Ph.D. Thesis Proposal

by

Andrea Garbo

(Advisor: Dr. Brian J. German)

10 AM, Friday, February 2nd, 2018

Weber building, CoVE room

A Sequential Adaptive Sampling Technique Based on Local Linear Model for Computer Experiment Applications

ABSTACT:

The objective of this dissertation research is to develop a model independent sequential adaptive sampling technique based on local linear model called Nearest Neighbors Adaptive Sampling (NNAS). With this approach, it is possible to obtain a sampling strategy that is conceptually simple, computationally robust, and easy to apply, all characteristics that are crucial for effective surrogate modeling application during early phases of the engineering design process. Surrogate Models (SMs) 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 especially valuable 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, new strategies are continuously 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.

The considerable influence of the sample distribution on SM accuracy motivates efforts to enhance the efficiency of the sampling phase, which has led the development of advanced techniques. In particular, the adoption of sequential adaptive sampling techniques has been empirically shown to reduce the number of samples required to obtain a SM of specified accuracy. However, these techniques are typically complex to implement, limited by assumptions about the response, and dependent on the SM formulation selected to supervise the sampling process (model dependence), making them impracticable for engineering design applications; examples are Cross Validation and Kriging based strategies. Model dependence is a common characteristic of most of state-of-the-art adaptive sequential sampling techniques which has been shown to deteriorate the sampling efficiency if the guiding SM is inaccurately chosen.

The proposed NNAS technique removes the model dependence limitation by introducing a new refinement metric – the Non-Linearity Index (NLI) – which estimates the local nonlinear characteristics from the training data. NLI at every training point is computed as the difference between the actual response value and the local function approximation obtained from the hyperplane that interpolates the closest D + 1 points in the neighborhood (where D is the domain dimensionality). NLI is then combined with a distance-based exploration measure, obtaining the sampling metric which is used by the NNAS technique to supervise the sampling process. The adoption of a local linear model to discover the nonlinear characteristics of the response from the training data removes the dependency of the sampling behavior from a global SM. Additionally, the ease of implementation of NNAS enhances the robustness and speed of the overall surrogate modeling process making NNAS a valuable sampling strategy during the early phases of engineering design.

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. NNAS is expected to considerably reduce both the number of required samples and total process time, thank to its sequential adaptive formulation and the computational simplicity inherited by the local linear model approach.

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