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Efficient imprecise reliability analysis using the Augmented Space Integral

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  • Yuan, Xiukai
  • Faes, Matthias G.R.
  • Liu, Shaolong
  • Valdebenito, Marcos A.
  • Beer, Michael

Abstract

This paper presents an efficient approach to compute the bounds on the reliability of a structure subjected to uncertain parameters described by means of imprecise probabilities. These imprecise probabilities arise from epistemic uncertainty in the definition of the hyper-parameters of a set of random variables that describe aleatory uncertainty in some of the structure’s properties. Typically, such calculation involves the solution of a so-called double-loop problem, where a crisp reliability problem is repeatedly solved to determine which realization of the epistemic uncertainties yields the worst or best case with respect to structural safety. The approach in this paper aims at decoupling this double loop by virtue of the Augmented Space Integral. The core idea of the method is to infer a functional relationship between the epistemically uncertain hyper-parameters and the probability of failure. Then, this functional relationship can be used to determine the best and worst case behavior with respect to the probability of failure. Three case studies are included to illustrate the effectiveness and efficiency of the developed methods.

Suggested Citation

  • Yuan, Xiukai & Faes, Matthias G.R. & Liu, Shaolong & Valdebenito, Marcos A. & Beer, Michael, 2021. "Efficient imprecise reliability analysis using the Augmented Space Integral," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:reensy:v:210:y:2021:i:c:s0951832021000454
    DOI: 10.1016/j.ress.2021.107477
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    References listed on IDEAS

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    1. Schöbi, Roland & Sudret, Bruno, 2019. "Global sensitivity analysis in the context of imprecise probabilities (p-boxes) using sparse polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 187(C), pages 129-141.
    2. Mullins, Joshua & Ling, You & Mahadevan, Sankaran & Sun, Lin & Strachan, Alejandro, 2016. "Separation of aleatory and epistemic uncertainty in probabilistic model validation," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 49-59.
    3. Utkin, Lev V. & Coolen, Frank P.A., 2018. "A robust weighted SVR-based software reliability growth model," Reliability Engineering and System Safety, Elsevier, vol. 176(C), pages 93-101.
    4. Simon, Christophe & Bicking, Frédérique, 2017. "Hybrid computation of uncertainty in reliability analysis with p-box and evidential networks," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 629-638.
    5. Mancuso, A. & Compare, M. & Salo, A. & Zio, E. & Laakso, T., 2016. "Risk-based optimization of pipe inspections in large underground networks with imprecise information," Reliability Engineering and System Safety, Elsevier, vol. 152(C), pages 228-238.
    6. Yin, Yi-Chao & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2017. "An imprecise statistical method for accelerated life testing using the power-Weibull model," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 158-167.
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    Cited by:

    1. Wang, Zihan & Daeipour, Mohamad & Xu, Hongyi, 2023. "Quantification and propagation of Aleatoric uncertainties in topological structures," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    2. Salomon, Julian & Winnewisser, Niklas & Wei, Pengfei & Broggi, Matteo & Beer, Michael, 2021. "Efficient reliability analysis of complex systems in consideration of imprecision," Reliability Engineering and System Safety, Elsevier, vol. 216(C).

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