Dimensionality Reduction Techniques Applied to the Design of Hypersonic Aerial Systems

Abstract

This study presents a methodology for the use of parametric Reduced Order Modeling (ROM) techniques to generate predictive models of hypersonic aerodynamic flow fields. The goal of this study is to synthesize a methodology for the development of these field surrogate models using techniques and procedures from the literature. This methodology is applied to two analytical test problems and one CFD application to demonstrate the functionality of the methodology and quantify the performance of models generated using various ROM techniques. The models compared in this study were generated using Proper Orthogonal Decomposition (POD) as a representative linear dimensionality reduction method, along with ISOMAP and Locally Linear Embedding (LLE) as representative Nonlinear Dimensionality Reduction (NLDR) methods. Based on the results of study, it is observed that the NLDR-based ROMs provide better predictions in the regions of fields near shocks, while linear methods are found to outperform non-linear methods when predicting steady-state behaviors far from shocks. Furthermore, nonlinear ROMs generated models of lower dimension than their linear counterparts, which resulted in significantly lower evaluation cost and could have significant ramifications if these predictive models are applied to coupled systems analyses.