Doctoral Dissertations


Yi Zhang

Keywords and Phrases

Adaptive Sampling; Mixed Uncertainty; NIPC; Robust Design Optimization; Stochastic Expansions; Uncertainty Quantification


"The main purpose of this study is to apply a computationally efficient uncertainty quantification approach, Non-Intrusive Polynomial Chaos (NIPC) based stochastic expansions, to robust aerospace analysis and design under mixed (aleatory and epistemic) uncertainties and demonstrate this technique on model problems and robust aerodynamic optimization. The proposed optimization approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes the stochastic measures which are minimized simultaneously to ensure the robustness of the final design to both aleatory and epistemic uncertainties. For model problems with mixed uncertainties, Quadrature-Based and Point-Collocation NIPC methods were used to create the response surfaces used in the optimization process. For the robust airfoil optimization under aleatory (Mach number) and epistemic (turbulence model) uncertainties, a combined Point-Collocation NIPC approach was utilized to create the response surfaces used as the surrogates in the optimization process. Two stochastic optimization formulations were studied: optimization under pure aleatory uncertainty and optimization under mixed uncertainty. As shown in this work for various problems, the NIPC method is computationally more efficient than Monte Carlo methods for moderate number of uncertain variables and can give highly accurate estimation of various metrics used in robust design optimization under mixed uncertainties. This study also introduces a new adaptive sampling approach to refine the Point-Collocation NIPC method for further improvement of the computational efficiency. Two numerical problems demonstrated that the adaptive approach can produce the same accuracy level of the response surface obtained with oversampling ratio of 2 using less function evaluations."--Abstract, page iii.


Hosder, Serhat

Committee Member(s)

Du, Xiaoping
Riggins, David W.
Finaish, Fathi
Leifsson, Leifur Thor


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Aerospace Engineering


Missouri University of Science and Technology

Publication Date

Spring 2013


xvii, 133 pages

Note about bibliography

Includes bibliographical references.


© 2013 Yi Zhang, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Aerodynamics -- Computer simulation
Stochastic analysis
Robust optimization

Thesis Number

T 10320

Electronic OCLC #