Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS)
Name
1011356422-MIT.pdf
Description
Full printable version
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4.07 MB
Format
Adobe PDF
Checksum (MD5)
f4c013f12094363342a07360553a479f
Author(s)
Ni, Angxiu
Advisor(s)
Qiqi Wang.
Date Issued
2017
Publisher
Massachusetts Institute of Technology
Abstract
This thesis develops the Non-Intrusive Least Squares Shadowing (NILSS) method, which computes the sensitivity for long-time averaged objectives in chaotic dynamical systems. In NILSS, we represent a tangent solution by a linear combination of one inhomogeneous tangent solution and several homogeneous tangent solutions. Next, we solve a least squares problem using this representation; thus, the resulting solution can be used for computing sensitivities. NILSS is easy to implement with existing solvers. In addition, for chaotic systems with many degrees of freedom but few unstable modes, NILSS has a low computational cost. NILSS is applied to two chaotic PDE systems: the Lorenz 63 system and a CFD simulation of flow over a backward-facing step. In both cases, the sensitivities computed by NILSS reflect the trends in the long-time averaged objectives of dynamical systems.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2017.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-63).
Subjects
Aeronautics and Astronautics.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
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