A method for reducing dimensionality in large design problems with computationally expensive analyses

Berguin, Steven Henri

Title:

A method for reducing dimensionality in large design problems with computationally expensive analyses

dc.contributor.advisor	Mavris, Dimitri N.
dc.contributor.author	Berguin, Steven Henri
dc.contributor.committeeMember	Ruffin, Stephen
dc.contributor.committeeMember	Kennedy, Graeme
dc.contributor.committeeMember	Lounici, Karim
dc.contributor.committeeMember	Hahn, Andrew
dc.contributor.department	Aerospace Engineering
dc.date.accessioned	2015-06-08T18:21:01Z
dc.date.available	2015-06-08T18:21:01Z
dc.date.created	2015-05
dc.date.issued	2015-02-06
dc.date.submitted	May 2015
dc.date.updated	2015-06-08T18:21:01Z
dc.description.abstract	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.
dc.description.degree	Ph.D.
dc.format.mimetype	application/pdf
dc.identifier.uri	http://hdl.handle.net/1853/53504
dc.language.iso	en_US
dc.publisher	Georgia Institute of Technology
dc.subject	Dimensionality reduction
dc.subject	Gradient
dc.subject	Aerodynamic shape optimization
dc.subject	Computational fluid dynamics
dc.subject	Principal component analysis
dc.subject	Principal orthogonal decomposition
dc.subject	Over-wing nacelle
dc.subject	Propulsion-airframe integration
dc.subject	Adjoint methods
dc.title	A method for reducing dimensionality in large design problems with computationally expensive analyses
dc.type	Text
dc.type.genre	Dissertation
dspace.entity.type	Publication
local.contributor.advisor	Mavris, Dimitri N.
local.contributor.corporatename	Daniel Guggenheim School of Aerospace Engineering
local.contributor.corporatename	Aerospace Systems Design Laboratory (ASDL)
local.contributor.corporatename	College of Engineering
local.relation.ispartofseries	Doctor of Philosophy with a Major in Aerospace Engineering
relation.isAdvisorOfPublication	d355c865-c3df-4bfe-8328-24541ea04f62
relation.isOrgUnitOfPublication	a348b767-ea7e-4789-af1f-1f1d5925fb65
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thesis.degree.level	Doctoral