A Critical Appraisal of Design of Experiments for Uncertainty Quantification

Surrogate models are widely used to predict response function of any system and in quantifying uncertainty associated with the response function. It is required to have response quantities at some preselected sample points to construct a surrogate model which can be processed in two way. Either the surrogate model is constructed using one shot experimental design techniques, or, the sample points can be generated in a sequential manner so that optimum sample points for a specific problem can be obtained. This paper addresses a comprehensive comparisons between these two types of sampling techniques for the construction of more accurate surrogate models. Two most popular one shot sampling strategies: Latin hypercube sampling and Sobol sequence, and four different type sequential experimental designs (SED) namely, Monte Carlo intersite projected (MCIP), Monte Carlo intersite projected threshold (MCIPT), optimizer projected (OP) and LOLA-Voronoi (LV) method are taken for the present study. Two most widely used surrogate models, namely polynomial chaos expansion and Kriging are used to check the applicability of the experimental design techniques. Three different types of numerical problems are solved using the two above-mentioned surrogate models considering all the experimental design techniques independently. Further, all the results are compared with the standard Monte Carlo simulation (MCS). Overall study depicts that SED performs well in predicting the response functions more accurately with an acceptable number of sample points even for high-dimensional problems which maintains the balance between accuracy and efficiency. More specifically, MCIPT and LV method based Kriging outperforms other combinations.