A Mathematical and Computational Framework for Multifidelity Design and Analysis with Computer Models

A multifidelity approach to design and analysis for complex systems seeks to exploit optimally all available models and data. Existing multifidelity approaches generally attempt to calibrate low-fidelity models or replace low-fidelity analysis results using data from higher fidelity analyses. This paper proposes a fundamentally different approach that uses the tools of estimation theory to fuse together information from multifidelity analyses, resulting in a Bayesian-based approach to mitigating risk in complex system design and analysis. This approach is combined with maximum entropy characterizations of model discrepancy to represent epistemic uncertainties due to modeling limitations and model assumptions. Mathematical interrogation of the uncertainty in system output quantities of interest is achieved via a variance-based global sensitivity analysis, which identifies the primary contributors to output uncertainty and thus provides guidance for adaptation of model fidelity. The methodology is applied to multidisciplinary design optimization and demonstrated on a wing-sizing problem for a high altitude, long endurance vehicle.