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.
| Identifer | oai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-1852 |
| Date | 06 May 2017 |
| Creators | Dettwiller, Ian Daniel |
| Publisher | Scholars Junction |
| Source Sets | Mississippi State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Theses and Dissertations |
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