Doctoral Dissertations

Keywords and Phrases

Design under uncertainty; Evidence theory; Reliability assessment; Robust optimization; Stochastic expansions; Uncertainty quantification


One of the primary objectives of this research is to develop a method to model and propagate mixed (aleatory and epistemic) uncertainty in aerospace simulations using DSTE. In order to avoid excessive computational cost associated with large scale applications and the evaluation of Dempster Shafer structures, stochastic expansions are implemented for efficient UQ. The mixed UQ with DSTE approach was demonstrated on an analytical example and high fidelity computational fluid dynamics (CFD) study of transonic flow over a RAE 2822 airfoil.

Another objective is to devise a DSTE based performance assessment framework through the use of quantification of margins and uncertainties. Efficient uncertainty propagation in system design performance metrics and performance boundaries is achieved through the use of stochastic expansions. The technique is demonstrated on: (1) a model problem with non-linear analytical functions representing the outputs and performance boundaries of two coupled systems and (2) a multi-disciplinary analysis of a supersonic civil transport.

Finally, the stochastic expansions are applied to aerodynamic shape optimization under uncertainty. A robust optimization algorithm is presented for computationally efficient airfoil design under mixed uncertainty using a multi-fidelity approach. This algorithm exploits stochastic expansions to create surrogate models utilized in the optimization process. To reduce the computational cost, output space mapping technique is implemented to replace the high-fidelity CFD model by a suitably corrected low-fidelity one. The proposed algorithm is demonstrated on the robust optimization of NACA 4-digit airfoils under mixed uncertainties in transonic flow. "--Abstract, page iii.


Hosder, Serhat

Committee Member(s)

Du, Xiaoping
Isaac, Kakkattukuzhy M.
Riggins, David W.
Leifsson, Leifur


Mechanical and Aerospace Engineering

Degree Name

Ph. D. in Aerospace Engineering


Missouri University of Science and Technology

Publication Date

Summer 2015

Journal article titles appearing in thesis/dissertation

  • A mixed uncertainty quantification approach using evidence theory and stochastic expansions
  • Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions
  • Multi-fidelity robust aerodynamic design optimization under mixed uncertainty


xvi, 158 pages

Note about bibliography

Includes bibliographic references.


© 2015 Harsheel R. Shah, All rights reserved.

Document Type

Dissertation - Open Access

File Type




Subject Headings

Aerodynamics -- Computer simulation
Stochastic analysis
Robust optimization

Thesis Number

T 10768

Electronic OCLC #