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An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations

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  • Guan, Xuefei
  • He, Jingjing
  • Jha, Ratneshwar
  • Liu, Yongming

Abstract

This paper presents an efficient analytical Bayesian method for reliability and system response updating without using simulations. The method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse first-order reliability method is developed to evaluate system responses given a reliability index or confidence interval. Since the proposed method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for methodology demonstration. The accuracy and computational efficiency of the proposed method are compared with traditional simulation-based methods.

Suggested Citation

  • Guan, Xuefei & He, Jingjing & Jha, Ratneshwar & Liu, Yongming, 2012. "An efficient analytical Bayesian method for reliability and system response updating based on Laplace and inverse first-order reliability computations," Reliability Engineering and System Safety, Elsevier, vol. 97(1), pages 1-13.
    • Handle: RePEc:eee:reensy:v:97:y:2012:i:1:p:1-13
    DOI: 10.1016/j.ress.2011.09.008
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    1. Graves, T.L. & Hamada, M.S. & Klamann, R.M. & Koehler, A.C. & Martz, H.F., 2008. "Using simultaneous higher-level and partial lower-level data in reliability assessments," Reliability Engineering and System Safety, Elsevier, vol. 93(8), pages 1273-1279.
    2. Wang, X. & Rabiei, M. & Hurtado, J. & Modarres, M. & Hoffman, P., 2009. "A probabilistic-based airframe integrity management model," Reliability Engineering and System Safety, Elsevier, vol. 94(5), pages 932-941.
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    Cited by:

    1. Liu, Jie & Hu, Yifeng & Xu, Can & Jiang, Chao & Han, Xu, 2016. "Probability assessments of identified parameters for stochastic structures using point estimation method," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 51-58.
    2. Soliman, Ahmed A. & Abd-Ellah, Ahmed H. & Abou-Elheggag, Naser A. & Ahmed, Essam A., 2012. "Modified Weibull model: A Bayes study using MCMC approach based on progressive censoring data," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 48-57.
    3. Jerez, D.J. & Jensen, H.A. & Beer, M., 2022. "An effective implementation of reliability methods for Bayesian model updating of structural dynamic models with multiple uncertain parameters," Reliability Engineering and System Safety, Elsevier, vol. 225(C).
    4. Chen, Jie & Yu, Yang & Liu, Yongming, 2022. "Physics-guided mixture density networks for uncertainty quantification," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    5. He, Jingjing & Huang, Min & Wang, Wei & Wang, Shaohua & Guan, Xuefei, 2021. "An asymptotic stochastic response surface approach to reliability assessment under multi-source heterogeneous uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 215(C).
    6. Zhou, Daoqing & He, Jingjing & Du, Yi-Mu & Sun, C.P. & Guan, Xuefei, 2021. "Probabilistic information fusion with point, moment and interval data in reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    7. Gao, Haifeng & Wang, Anjenq & Zio, Enrico & Bai, Guangchen, 2020. "An integrated reliability approach with improved importance sampling for low-cycle fatigue damage prediction of turbine disks," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    8. Jingjing He & Wei Wang & Min Huang & Shaohua Wang & Xuefei Guan, 2021. "Bayesian Inference under Small Sample Sizes Using General Noninformative Priors," Mathematics, MDPI, vol. 9(21), pages 1-20, November.
    9. Lin, Yi-Kuei & Chang, Ping-Chen, 2012. "Evaluate the system reliability for a manufacturing network with reworking actions," Reliability Engineering and System Safety, Elsevier, vol. 106(C), pages 127-137.
    10. R. Jamshidi & Mir Seyyed Esfahani, 2014. "Human resources scheduling to improve the product quality according to exhaustion limit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 1028-1041, October.
    11. Guan, Xuefei, 2024. "Sparse moment quadrature for uncertainty modeling and quantification," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    12. Li, Pei-Pei & Zhang, Yi & Zhao, Yan-Gang & Zhao, Zhao & Cai, Enjian, 2023. "An information reuse-based method for reliability updating," Reliability Engineering and System Safety, Elsevier, vol. 239(C).

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