Strides in modern computational fluid dynamics and leaps in high-power computing have led to unprecedented capabilities for handling large aerodynamic problem. In particular, the emergence of adjoint design methods has been a break-through in the field of aerodynamic shape optimization. It enables expensive, high-dimensional optimization problems to be tackled efficiently using gradient-based methods in CFD; a task that was previously inconceivable. However, adjoint design methods are intended for gradient-based optimization; the curse of dimensionality is still very much alive when it comes to design space exploration, where gradient-free methods cannot be avoided. This research describes a novel approach for reducing dimensionality in large, computationally expensive design problems to a point where gradient-free methods become possible. This is done using an innovative application of Principal Component Analysis (PCA), where the latter is applied to the gradient distribution of the objective function; something that had not been done before. This yields a linear transformation that maps a high-dimensional problem onto an equivalent low-dimensional subspace. None of the original variables are discarded; they are simply linearly combined into a new set of variables that are fewer in number. The method is tested on a range of analytical functions, a two-dimensional staggered airfoil test problem and a three-dimensional Over-Wing Nacelle (OWN) integration problem. In all cases, the method performed as expected and was found to be cost effective, requiring only a relatively small number of samples to achieve large dimensionality reduction.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/53504 |
| Date | 08 June 2015 |
| Creators | Berguin, Steven Henri |
| Contributors | Mavris, Dimitri N. |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
| Format | application/pdf |
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