Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity

TLDR: In this article, an interpolation method based on the Grassmann manifold and its tangent space at a point that is applicable to structural, aerodynamic, aeroelastic, and many other reduced-order models based on projection schemes is presented.

Abstract: Reduced-order models are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real-time analysis. Although most reduced-order models can operate in near real-time, their construction can be computationally expensive, as it requires accumulating a large number of system responses to input excitations. Furthermore, reduced-order models usually lack robustness with respect to parameter changes and therefore must often be rebuilt for each parameter variation. Together, these two issues underline the need for a fast and robust method for adapting precomputed reduced-order models to new sets of physical or modeling parameters. To this effect, this paper presents an interpolation method based on the Grassmann manifold and its tangent space at a point that is applicable to structural, aerodynamic, aeroelastic, and many other reduced-order models based on projection schemes. This method is illustrated here with the adaptation of computational-fluid-dynamics-based aeroelastic reduced-order models of complete fighter configurations to new values of the freestream Mach number. Good correlations with results obtained from direct reduced-order model reconstruction, high-fidelity nonlinear and linear simulations are reported, thereby highlighting the potential of the proposed reduced-order model adaptation method for near real-time aeroelastic predictions using precomputed reduced-order model databases.