An effective method for quantifying and incorporating uncertainty in metamodel selection

Abstract

In complex engineering systems, metamodels are extensively used to replace the computationally expensive simulation and analysis process. Different metamodels can be constructed by using different metamodeling techniques. Uncertainty exists in selecting the best metamodel among a set of alternatives. This study introduces an effective method based on Bayes’ theorem and additive adjustment factor for quantifying and incorporating this uncertainty in metamodel selection. In this method, the posterior probability of each metamodel evaluated by Bayes’ theorem is employed to quantify the uncertainty. The metamodel with the largest posterior probability is considered as the best. Then, the uncertainty in metamodel selection is accounted for by an additive adjustment factor and incorporated into the prediction of the best metamodel. Mathematical examples and the resistance and volume prediction example of a submersible are presented to showcase the introduced method. In these examples, metamodels are constructed by different metamodeling techniques, such as polynomial response surface (PRS), locally weighted regression (LWP), k-nearest neighbors (KNN), radial basis functions (RBF), multivariate adaptive regression splines (MARS) and Kriging. Results indicate that the introduced method can effectively quantify the uncertainty in metamodel selection and incorporate it into the prediction of a system output, hence achieving a prediction with good accuracy and small uncertainty.