a novel stochastic simulation approach combining sparse polynomial chaos expansion (PCE) and Stochastic Kriging (SK). Specifically, the proposed approach adopts adaptive sparse PCE as the trend model in SK, achieving both global and local prediction capabilities and maximizing the role of the stochastic term to conduct uncertainty quantification. To maximize the generalization and computational efficiency of the meta-model, the Least Angle Regression (LAR) algorithm is adopted to automatically select the optimal polynomial basis in the PCE. The computational effectiveness and accuracy of the proposed approach are appraised through a comprehensive set of case studies and different quality metrics. The presented numerical results and discussion demonstrate the superior performance of the proposed approach compared to the classical ordinary SK model, offering high flexibility for the characterization of both extrinsic and intrinsic uncertainty for a wide variety of problems.