IDEAS home Printed from https://ideas.repec.org/a/sae/risrel/v233y2019i6p943-957.html
   My bibliography  Save this article

Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods

Author

Listed:
  • Pengfei Wei
  • Chenghu Tang
  • Yuting Yang

Abstract

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

Suggested Citation

  • Pengfei Wei & Chenghu Tang & Yuting Yang, 2019. "Structural reliability and reliability sensitivity analysis of extremely rare failure events by combining sampling and surrogate model methods," Journal of Risk and Reliability, , vol. 233(6), pages 943-957, December.
    • Handle: RePEc:sae:risrel:v:233:y:2019:i:6:p:943-957
    DOI: 10.1177/1748006X19844666
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/1748006X19844666
    Download Restriction: no
    File URL: https://libkey.io/10.1177/1748006X19844666?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Cadini, F. & Santos, F. & Zio, E., 2014. "An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability," Reliability Engineering and System Safety, Elsevier, vol. 131(C), pages 109-117.
    2. Wei, Pengfei & Lu, Zhenzhou & Song, Jingwen, 2015. "Variable importance analysis: A comprehensive review," Reliability Engineering and System Safety, Elsevier, vol. 142(C), pages 399-432.
    3. Echard, B. & Gayton, N. & Lemaire, M. & Relun, N., 2013. "A combined Importance Sampling and Kriging reliability method for small failure probabilities with time-demanding numerical models," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 232-240.
    4. Sobol, I.M., 1998. "On quasi-Monte Carlo integrations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 47(2), pages 103-112.
    5. Wu, Y-T. & Mohanty, Sitakanta, 2006. "Variable screening and ranking using sampling-based sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 91(6), pages 634-647.
    6. Song, Shufang & Lu, Zhenzhou & Qiao, Hongwei, 2009. "Subset simulation for structural reliability sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 658-665.
    7. Wei, Pengfei & Song, Jingwen & Lu, Zhenzhou & Yue, Zhufeng, 2016. "Time-dependent reliability sensitivity analysis of motion mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 107-120.
    8. Cheng, Kai & Lu, Zhenzhou, 2018. "Sparse polynomial chaos expansion based on D-MORPH regression," Applied Mathematics and Computation, Elsevier, vol. 323(C), pages 17-30.
    9. Borgonovo, Emanuele & Plischke, Elmar, 2016. "Sensitivity analysis: A review of recent advances," European Journal of Operational Research, Elsevier, vol. 248(3), pages 869-887.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wei, Pengfei & Liu, Fuchao & Tang, Chenghu, 2018. "Reliability and reliability-based importance analysis of structural systems using multiple response Gaussian process model," Reliability Engineering and System Safety, Elsevier, vol. 175(C), pages 183-195.
    2. Yun, Wanying & Lu, Zhenzhou & Feng, Kaixuan & Li, Luyi, 2019. "An elaborate algorithm for analyzing the Borgonovo moment-independent sensitivity by replacing the probability density function estimation with the probability estimation," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 99-108.
    3. Xiao, Sinan & Oladyshkin, Sergey & Nowak, Wolfgang, 2020. "Reliability analysis with stratified importance sampling based on adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    4. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    5. Wenxuan Wang & Hangshan Gao & Pengfei Wei & Changcong Zhou, 2017. "Extending first-passage method to reliability sensitivity analysis of motion mechanisms," Journal of Risk and Reliability, , vol. 231(5), pages 573-586, October.
    6. Ling, Chunyan & Lu, Zhenzhou & Zhu, Xianming, 2019. "Efficient methods by active learning Kriging coupled with variance reduction based sampling methods for time-dependent failure probability," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 23-35.
    7. Jiang, Chen & Qiu, Haobo & Yang, Zan & Chen, Liming & Gao, Liang & Li, Peigen, 2019. "A general failure-pursuing sampling framework for surrogate-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 183(C), pages 47-59.
    8. Keshtegar, Behrooz & Chakraborty, Subrata, 2018. "An efficient-robust structural reliability method by adaptive finite-step length based on Armijo line search," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 195-206.
    9. Xu, Jun & Kong, Fan, 2018. "A new unequal-weighted sampling method for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 172(C), pages 94-102.
    10. Zhu, Xianming & Lu, Zhenzhou & Yun, Wanying, 2020. "An efficient method for estimating failure probability of the structure with multiple implicit failure domains by combining Meta-IS with IS-AK," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    11. Derennes, Pierre & Morio, Jérôme & Simatos, Florian, 2021. "Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 721-737.
    12. Shi, Yan & Lu, Zhenzhou & He, Ruyang & Zhou, Yicheng & Chen, Siyu, 2020. "A novel learning function based on Kriging for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    13. Cao, Quoc Dung & Choe, Youngjun, 2019. "Cross-entropy based importance sampling for stochastic simulation models," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    14. Pengfei Wei & Jingwen Song & Zhenzhou Lu, 2016. "Global reliability sensitivity analysis of motion mechanisms," Journal of Risk and Reliability, , vol. 230(3), pages 265-277, June.
    15. Chabridon, Vincent & Balesdent, Mathieu & Bourinet, Jean-Marc & Morio, Jérôme & Gayton, Nicolas, 2018. "Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 178(C), pages 164-178.
    16. Zhaoyin Shi & Zhenzhou Lu & Xiaobo Zhang & Luyi Li, 2021. "A novel adaptive support vector machine method for reliability analysis," Journal of Risk and Reliability, , vol. 235(5), pages 896-908, October.
    17. Xiao, Mi & Zhang, Jinhao & Gao, Liang, 2021. "A Kriging-assisted sampling method for reliability analysis of structures with hybrid uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 210(C).
    18. Zhan, Hongyou & Xiao, Ning-Cong & Ji, Yuxiang, 2022. "An adaptive parallel learning dependent Kriging model for small failure probability problems," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    19. Xu, Jun & Wang, Ding, 2019. "Structural reliability analysis based on polynomial chaos, Voronoi cells and dimension reduction technique," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 329-340.
    20. Menz, Morgane & Gogu, Christian & Dubreuil, Sylvain & Bartoli, Nathalie & Morio, Jérôme, 2020. "Adaptive coupling of reduced basis modeling and Kriging based active learning methods for reliability analyses," Reliability Engineering and System Safety, Elsevier, vol. 196(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sae:risrel:v:233:y:2019:i:6:p:943-957. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: SAGE Publications (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.