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Research Papers: Design Automation

Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation

[+] Author and Article Information
Chwail Kim

 Agency for Defense Development, P.O. Box 18 Jinhae, Kyungnam 645-600, Koreaadder@add.re.kr

K. K. Choi1

Department of Mechanical and Industrial Engineering, College of Engineering, The University of Iowa, Iowa City, IA 52242kkchoi@engineering.uiowa.edu

1

Corresponding author.

J. Mech. Des 130(12), 121401 (Oct 07, 2008) (12 pages) doi:10.1115/1.2988476 History: Received July 24, 2007; Revised July 30, 2008; Published October 07, 2008

Since variances in the input variables of the engineering system cause subsequent variances in the product output performance, reliability-based design optimization (RBDO) is getting much attention recently. However, RBDO requires expensive computational time. Therefore, the response surface method is often used for computational efficiency in solving RBDO problems. A method to estimate the effect of the response surface error on the RBDO result is developed in this paper. The effect of the error is expressed in terms of the prediction interval, which is utilized as the error metric for the response surface used for RBDO. The prediction interval provides upper and lower bounds for the confidence level that the design engineer specified. Using the prediction interval of the response surface, the upper and lower limits of the reliability are computed. The lower limit of reliability is compared with the target reliability to obtain a conservative optimum design and thus safeguard against the inaccuracy of the response surface. On the other hand, in order to avoid obtaining a design that is too conservative, the developed method also constrains the upper limit of the reliability in the design optimization process. The proposed procedure is combined with an adaptive sampling strategy to refine the response surface. Numerical examples show the usefulness and the efficiency of the proposed method.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Error in reliability estimation due to response surface error

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Figure 2

Projection of the estimated interval. (a) interval of response and interval of reliability and (b) upper and lower limits of reliability.

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Figure 3

Normality test of the first test function

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Figure 4

Normality test of the second test function

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Figure 5

Test of confidence and prediction intervals. (a) Confidence level=95%; (b) confidence level=90%; (c) confidence level=80%; and (d) confidence level=70%.

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Figure 6

Computational flow chart of proposed formulation

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Figure 7

Contour plots of four different design formulations

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Figure 8

Contour plots of result of the formulation (d) for different sampling stages

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Figure 9

Design variables of the DFS system

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Figure 10

The optimized finite element model for the formulation (d)

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