A Multi-Fidelity Adaptive Sampling Method for Metamodel-Based Uncertainty Quantification of Computer Simulations

Abstract

A multi-fidelity global metamodel is presented for uncertainty quantification of computationally expensive simulations. The multi-fidelity approximation is built as the sum of a low-fidelity-trained metamodel and the metamodel of the difference (error) between high-and low-fidelity simulations. The metamodel is based on dynamic stochastic radial basis functions, which provide the prediction along with the associated uncertainty. New training points are added where the prediction uncertainty is largest, according to an adaptive sampling procedure. The prediction uncertainty of both the low-fidelity and the error metamodel are considered for the adaptive training of the low-and high-fidelity metamodels, respectively. The method is applied to a steady fluid-structure interaction (FSI) problem of a 3D NACA 0009 stainless steel hydrofoil. Two functions are considered simultaneously, namely lift and drag coefficients, versus angle of attack and Reynolds number. Two problems are presented: in the first problem the high-fidelity evaluations are obtained through steady FSI computer simulations, whereas in the second problem they are given by available experimental data from literature. Low-fidelity evaluations are provided in both cases by steady hydrodynamic simulations. The overall uncertainty of the multi-fidelity metamodel is used as a convergence criterion.

A Strategy for Adaptive Sampling of Multi-Fidelity Gaussian Processes to Reduce Predictive Uncertainty

“…1. Typically, a two step strategy is used in multi-fidelity adaptive sampling strategy [30], where in the first step x * is determined without considering the cost impact. Once x * is determined, then fidelity of analysis is decided based on the cost ratio between high and low fidelity analyses.…”

“…We found that the adaptive sampling schemes for the multi-fidelity GP surrogate are two step process, where in the first step location or design point on input parameters are determined by finding the location of maximum predictive uncertainty. Then in the second step, decision is made whether to run high-fidelity or low-fidelity analysis based on the cost ratio of these analyses [30]. In this work a new criteria is proposed where the selection of next design point as well as fidelity is done in a single step.…”