Metamodel Uncertainty Quantification by Using Bayes’ Theorem

Abstract

In complex engineering systems, approximation models, also called metamodels, are extensively constructed to replace the computationally expensive simulation and analysis codes. With different sample data and metamodeling methods, different metamodels can be constructed to describe the behavior of an engineering system. Then, metamodel uncertainty will arise from selecting the best metamodel from a set of alternative ones. In this study, a method based on Bayes’ theorem is used to quantify this metamodel uncertainty. With some mathematical examples, metamodels are built by six metamodeling methods, i.e., polynomial response surface, locally weighted polynomials (LWP), k-nearest neighbors (KNN), radial basis functions (RBF), multivariate adaptive regression splines (MARS), and kriging methods, and under four sampling methods, i.e., parameter study (PS), Latin hypercube sampling (LHS), optimal LHS and full factorial design (FFD) methods. The uncertainty of metamodels created by different metamodeling methods and under different sampling methods is quantified to demonstrate the process of implementing the method.