  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.
