Title page for ETD etd-09012011-162500


Type of Document Dissertation
Author Hays, Joseph T
Author's Email Address joehays@vt.edu
URN etd-09012011-162500
Title Parametric Optimal Design Of Uncertain Dynamical Systems
Degree PhD
Department Mechanical Engineering
Advisory Committee
Advisor Name Title
Hong, Dennis W. Committee Co-Chair
Sandu, Adrian Committee Co-Chair
Sandu, Corina Committee Co-Chair
Ross, Shane D. Committee Member
Southward, Steve C. Committee Member
Keywords
  • Ordinary Differential Equations (ODEs)
  • Trajectory Planning
  • Motion Planning
  • Generalized Polynomial Chaos (gPC)
  • Uncertainty Quantification
  • Multi-Objective Optimization (MOO)
  • Nonlinear Programming (NLP)
  • Dynamic Optimization
  • Optimal Control
  • Robust Design Optimization (RDO)
  • Collocation
  • Uncertainty Apportionment
  • Tolerance Allocation
  • Multibody Dynamics
  • Differential Algebraic Equations (DAEs)
Date of Defense 2011-08-25
Availability unrestricted
Abstract
This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs.

Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible.

The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework

advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost.

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