Uncertainty is inevitable in engineering design. The existence of uncertainty may change the optimality and/or the feasibility of the obtained optimal solutions. In simulation-based engineering design, uncertainty could have various types of sources, such as parameter uncertainty, model uncertainty, and other random errors. To deal with uncertainty, robust optimization (RO) algorithms are developed to find solutions which are not only optimal but also robust with respect to uncertainty. Parameter uncertainty has been taken care of by various RO approaches. While model uncertainty has been ignored in majority of existing RO algorithms with the hypothesis that the simulation model used could represent the real physical system perfectly. In the authors’ earlier work, a RO framework was proposed to consider both parameter and model uncertainties using the Bayesian approach with Gaussian processes (GP), where metamodeling uncertainty introduced by GP modeling is ignored by assuming the constructed GP model is accurate enough with sufficient training samples. However, infinite samples are impossible for real applications due to prohibitive time and/or computational cost. In this work, a new RO framework is proposed to deal with both parameter and model uncertainties using GP models but only with limited samples. The compound effect of parameter, model, and metamodeling uncertainties is derived with the form of the compound mean and variance to formulate the proposed RO approach. The proposed RO approach will reduce the risk for the obtained robust optimal designs considering parameter and model uncertainties becoming non-optimal and/or infeasible due to insufficiency of samples for GP modeling. Two test examples with different degrees of complexity are utilized to demonstrate the applicability and effectiveness of the proposed approach.
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ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 6–9, 2017
Cleveland, Ohio, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5813-4
PROCEEDINGS PAPER
Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes With Limited Samples
Yanjun Zhang,
Yanjun Zhang
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China
Search for other works by this author on:
Mian Li
Mian Li
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China
Search for other works by this author on:
Yanjun Zhang
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China
Mian Li
University of Michigan-Shanghai Jiao Tong University Joint Institute, Shanghai, China
Paper No:
DETC2017-67291, V02BT03A048; 13 pages
Published Online:
November 3, 2017
Citation
Zhang, Y, & Li, M. "Robust Optimization With Parameter and Model Uncertainties Using Gaussian Processes With Limited Samples." Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2B: 43rd Design Automation Conference. Cleveland, Ohio, USA. August 6–9, 2017. V02BT03A048. ASME. https://doi.org/10.1115/DETC2017-67291
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