Parametric Optimal Design Of Uncertain Dynamical Systems

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mechanical Engineering

Department dc:contributor.department

Mechanical Engineering

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2011

Author dc:creator

• Hays, Joseph T.

Chairs dc:contributor.committeechair

• Sandu, Adrian
• Sandu, Corina
• Hong, Dennis W.

Committee members dc:contributor.committeemember

• Ross, Shane D.
• Southward, Steve C.

• 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)

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-09012011-162500

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28850