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Research Papers: Design Automation

An Adaptive Bayesian Sequential Sampling Approach for Global Metamodeling

[+] Author and Article Information
Haitao Liu

School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: lht@mail.dlut.edu.cn

Shengli Xu

School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: xusl@dlut.edu.cn

Ying Ma

School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: maying@mail.dlut.edu.cn

Xudong Chen

School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: xdchen@mail.dlut.edu.cn

Xiaofang Wang

School of Energy and Power Engineering,
Dalian University of Technology,
Dalian 116024, China
e-mail: dlwxf@dlut.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 26, 2015; final manuscript received October 16, 2015; published online November 16, 2015. Assoc. Editor: Gary Wang.

J. Mech. Des 138(1), 011404 (Nov 16, 2015) (12 pages) Paper No: MD-15-1042; doi: 10.1115/1.4031905 History: Received January 26, 2015; Revised October 16, 2015

Computer simulations have been increasingly used to study physical problems in various fields. To relieve computational budgets, the cheap-to-run metamodels, constructed from finite experiment points in the design space using the design of computer experiments (DOE), are employed to replace the costly simulation models. A key issue related to DOE is designing sequential computer experiments to achieve an accurate metamodel with as few points as possible. This article investigates the performance of current Bayesian sampling approaches and proposes an adaptive maximum entropy (AME) approach. In the proposed approach, the leave-one-out (LOO) cross-validation error estimates the error information in an easy way, the local space-filling exploration strategy avoids the clustering problem, and the search pattern from global to local improves the sampling efficiency. A comparison study of six examples with different types of initial points demonstrated that the AME approach is very promising for global metamodeling.

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Figures

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Fig. 1

The plot of parameter η for different values of γ

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Fig. 3

The boxplots of NFE values of different sampling approaches for the one-dimensional case

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Fig. 4

The convergence histories of different sampling approaches for the one-dimensional case

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Fig. 2

The one-dimensional function and a Kriging model through five evenly distributed initial points

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Fig. 5

The point distributions of different sampling approaches for the one-dimensional case

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Fig. 6

A Kriging model and its local optima in one iteration of SAI

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Fig. 13

The convergence histories of different sampling approaches with (a) S-40, (b) S-60, (c) SP-40, and (d) SP-60 for the borehole function

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Fig. 7

The boxplots of NFE values of different sampling approaches with different types of initial points for Peak

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Fig. 8

The convergence histories of different sampling approaches with (a) S-5, (b) S-10, (c) S-20, (d) SP-5, (e) SP-10, and (f) SP-20 for Peak

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Fig. 11

The boxplots of NFE values of different sampling approaches with different types of initial points for Hart3

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Fig. 12

The convergence histories of different sampling approaches with (a) S-10, (b) S-20, (c) S-30, (d) SP-10, (e) SP-20, and (f) SP-30 for Hart3

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Fig. 14

The convergence histories of different sampling approaches with (a) S-80, (b) S-160, (c) SP-80, and (d) SP-160 for the robot arm function

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Fig. 9

The boxplots of NFE values of different sampling approaches with different types of initial points for SC

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Fig. 10

The convergence histories of different sampling approaches with (a) S-5, (b) S-10, (c) S-20, (d) SP-5, (e) SP-10, and (f) SP-20 for SC

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