Structural and Multidisciplinary Optimization

, Volume 59, Issue 5, pp 1835–1851 | Cite as

Multi-objective reliability-based design optimization for the VRB-VCS FLB under front-impact collision

  • Libin DuanEmail author
  • Haobin Jiang
  • Aiguo Cheng
  • Hongtao Xue
  • Guoqing Geng
Industrial Application


The front longitudinal beam (FLB) is the most important energy-absorbing and crashing-force-transmitting structure of a vehicle in a front crash. Its structure directly determines the safety performance of a car in front collisions and the effectiveness of passenger protection. In this study, a new structure, variable-rolled-blank and variable-cross-sectional-shape FLB (VRB-VCS FLB), is developed. It possesses both the continuous variation of thickness and variable cross-section shape in space. To make the VRB-VCS FLB structure more lightweight and crashworthy under reliability constraints, multi-objective reliability-based design optimization (RBDO) is performed in this paper. The multimodal radial-based importance sampling (MRBIS) method is integrated into the multi-objective RBDO to solve the system reliability for multiply-constrained problems, while the non-dominated sorting genetic algorithm II (NSGA-II) is used for solving deterministic optimization. The numerical results show that the crashworthiness performance and reliability of the VRB-VCS FLB is significantly improved when compared with uniform-thickness FLB.


Multi-objective reliability-based design optimization Front longitudinal beam (FLB) Variable-rolled-blank (VRB) Variable-cross-sectional shape (VCS) 







Front longitudinal beam


FLB inner plate


FLB outer plate


Variable-rolled-blank FLB


Variable-cross-sectional-shape FLB


Variable-rolled-blank-variable-cross-sectional-shape FLB


VRB-VCS FLB inner plate


Constant thickness zone


Thickness transition zone


Multi-objective optimization


Reliability-based design optimization


Multi-modal radial-based importance sampling


Non-dominated sorting genetic algorithm-II


Optimal Latin hypercube sampling


epsilon-support vector regression


Funding information

The authors would like to thank the support of National Natural Science Foundation of China (Grant No. 51805221, 61232014) and Research Project funded by China Postdoctoral Science Foundation (No. 2018M640460). The authors also wish to thank Jiangsu Planned Projects for Postdoctoral Research Fund (NO. 2018K018C). This work was supported by the high-performance computing platform of Jiangsu University.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Automotive and Traffic EngineeringJiangsu UniversityZhenjiangChina
  2. 2.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina

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