Reduced Order Modelling
Figure 1: F-16 Block 40 CFD surface grid.
Reduced-order models are neither robust with respect to parameter changes nor cheap to generate. A method based on a database of ROMs coupled with a suitable interpolation schemes greatly reduces the computational cost for aeroelastic predictions while retaining good accuracy.

For more information:
David Amsallem

Reduced-order models (ROMs) are usually thought of as computationally inexpensive mathematical representations that offer the potential for near real-time analysis. While most ROMs can operate in near real-time, their construction can however be computationally expensive as it requires accumulating a large number of system responses to input excitations. Furthermore, ROMs 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 pre-computed ROMs to new sets of physical or modeling parameters. However, ROMs and their corresponding reduced-order bases (ROBs) are quantities that typically belong to nonlinear, matrix manifolds. As such, classical interpolation methods fail, as they are not able to enforce the constraints characterizing those manifolds. The first part of the project consists of designing a suitable interpolation method enforcing those constraints. A schematic representation of the algorithm is shown below: it relies on identifying the correct manifold for the given application, constructing the appropriate logarithm mapping to move the interpolation data to a tangent space to this manifold where a standard multivariate interpolation algorithm can be applied, and constructing the appropriate exponential mapping to bring back the computed result to the manifold of interest.

An approach based on database of reduced-order fluid bases and reduced-order structural models coupled with this method of interpolation on a manifold, has been recently shown to greatly reduce computational cost for aeroelastic predictions of a full F16 Block 40 aircraft while retaining good accuracy. The proposed method enables test operation calls for new, ``last minute'' flight configurations and thus paves the way for on-line, routine usage of reduced-order modeling including during flight testing. Currently, its full potential is limited by the need to recompute a steady state flow for each desired set of flight conditions not represented in the database.

Current work focuses on removing this limitation by developing a method for interpolating directly the fluid ROMs instead of the underlying fluid ROBs.


Figure 2: Interpolation on a matrix manifold.