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Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design

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Abstract

Robust design is an effective approach to design under uncertainty. Many works exist on mitigating the influence of parametric uncertainty associated with design or noise variables. However, simulation models are often computationally expensive and need to be replaced by metamodels created using limited samples. This introduces the so-called metamodeling uncertainty. Previous metamodel-based robust designs often treat a metamodel as the real model and ignore the influence of metamodeling uncertainty. In this study, we introduce a new uncertainty quantification method to evaluate the compound effect of both parametric uncertainty and metamodeling uncertainty. Then the new uncertainty quantification method is used for robust design. Simplified expressions of the response mean and variance is derived for a Kriging metamodel. Furthermore, the concept of robust design is extended for metamodel-based robust design accounting for both sources of uncertainty. To validate the benefits of our method, two mathematical examples without constraints are first illustrated. Results show that a robust design solution can be misleading without considering the metamodeling uncertainty. The proposed uncertainty quantification method for robust design is shown to be effective in mitigating the effect of metamodeling uncertainty, and the obtained solution is found to be more “robust” compared to the conventional approach. An automotive crashworthiness example, a highly expensive and non-linear problem, is used to illustrate the benefits of considering both sources of uncertainty in robust design with constraints. Results indicate that the proposed method can reduce the risk of constraint violation due to metamodel uncertainty and results in a “safer” robust solution.

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Acknowledgements

The grant support from the National Natural Science Foundation of China (Grant No. 50875164) and US National Science Foundation (CMMI-0758557) is greatly acknowledged. This collaborative work is also made possible by the Chang Jiang Scholar Funds provided to Professor Wei Chen by China Education Ministry through Shanghai Jiaotong University.

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Authors and Affiliations

  1. The State Key Laboratory of Mechanical System and Vibration, Shanghai Key Laboratory of Digital Autobody Engineering, Shanghai Jiao Tong University, Shanghai, People’s Republic of China

    Siliang Zhang, Ping Zhu & Wei Chen

  2. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan RD Tech B224, Evanston, IL, 60201, USA

    Wei Chen & Paul Arendt

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  1. Siliang Zhang
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  2. Ping Zhu
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  3. Wei Chen
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  4. Paul Arendt
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Correspondence to Ping Zhu.

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Zhang, S., Zhu, P., Chen, W. et al. Concurrent treatment of parametric uncertainty and metamodeling uncertainty in robust design. Struct Multidisc Optim 47, 63–76 (2013). https://doi.org/10.1007/s00158-012-0805-5

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  • DOI: https://doi.org/10.1007/s00158-012-0805-5

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