KSCE Journal of Civil Engineering

, Volume 23, Issue 9, pp 3978–3992 | Cite as

Non-probabilistic Integrated Reliability Analysis of Structures with Fuzzy Interval Uncertainties using the Adaptive GPR-RS Method

  • Minghui Liu
  • Xiaoling WangEmail author
  • Xiaobin Zhu
  • Wenlong Chen
  • Xiao Li
Hydraulic Engineering


Due to its weak dependence on the quantity of variable samples, the non-probabilistic reliability analysis method based on the convex set model is applicable to practical problems in structural engineering with inherent uncertainties. However, when dealing with the black-box limit-state function issues in practical complex structural engineering, the traditional quadratic polynomial response surface (QP-RS) method has the problem of insufficient precision in approximating a highly nonlinear function. Meanwhile, fixing the limits of interval variables is trickier in case of scant samples and meager statistical information. To remedy the above deficiencies, this paper introduces a reasonable integrated reliability analysis approach. First, an adaptive Gaussian process regression response surface (GPR-RS) method that dynamically improves the fitted accuracy near the design point of the black-box limit-state function is formulated. Furthermore, the integrated reliability index with consideration of fuzzy interval uncertainties is presented. Three validation and two application examples are employed, which have justified the approach as a more reasonable assessor of practical complex structural reliability with safer results.


structural integrated reliability interval variable non-probabilistic reliability fuzzy set theory adaptive Gaussian process regression response surface method 


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This work is supported by the National Key R&D Program of China (grant number 2018YFC0407101); the Joint Funds of the National Natural Science Foundation of China (grant number U1765205); and the Natural Science Foundation of China (grant number 51439005).


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© Korean Society of Civil Engineers 2019

Authors and Affiliations

  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and SafetyTianjin UniversityTianjinChina

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