Design of experiments for uncertainty quantification based on polynomial chaos expansion metamodels

In the past decade, uncertainty quantification (UQ) has received much attention, particularly in the research areas of reliability and risk analysis, sensitivity analysis, and optimization under uncertainty, to mention a few. In the context of UQ, one of the major challenges is the computational demand of the numerical (finite element) model that is used to analyze the large-scale engineering systems under consideration. Metamodels or surrogate models are often used as substitutes to those high-fidelity numerical models to overcome this issue. Polynomial chaos expansion (PCE) has been considered as one of the promising metamodeling methods. To build a PCE metamodel, design of experiments (DoEs) are carried out, i.e., determining the design points (in the input space) where the original (high-fidelity) computational model needs to be evaluated. The accuracy level of the metamodel depends on the DoE over the input design space. This chapter will introduce some state-of-the-art DoEs used for uncertainty quantification problems. A comparative study is performed to show the efficiency and limitations of the various experimental designs in uncertainty quantification of engineered systems with varying input dimensionality and computational complexity.