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Ph.D. Thesis Proposal
by
Andrea Garbo
(Advisor: Dr. Brian J. German)
10 AM, Thursday, November 9, 2017
Montgomery Knight building
Room 317
A Sequential Adaptive Sampling Technique Based on a Local Linear Model for Computer Experiment Applications
ABSTACT:
Surrogate models (SM) are now regarded as powerful tools for engineering applications to approximate an expensive response—obtained either from a computer simulation or a real experiment—with less computationally expensive mathematical models. The use of SMs is crucial during the preliminary design phase when engineers need fast and accurate tools to assess the performance of different configurations and to define the top-level specifications that will guide the entire design process.
Due to the increasing importance of SMs, strategies have been devised to build more flexible SM formulations, to rigorously select a SM technique among a set of candidates, and to efficiently sample the design space to collect the data required to train a SM. Many studies have shown how the quality of the sample distribution across the design space is crucial for SM accuracy. The importance of the sample distribution has led to the development of techniques that sequentially sample the design space and adapt the subsequent sampling locations based on response information that successively becomes available. The use of these sequential adaptive sampling techniques has been empirically shown to reduce the number of samples required to obtain an SM of specified accuracy; however, the techniques are typically complex to implement, limited by assumptions about the response, and impracticable for engineering design applications.
This dissertation proposes a new sequential adaptive sampling strategy that is simple, robust, easy to apply, and suitable for engineering design applications. The simplicity and robustness of the formulation is achieved by defining a sampling procedure based on two different sampling metrics: a distance-based metric to enforce exploration and a Non Linearity Index (NLI) to identify design space regions that require sample refinement. In the dissertation research, this NLI approach will be extended to include directionality in the sampling process by considering the information obtained by a principal direction analysis. A comprehensive set of tests on various example functions – from low to high complexity and from low to high dimensionality – will be conducted to exhaustively compare the performance of the proposed technique with that of other state-of-the-art sampling strategies.
Committee:
Dr. Brian J. German, School of Aerospace Engineering, Georgia Institute of Technology
Dr. Graeme J. Kennedy, School of Aerospace Engineering, Georgia Institute of Technology
Dr. E. Glenn Lightsey, School of Aerospace Engineering, Georgia Institute of Technology
Dr Dimitri N. Mavris, School of Aerospace Engineering, Georgia Institute of Technology
Dr. Daniel W. Apley, School of Engineering and Applied Science, Northwestern University
