Computational aeroelasticity is vital to modern aircraft design, as common objectives and aeroelastic constraints often trend in opposite directions in the design space. While linear structural and aerodynamic equations are reasonably well suited for subsonic and supersonic flight conditions, aeroelastic behavior in the transonic regime must be assessed with nonlinear aerodynamics equations. If readily available early in the design process, these more accurate models can help avoid the late discovery of design defects, and as a result, cost and schedule overruns. The use of these transient computational fluid dynamics simulations introduces significant challenges to the aircraft design process. These include (1) the time-consuming model evaluations, (2) the numerous flight conditions encountered within the flight envelope, and (3) the number of designable parameters in aircraft design. The overarching research objective of this work is to reduce the computational cost required to locate an aircraft's aeroelastic stability boundary throughout its flight envelope, while also making use of existing tools in industry to allow a faster transition or simpler interchangeability of computational tools. In particular, the objective is to create and evaluate multifidelity metamodeling approaches that focus on intermediate frequency-domain aerodynamic quantities, rather than quantities of interest (QoI). Due to the lack of available aerodynamic sensitivities, the scope of this work is limited to the fast flutter calculation of a particular design across its operating conditions, rather than a full flutter-constrained design optimization.

The major contributions of this work are as follows. Regression cokriging (RCK) and manifold mapping (MM) metamodels are applied to underlying frequency-domain aerodynamic matrices to adaptively compute flutter boundaries and matched flutter solutions. A simple and affordable approach for RCK-based model uncertainty propagation is introduced, providing uncertainties of flutter quantities which correspond to the numerous underlying model uncertainties. This allows common kriging-based infill criteria (such as mean squared error or expected improvement) to be applied using flutter speed or frequency uncertainties in combination with various objectives. The MM-based approach is generally easier to implement and can begin iterating with as few as three high-fidelity matrix evaluations, whereas the RCK-based approach requires a larger initial sampling plan. RCK, on the other hand, is capable of handling numerical noise in the underlying matrix terms, and can globally optimize an infill criterion, whereas the MM-based approach focuses only on the nearest matched point. While the MM-based approach has no directly comparable single-fidelity approach, RCK is compared against regression kriging (RK) using the same initial high-fidelity data, thus providing an estimated value of using multiple fidelity levels rather than just one.

The proposed methods are demonstrated on benchmark wing and airfoil cases for continuous ranges of Mach number (up to 1.2), where atmospheric fluid density and sound speed (when applicable) are held fixed to represent a particular altitude. The results show that using multiple fidelity levels reduces cost and error metrics by factors of around 1.5-2. Additional benefits include the use of low-fidelity modal participation factors, which can indicate which modes to evaluate with the high-fidelity model, as well as low-fidelity flutter reduced frequencies, which can be used when generating initial sampling plans for RCK. The use of intermediate quantities, rather than QoI, was found to reduce cost and error metrics by factors of around 5-10.