Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Aerospace Engineering


Aerospace Engineering

First Advisor

Leifur Leifsson


Physics-based simulation models are important to the decision-making process in the

design of modern engineered systems. The key challenges of using accurate predictive

simulations in this process are (1) time-consuming model evaluations, (2) a large number of

parameters, (3) often complex and highly coupled systems, and (4) conventional modeling

and optimization techniques typically require a large amount of model evaluations. The

research objective of this work is to accelerate the process of UP and optimum design

under uncertainty when the high-delity computational budget is limited. In particular,

the objective is to create and evaluate new metamodeling and multidelity methods that

enable the solution of problems that cannot be addressed with the current state-of-the-art

methods. The scope of the work is limited to nondestructive testing (NDT) systems and

aerodynamic surfaces.

In this work, the least-angle regression (LARS)-based polynomial chaos expansions

(PCE), polynomial chaos-based Kriging (PCKriging) metamodeling, Cokriging and the proposed

polynomial chaos-based Cokriging (PC-Cokriging) multidelity method are used to

enable the fast uncertainty propagation (UP) for reliability and sensitivity analysis of NDT

systems for the rst time. In addition, the manifold mapping (MM) multidelity metamodeling

method was implemented for ecient aerodynamic forward/inverse shape optimization

for the rst time. Lastly, utility theory was introduced for aerodynamic optimum shape

design under uncertainty.

The results of several numerical examples show that the aforementioned metamodeling

and multidelity methods proposed in this work for the reliability and sensitivity analysis of

NDT systems outperformed the current state-of-the-art Kriging and ordinary least-squares

(OLS)-based PCE by reducing the high-delity (HF) training data from one to two orders of

magnitude. In particular, the new and unique PC-Cokriging multidelity method reduced

the cost by up to two orders of magnitude in the NDT benchmark cases. Furthermore, the

proposed PC-Cokriging method is shown to be robust in terms of the user-specied detection

thresholds. For the aerodynamic shape design, the MM-based aerodynamic local optimization

algorithm alleviated the computational cost of direct HF model-based optimization by

up to one order of magnitude. Moreover, utility theory was shown to yield ecient decision

making for aerodynamic design under uncertainty without using weighted-sum method and

estimating statistics of the objective function.

Copyright Owner

Xiaosong Du



File Format


File Size

245 pages