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Adaptive Bayesian quadrature based statistical moments estimation for structural reliability analysis

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  • Zhou, Tong
  • Peng, Yongbo

Abstract

An efficient method for structural reliability analysis is presented, which combines the statistical moments estimation and a versatile probability distribution model, i.e., the shifted generalized lognormal distribution (SGLD) model. In this method, a complete adaptive Bayesian quadrature (ABQ)-based procedure is developed to evaluate the first-four central moments of the equivalent extreme value (EEV) of structural responses, where an adaptive sampling scheme is formulated to iteratively add new integration points so as to satisfy the prescribed accuracy requirement with as fewer deterministic response analyses as possible. The probability density function (PDF) of the EEV is then recovered by fitting the SGLD model using the estimated statistical moments. Finally, the structural reliability is obtained by a simple one-dimensional integral of the PDF of the EEV over the safe domain. To demonstrate the efficacy of the proposed methodology, two numerical examples are carried out, involving the statistical moments estimation of analytical functions with different mathematical characteristics and the dynamic reliability assessment of nonlinear stochastic structures subjected to seismic excitations. It is revealed that the proposed method is capable of attaining fairly desired reliability measures on engineering structures with satisfactory accuracy and efficiency.

Suggested Citation

  • Zhou, Tong & Peng, Yongbo, 2020. "Adaptive Bayesian quadrature based statistical moments estimation for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    • Handle: RePEc:eee:reensy:v:198:y:2020:i:c:s0951832019307306
    DOI: 10.1016/j.ress.2020.106902
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    References listed on IDEAS

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    1. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
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    Cited by:

    1. Zhou, Tong & Peng, Yongbo, 2022. "Ensemble of metamodels-assisted probability density evolution method for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    2. Dang, Chao & Wei, Pengfei & Faes, Matthias G.R. & Valdebenito, Marcos A. & Beer, Michael, 2022. "Parallel adaptive Bayesian quadrature for rare event estimation," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    3. Peng, Yongbo & Ma, Yangying & Huang, Tianchen & De Domenico, Dario, 2021. "Reliability-based design optimization of adaptive sliding base isolation system for improving seismic performance of structures," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    4. Zhou, Tong & Peng, Yongbo, 2022. "Reliability analysis using adaptive Polynomial-Chaos Kriging and probability density evolution method," Reliability Engineering and System Safety, Elsevier, vol. 220(C).

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