(Advisor: Professor Dimitri Mavris)
"Uncertainty Propagation in High-dimensional Fields Using Reduced Order Modeling"
Thursday, December 14
Weber Space Science and Technology Building (SST II), Collaborative Visualization Environment (CoVE)
Across the world, there is a growing interest in re-introducing commercial supersonic transport aircraft (SST). However, the development of SSTs is dependent on the mitigation of sonic boom loudness to acceptable levels. Moreover, uncertainties in the atmosphere and flight conditions can drastically impact the loudness of an aircraft and must be accounted for during the design process to avoid certification delays.
Given this need, there has been significant research on modeling the aerodynamic field around SSTs, which is characterized by the presence of strong shocks and nonlinearities, to accurately shape the aircraft sonic boom signature and guide downstream sub-system analyses. Computational fluid dynamics (CFD) simulations closely match experimental aerodynamic and noise data, but each simulation can take hours or days to output a solution. For multi-query problems, such as uncertainty quantification (UQ), which require repeated evaluation of the expensive simulation, this cost becomes computationally intractable.
Surrogate models have been identified as a key enabler for leveraging high-fidelity numerical simulations earlier in the design process because they are non-intrusive, data-driven, and cheap to evaluate. However, there exist several challenges when creating surrogate models for uncertain field outputs with shocks that this thesis tackles.
In particular, this thesis presents a non-intrusive, parametric reduced order modeling method for computationally expensive full-order models (FOM). The central idea is to identify a low-dimensional subspace that effectively captures the dynamics of the FOM. Unlike classical methods for dimensionality reduction (DR) that approximate models using flat surfaces, this study explores nonlinear DR to identify the low-dimensional invariant manifold on which the data exists. A non-linear extension of generalized polynomial chaos (gPC) is then utilized to learn the dynamics in the latent space. The capabilities and robustness of the proposed method are assessed on several CFD test problems with stochastic inputs and outputs with thousands of random variables. Lastly, by leveraging this reduced order model, a procedure is designed to efficiently propagate the impact of atmospheric and flight uncertainties on the sonic boom pressure signatures of a low-boom supersonic aircraft. This research not only provides novel insight into the performance of gPC models in high-dimensional aerodynamic problems, but also enables uncertainty quantification in fields with complex flow structures necessary for the robust design of novel aircraft.
- Prof. Dimitri Mavris – School of Aerospace Engineering (Advisor)
- Prof. Graeme Kennedy – School of Aerospace Engineering
- Prof. Lakshmi Sankar – School of Aerospace Engineering
- Dr. Olivia Fischer – School of Aerospace Engineering
- Dr. Dushhyanth Rajaram – Sr. Systems Engineer, Kodiak Robotics