Research Papers

An Adaptive Response Surface Method Using Bayesian Metric and Model Bias Correction Function

[+] Author and Article Information
Lei Shi

State Key Laboratory of Mechanical
System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: lshi1340@gmail.com

Ren-Jye Yang

Research and Advanced Engineering,
Ford Motor Company,
2101 Village Rd,
Dearborn, MI 48121
e-mail: ryang@ford.com

Ping Zhu

State Key Laboratory of
Mechanical System and Vibration,
School of Mechanical Engineering,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: pzhu@sjtu.edu.cn

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received January 31, 2013; final manuscript received November 12, 2013; published online January 10, 2014. Assoc. Editor: Wei Chen.

J. Mech. Des 136(3), 031005 (Jan 10, 2014) (8 pages) Paper No: MD-13-1043; doi: 10.1115/1.4026095 History: Received January 31, 2013; Revised November 12, 2013

The Bayesian metric was used to select the best available response surface in the literature. One of the major drawbacks of this method is the lack of a rigorous method to quantify data uncertainty, which is required as an input. In addition, the accuracy of any response surface is inherently unpredictable. This paper employs the Gaussian process based model bias correction method to quantify the data uncertainty and subsequently improve the accuracy of a response surface model. An adaptive response surface updating algorithm is then proposed for a large-scale problem to select the best response surface. The proposed methodology is demonstrated by a mathematical example and then applied to a vehicle design problem.

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Fig. 1

Response surfaces with and without model bias correction updating

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Fig. 2

Algorithm of response surface updating methodology

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Fig. 5

Design variable selection for main front-end structure

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Fig. 3

Comparison of structure deformation between finite element simulation and test: (a) Full frontal impact and (b) 40% offset impact

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Fig. 4

Acceleration history comparison of rocker at B-pillar: (a) Full frontal impact, and (b) 40% offset impact (Note: the physical test data for full frontal impact and 40% offset impact can be referred to the link.3




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