Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Bhushan, Shanti
Committee Member
Collins, Eric M.
Committee Member
Sescu, Adrian
Date of Degree
5-13-2022
Document Type
Graduate Thesis - Open Access
Major
Computational Engineering
Degree Name
Master of Science (M.S.)
College
James Worth Bagley College of Engineering
Department
Computational Engineering Program
Abstract
The direct and adjoint methods are to linearize the time-averaged solution of bounded dynamical systems about one or more design parameters. Hence, such methods are one way to obtain the gradient necessary in locally optimizing a dynamical system’s time-averaged behavior over those design parameters. However, when analyzing nonlinear systems whose solutions exhibit chaos, standard direct and adjoint sensitivity methods yield meaningless results due to time-local instability of the system. The present work proposes a new method of solving the direct and adjoint linear systems in time, then tests that method’s ability to solve instances of the Lorenz system that exhibit chaotic behavior. Promising results emerge and are presented in the form of a regression analysis across a parametric study of the Lorenz system.
Recommended Citation
Spencer-Coker, Christian A., "A novel method for sensitivity analysis of time-averaged chaotic system solutions" (2022). Theses and Dissertations. 5479.
https://scholarsjunction.msstate.edu/td/5479
Included in
Computational Engineering Commons, Dynamic Systems Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Ordinary Differential Equations and Applied Dynamics Commons, Theory and Algorithms Commons