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Title: Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

Abstract

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction methodmore » revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.« less

Authors:
 [1]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1637464
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
AIAA Journal
Additional Journal Information:
Journal Volume: 58; Journal Issue: 5; Journal ID: ISSN 0001-1452
Publisher:
AIAA
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Renganathan, S. Ashwin. Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation. United States: N. p., 2020. Web. https://doi.org/10.2514/1.j058744.
Renganathan, S. Ashwin. Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation. United States. https://doi.org/10.2514/1.j058744
Renganathan, S. Ashwin. Tue . "Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation". United States. https://doi.org/10.2514/1.j058744. https://www.osti.gov/servlets/purl/1637464.
@article{osti_1637464,
title = {Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation},
author = {Renganathan, S. Ashwin},
abstractNote = {A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. is further extended here toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.},
doi = {10.2514/1.j058744},
journal = {AIAA Journal},
number = 5,
volume = 58,
place = {United States},
year = {2020},
month = {3}
}

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