A Novel Surrogate Modeling Technique for Parametric Uncertainty Quantification in Simulation-Based Design

Abstract

Due to the excessive computational cost associated with the subsequent function evaluations often utilized in parametric uncertainty quantification methods, metamodels are often utilized as a resource to alleviate the computational cost associated with repeated evaluations of full-scale simulations through lower-order representations of the design space. However, for these metamodels to be practical within the uncertainty quantification scheme, they must provide an accurate representation of the design space at a minimal computational cost. As such, much time has been invested at developing accurate surrogate modeling techniques to develop closed-form representations of complex problems using a minimal number of data points. This work details a novel surrogate modeling methodology design for application with the Fast Fourier Transform method for parametric uncertainty quantification. Utilizing k-fold sampling of the design space, the proposed methodology utilizes independent validation metrics from a limited sample to develop an efficient response surface model for application in the Fast Fourier Transform approach to parametric uncertainty quantification. The proposed surrogate modeling approach will first be validated on a benchmark surrogate modeling problems. Following, an application of the approach to the parametric uncertainty quantification of a high-complexity finite element simulation will be demonstrated.