A credibilistic failure indicator for modeling structural reliability design optimization

  • Hao Zhai
  • Jianguo ZhangEmail author


Structural reliability design optimization under epistemic uncertainty has attracted the attention of many researchers, which plays a pivotal role both in theory and engineering application. However, many traditional fuzzy reliability indicators are formulated by fuzzy measure without self-duality. For this reason, we reconsider structural system with fuzzy parameters, and a new credibilistic failure indicator (CFI) is presented based on self-dual credibility measure, which provides the exact expression of structural failure degree under fuzzy environment. Then, for the structure with fuzzy trapezoidal parameters, the explicit expressions of the CFI formulations are presented under fuzzy linear limit-state function and nonlinear limit-state function. Furthermore, CFI-based design optimization is formulated to obtain the optimal structural design under the given reliability level. Meanwhile, one theorem on the reliability constraint is provided to facilitate us to obtain the equivalent deterministic constraint of the reliability constraint. Finally, two illustrative examples are performed to demonstrate the efficiency of the proposed CFI formulation and the corresponding computational methods.


Structural reliability Credibilistic failure indicator Limit-state function Trapezoidal distribution 



This research was supported by the National Natural Science Foundation of China (No. 51675026).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this article.

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.


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

Authors and Affiliations

  1. 1.Science and Technology on Reliability and Environmental Engineering Laboratory, School of Reliability and Systems EngineeringBeihang UniversityBeijingChina

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