Theses and Dissertations

Issuing Body

Mississippi State University

Advisor

Rais-Rohani, Masoud.

Committee Member

Lacy, Thomas E.

Committee Member

Patil, Prakash.

Committee Member

Cheng, Yang.

Committee Member

Vahedifard, Farshid.

Date of Degree

5-6-2017

Document Type

Dissertation - Open Access

Major

Aerospace Engineering

Degree Name

Doctor of Philosophy

College

James Worth Bagley College of Engineering

Department

Department of Aerospace Engineering

Abstract

Bayesian updating is used to approximate discontinuous multi-interval uncertainty representations (i.e., belief structures) of epistemic uncertainty. Several Bayesian-based approaches are examined for assessing the accuracy of approximating the mean and standard deviation of a belief structure and calculating reliability using posterior distributions. Moreover, a Bayesian-based belief structure approximation is integrated with a decomposed multilevel optimization solution strategy through analytical target cascading, where the ensuing reliability-based design optimization problem within each decomposed element is solved using a single loop single vector approach. The non-deterministic decomposed multilevel optimization approach is demonstrated through solutions to four analytical benchmark problems with mixed aleatory and epistemic uncertainties as well as a nano-enhanced composite sandwich plate problem. Consistent with the integrated computational materials engineering philosophy, the proposed solution strategy for the sandwich plate problem combines micro- and macro-level material modeling and design with structural level analysis and optimization. The orientation distribution of the carbon nanofibers in the micro-mechanical model is described through a belief structure and modeled using a Bayesian approach. Aleatory uncertainty in the ply thickness of the composite facesheets is also considered. This problem is used to demonstrate computationally efficient integration of epistemic uncertainty described through a belief structure for a complex design problem with mixed uncertainties. The results of this study show that the posterior distributions from some of the Bayesian-based approaches are suitable for direct calculation of reliability through joint probability density functions. Moreover, the Bayesian-based approach can provide a computationally efficient method for integrating epistemic and aleatory uncertainties in decomposed multilevel optimization of complex problems.

URI

https://hdl.handle.net/11668/16856

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