Novel decoupling method for time-dependent reliability-based design optimization

  • Yan Shi
  • Zhenzhou LuEmail author
  • Liyang Xu
  • Yicheng Zhou
Research Paper


Time-dependent reliability-based design optimization (RBDO) can provide the optimal design parameter solutions for the time-dependent structure, and thus plays a significant role in engineering application. Directly solving the time-dependent RBDO needs a nested double-loop optimization procedure, which undoubtedly leads to large computational costs. A novel decoupling method called two-step method (TSM) is proposed to efficiently solve the time-dependent RBDO. In the two-step method, the first step makes the minimum instantaneous reliability index satisfy the reliability target index by solving a transformed time-independent RBDO, and the second step performs time-dependent reliability analysis and deterministic optimization to obtain the optimal design parameters which meet the reliability target. Only a few time-dependent reliability analyses and several deterministic optimizations are involved in the proposed procedure; thus, the time-dependent RBDO can be efficiently solved. Several examples containing one numerical example and two engineering examples are introduced to show the effectiveness of the proposed TSM.


Time-dependent RBDO Decoupling method Minimum instantaneous reliability Time-dependent reliability Shifting vector increment 



This work was supported by the National Natural Science Foundation of China (Grant 51475370), the National Science and Technology Major Project (2017-IV-0009-0046) and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant CX201931). The authors would like to thank the reviewers’ for the constructive and helpful suggestions and comments on our paper.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anPeople’s Republic of China
  2. 2.Department of Civil EngineeringUniversity of BristolBristolUK

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