An Adaptive N-fidelity Metamodel for Design and Operational-Uncertainty Space Exploration of Complex Industrial Problems

An adaptive N -fidelity (NF) metamodel is presented for the solution of simulation-based design optimization and uncertainty quantification problems. A multi-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of hierarchical differences (errors) between higher-fidelity levels. The metamodel is based on the expected value of an ensemble of stochastic radial-basis functions, which also provides the uncertainty associated to the prediction. New training points are added to the appropriate fidelity level, based on the NF prediction uncertainty and the computational cost. The method is demonstrated for an analytical test function, the shape optimization of a NACA hydrofoil, and the operational-uncertainty quantification of a RoPax ferry. The fidelity levels are defined by adaptive-grid refinement and multi-grid approach, for the NACA hydrofoil and the RoPax ferry, respectively. The generalization of the multi-fidelity concept to N fidelities shows promising results both in terms of accuracy and computational cost.