Research Papers

Conservative Surrogate Model Using Weighted Kriging Variance for Sampling-Based RBDO

[+] Author and Article Information
Liang Zhao

1310 Rankin Road,
Houston, TX 77073
e-mail: lzhao01@slb.com

K. K. Choi

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

Ikjin Lee

Department of Mechanical Engineering,
University of Connecticut,
Storrs, CT 06269
e-mail: ilee@engr.uconn.edu

David Gorsich

Warren, MI 48397-5000
e-mail: gorsichd@tacom.army.mil

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received July 12, 2012; final manuscript received February 12, 2013; published online July 2, 2013. Assoc. Editor: Irem Y. Tumer.

J. Mech. Des 135(9), 091003 (Jul 02, 2013) (10 pages) Paper No: MD-12-1356; doi: 10.1115/1.4024731 History: Received July 12, 2012; Revised February 12, 2013

In sampling-based reliability-based design optimization (RBDO) of large-scale engineering applications, the Monte Carlo simulation (MCS) is often used for the probability of failure calculation and probabilistic sensitivity analysis using the prediction from the surrogate model for the performance function evaluations. When the number of samples used to construct the surrogate model is not enough, the prediction from the surrogate model becomes inaccurate and thus the Monte Carlo simulation results as well. Therefore, to count in the prediction error from the surrogate model and assure the obtained optimum design from sampling-based RBDO satisfies the probabilistic constraints, a conservative surrogate model, which is not overly conservative, needs to be developed. In this paper, a conservative surrogate model is constructed using the weighted Kriging variance where the weight is determined by the relative change in the corrected Akaike Information Criterion (AICc) of the dynamic Kriging model. The proposed conservative surrogate model performs better than the traditional Kriging prediction interval approach because it reduces fluctuation in the Kriging prediction bound and it performs better than the constant safety margin approach because it adaptively accounts large uncertainty of the surrogate model in the region where samples are sparse. Numerical examples show that using the proposed conservative surrogate model for sampling-based RBDO is necessary to have confidence that the optimum design satisfies the probabilistic constraints when the number of samples is limited, while it does not lead to overly conservative designs like the constant safety margin approach.

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Grahic Jump Location
Fig. 2

Leave-one-out Kriging prediction and importance values. (a) Kriging prediction without sample #2, (b) Kriging prediction without sample #3, (c) Kriging prediction without sample #4, (d) Kriging prediction without sample #5, and (e) Kriging prediction without sample #6.

Grahic Jump Location
Fig. 3

Conservative surrogate model using weighted Kriging variance

Grahic Jump Location
Fig. 4

Cost and constraint functions plot

Grahic Jump Location
Fig. 1

One-dimensional problem. (a) 7 samples and (b) 6 samples.

Grahic Jump Location
Fig. 6

Cantilever tube design

Grahic Jump Location
Fig. 5

Different conservative surrogate models and optimum designs



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