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Research Papers

Metamodeling for High Dimensional Simulation-Based Design Problems

[+] Author and Article Information
Songqing Shan

Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, MB, R3T 5V6, Canadashans@cc.umanitoba.ca

G. Gary Wang1

School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canadagary_wang@sfu.ca

1

Corresponding author.

J. Mech. Des 132(5), 051009 (May 17, 2010) (11 pages) doi:10.1115/1.4001597 History: Received June 01, 2009; Revised April 07, 2010; Published May 17, 2010; Online May 17, 2010

Computational tools such as finite element analysis and simulation are widely used in engineering, but they are mostly used for design analysis and validation. If these tools can be integrated for design optimization, it will undoubtedly enhance a manufacturer’s competitiveness. Such integration, however, faces three main challenges: (1) high computational expense of simulation, (2) the simulation process being a black-box function, and (3) design problems being high dimensional. In the past two decades, metamodeling has been intensively developed to deal with expensive black-box functions, and has achieved success for low dimensional design problems. But when high dimensionality is also present in design, which is often found in practice, there lacks of a practical method to deal with the so-called high dimensional, expensive, and black-box (HEB) problems. This paper proposes the first metamodel of its kind to tackle the HEB problem. This paper integrates the radial basis function with high dimensional model representation into a new model, RBF-HDMR. The developed RBF-HDMR model offers an explicit function expression, and can reveal (1) the contribution of each design variable, (2) inherent linearity/nonlinearity with respect to input variables, and (3) correlation relationships among input variables. An accompanying algorithm to construct the RBF-HDMR has also been developed. The model and the algorithm fundamentally change the exponentially growing computation cost to be polynomial. Testing and comparison confirm the efficiency and capability of RBF-HDMR for HEB problems.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Distribution of sample points for the example problem

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Figure 2

Performance metrics mean with respect to d (x-axis) for the study problem

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Figure 3

Comparison of NoE with Latin Hypercube points from Ref. 5

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Figure 4

Model accuracy comparison. Data for models other than RBF-HDMR are from Ref. 5. R2 values are for large-scale problems only, while RMAE and RAAE values are for all 14 test problems.

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