University of Illinois Urbana-Champaign

A new method for projection based model reduction of linear inequality constrained systems

Turner, Jason Eric

Content Files
TURNER-THESIS-2019.pdf

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https://hdl.handle.net/2142/104952

Description

Title
A new method for projection based model reduction of linear inequality constrained systems
Author(s)
Turner, Jason Eric
Issue Date
2019-04-26
Director of Research (if dissertation) or Advisor (if thesis)
Balajewicz, Maciej
Department of Study
Aerospace Engineering
Discipline
Aerospace Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Date of Ingest
2019-08-23T20:05:25Z
Keyword(s)
  • Constrained Optimization
  • Model Reduction
  • POD
  • Generalized Coordinate Bounding
Abstract
Computational modeling research centers around developing ever better representations of physics. The objective of model reduction specialists is to take that high fidelity understanding and compress it into a Reduced Order Model (ROM) capable of replicating the physical accuracy of the more complicated model with a significantly reduced computational cost. A current challenge in reduced order modeling is the presence of linear inequality constraints in optimization problems. Constrained optimization problems arise in design, contact modeling, financial engineering and other subfields of mathematical modeling. As such, there is a strong motivation to leverage the repeatability of ROMs to rapidly address these engineering challenges. Inherent to the problem of con- strained optimization is feasibility of solutions, and while all FOMs are expected to comply perfectly with their constraints, that property is not necessarily preserved in their corresponding ROMs. The problem is then two fold. First the issue of the constraint must be addressed, and second the resulting ROM must obey the constraints. This thesis develops a method, in a projection-based framework, capable of reducing the linear inequality constraints while preserving a strong degree of feasibility. The proposed method is successfully applied to the reduction of the one-dimensional, constrained Poisson Equation with varied parameters.
Graduation Semester
2019-05
Type of Resource
text
Permalink
http://hdl.handle.net/2142/104952
Copyright and License Information
Copyright 2019 Jason Turner

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Graduate Dissertations and Theses at Illinois PRIMARY
Graduate Theses and Dissertations at Illinois
Dissertations and Theses - Aerospace Engineering