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Research Papers: Design Automation

Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes

[+] Author and Article Information
Yanjun Zhang

University of Michigan—Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China

Mian Li

University of Michigan—Shanghai Jiao Tong
University Joint Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: mianli@sjtu.edu.cn

Jun Zhang, Guoshu Li

Science and Technology on Space Physics
Laboratory,
Beijing 100076, China

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received February 27, 2016; final manuscript received July 10, 2016; published online September 12, 2016. Assoc. Editor: Sankaran Mahadevan.

J. Mech. Des 138(11), 111405 (Sep 12, 2016) (11 pages) Paper No: MD-16-1156; doi: 10.1115/1.4034222 History: Received February 27, 2016; Revised July 10, 2016

Uncertainty is unavoidable in engineering design, which may result in variations in the objective functions and/or constraints. The former may degrade the designed performance while the latter can even change the feasibility of the obtained optimal solutions. Taking uncertainty into consideration, robust optimization (RO) algorithms aim to find optimal solutions that are also insensitive to uncertainty. Uncertainty may include variation in parameters and/or design variables, inaccuracy in simulation models used in design problems, and other possible errors. Most existing RO algorithms only consider uncertainty in parameters, but overlook that in simulation models by assuming that the simulation model used can always provide identical outputs to those of the real physical systems. In this paper, we propose a new RO framework using Gaussian processes, considering not only parameter uncertainty but also uncertainty in simulation models. The consideration of model uncertainty in RO could reduce the risk for the obtained robust optimal designs becoming infeasible even if the parameter uncertainty has been considered. Two test examples with different degrees of complexity are utilized to demonstrate the applicability and effectiveness of our proposed algorithm.

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Figures

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Fig. 1

Flow chart of the proposed RO approach

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Fig. 2

A three-bar truss (Courtesy of [42])

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Fig. 3

Accuracy check of three GP models: (a) check error of GP model for ym(•), (b). check error of GP model for δ(•), and (c) check error of GP model for g2(•).

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Fig. 4

Comparison of objective robustness: (a) objective variation for deterministic solution, (b) objective variation for robust solution with respect to parameter uncertainty, and (c) objective variation for robust solution with respect to parameter and model uncertainties

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Fig. 5

Comparison of feasibility robustness: (a) variation of g7 for deterministic solution, (b) variation of g7 for robust solution with respect to parameter uncertainty, and (c) variation of g7 for robust solution with respect to parameter and model uncertainties

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Fig. 6

Comparison of feasibility robustness: (a). variation of g7 and g9 for deterministic solution, (b) variation of 7 and g9 for robust solution with respect to parameter uncertainty, and (c). variation of g7 and g9 for robust solution with respect to parameter and model uncertainties.

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