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. / Ph. D.
Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/28850 |
Date | 02 September 2011 |
Creators | Hays, Joseph T. |
Contributors | Mechanical Engineering, Ross, Shane D., Southward, Steve C., Sandu, Adrian, Sandu, Corina, Hong, Dennis W. |
Publisher | Virginia Tech |
Source Sets | Virginia Tech Theses and Dissertation |
Detected Language | English |
Type | Dissertation |
Format | application/pdf |
Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
Relation | Hays_JT_T_2011.pdf |
Page generated in 0.0017 seconds