上海交通大学学报（英文版） ›› 2013, Vol. 18 ›› Issue (3): 257-263.doi: 10.1007/s12204-013-1391-4

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Robust Expected Violation Criterion for Constrained Robust Design Problems and Its Application in Automotive Lightweight Design

ZHANG Si-liang1 (章斯亮), ZHU Ping1* (朱 平), CHEN Wei1,2 (陈 卫)   

  1. (1. Shanghai Key Laboratory of Digital Autobody Engineering, Shanghai Jiaotong University, Shanghai 200240, China; 2. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60201, USA)
  • 出版日期:2013-06-28 发布日期:2013-08-12
  • 通讯作者: ZHU Ping (朱 平) E-mail:pzhu@sjtu.edu.cn

Robust Expected Violation Criterion for Constrained Robust Design Problems and Its Application in Automotive Lightweight Design

ZHANG Si-liang1 (章斯亮), ZHU Ping1* (朱 平), CHEN Wei1,2 (陈 卫)   

  1. (1. Shanghai Key Laboratory of Digital Autobody Engineering, Shanghai Jiaotong University, Shanghai 200240, China; 2. Department of Mechanical Engineering, Northwestern University, Evanston, IL 60201, USA)
  • Online:2013-06-28 Published:2013-08-12
  • Contact: ZHU Ping (朱 平) E-mail:pzhu@sjtu.edu.cn

摘要： Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.

关键词: robust design, robust expected violation (REV), sequential sampling method, automotive lightweight design

Abstract: Metamodeling techniques are commonly used to replace expensive computer simulations in robust design problems. Due to the discrepancy between the simulation model and metamodel, a robust solution in the infeasible region can be found according to the prediction error in constraint responses. In deterministic optimizations, balancing the predicted constraint and metamodeling uncertainty, expected violation (EV) criterion can be used to explore the design space and add samples to adaptively improve the fitting accuracy of the constraint boundary. However in robust design problems, the predicted error of a robust design constraint cannot be represented by the metamodel prediction uncertainty directly. The conventional EV-based sequential sampling method cannot be used in robust design problems. In this paper, by investigating the effect of metamodeling uncertainty on the robust design responses, an extended robust expected violation (REV) function is proposed to improve the prediction accuracy of the robust design constraints. To validate the benefits of the proposed method, a crashworthiness-based lightweight design example, i.e. a highly nonlinear constrained robust design problem, is given. Results show that the proposed method can mitigate the prediction error in robust constraints and ensure the feasibility of the robust solution.

Key words: robust design, robust expected violation (REV), sequential sampling method, automotive lightweight design

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