(Georgia Institute of Technology. School of Aerospace Engineering, 2023-06)
Sampaio Felix, Barbara; Perron, Christian; Ahuja, Jai; Mavris, Dimitri N.
The present work proposes an efficient parametric approximation of mission drag polars by combining multi-fidelity surrogate models with parametric reduced order modeling techniques. Traditionally, semi-empirical aerodynamic analyses are used to provide drag polars needed for mission analysis during the conceptual design of aircraft. The database needed for these methods is unavailable for unconventional vehicles, and for this reason, many studies rely on higher-fidelity models typical of preliminary design to perform design space exploration for novel vehicle geometries. Due to the high computational cost and evaluation time of these higher-fidelity models, researchers constrain the design space exploration of vehicles by either relying on single discipline optimization or obtaining mission drag polars for a few vehicle geometries within their design loop. The present work demonstrates the application of Hierarchical Kriging surrogate models to obtain mission drag polars for fixed vehicle geometries. Then, the proper orthogonal decomposition reduced order model with Kriging interpolation is used to approximate the coherent structure of mission drag polars. The proposed method is demonstrated on a supersonic commercial aircraft. Experiments showed that both the multi-fidelity surrogate model and the reduced order model are able to emulate vehicle drag polars well for fixed and varying vehicle geometries, respectively.
(Georgia Institute of Technology, 2023-06)
Mufti, Bilal; Perron, Christian; Gautier, Raphaël; Mavris, Dimitri N.
The parameterization of aerodynamic design shapes often results in high-dimensional design
spaces, creating challenges when constructing surrogate models for aerodynamic coefficients.
Active subspaces offer an effective way to reduce the dimensionality of such spaces, but
existing approaches often require a substantial number of gradient evaluations, making them
computationally expensive. We propose a multi-fidelity, model-based approach to finding
an active subspace that relies solely on direct function evaluations. By using both high- and
low-fidelity samples, we develop a model-based approximation of the projection matrix of the
active subspace. We evaluate the proposed method by assessing its active subspace recovery
characteristics and resulting model prediction accuracy for airfoil and wing drag prediction
problems. Our results show that the proposed method successfully recovers the active subspace
with an acceptable model prediction error. Furthermore, a cost vs. accuracy comparison with
the multi-fidelity gradient-based active subspace method demonstrates that our approach offers
comparable predictive performance with lower computational costs. Our findings provide
strong evidence supporting the usage of the proposed method to reduce the dimensionality of
design spaces when gradient samples are unavailable or expensive to obtain.
(Georgia Institute of Technology, 2022-06)
Mufti, Bilal; Chen, Mengzhen; Perron, Christian; Mavris, Dimitri N.
Modern design problems routinely involve high-dimensional inputs and the active subspace
has been recognized as a potential solution to this issue. However, the computational cost
for collecting training data with high-fidelity simulations can be prohibitively expensive. This
paper presents a multi-fidelity strategy where low-fidelity simulations are leveraged to extract
an approximation of the high-fidelity active subspace. Both gradient-based and gradient-free
active subspace methods are incorporated with the proposed multi-fidelity strategy and are
compared with the equivalent single-fidelity method. To demonstrate the effectiveness of our
proposed multi-fidelity strategy, the aerodynamic analysis of an airfoil and a wing are used
to define two application problems. The effectiveness of the current approach is evaluated
based on its prediction accuracy and training cost improvement. Results show that using a
low-fidelity analysis to approximate the active subspace of high-fidelity data is a viable solution
and can provide substantial computational savings, yet this is counterbalanced with slightly
worse prediction accuracy.