IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v196y2020ics0951832018310858.html
   My bibliography  Save this article

On confidence intervals for failure probability estimates in Kriging-based reliability analysis

Author

Listed:
  • Wang, Zeyu
  • Shafieezadeh, Abdollah

Abstract

Despite recent advancements in adaptive Kriging-based reliability analysis for complex limit states, estimation of the accuracy of extant techniques when the true failure probability is unknown remains an important challenge. The present study addresses this gap by developing analytical confidence intervals (CIs) for failure probability estimates. This is facilitated here by leveraging statistical properties of Poisson Binomial distribution for the expected number of failure points in the set of candidate design samples in adaptive Kriging as well as Lindeberg's condition for central limit theorem. Concerning computational demands involved in the computation of CIs, a simpler case where Kriging correlations are neglected is also derived. The performance of the proposed CIs is subsequently analyzed for five examples with different and varying complexities. Results indicate that the proposed CI with correlations considered offers the most accurate intervals. Additionally, whereas the CI estimated without Kriging correlation is not entirely satisfactory at early-stages of adaptive reliability analysis, it converges to accurate bounds at later stages.

Suggested Citation

  • Wang, Zeyu & Shafieezadeh, Abdollah, 2020. "On confidence intervals for failure probability estimates in Kriging-based reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    • Handle: RePEc:eee:reensy:v:196:y:2020:i:c:s0951832018310858
    DOI: 10.1016/j.ress.2019.106758
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832018310858
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2019.106758?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sun, Zhili & Wang, Jian & Li, Rui & Tong, Cao, 2017. "LIF: A new Kriging based learning function and its application to structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 152-165.
    2. Marrel, Amandine & Iooss, Bertrand & Laurent, Béatrice & Roustant, Olivier, 2009. "Calculations of Sobol indices for the Gaussian process metamodel," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 742-751.
    3. Fauriat, W. & Gayton, N., 2014. "AK-SYS: An adaptation of the AK-MCS method for system reliability," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 137-144.
    4. Li, Junxiang & Chen, Jianqiao, 2019. "Solving time-variant reliability-based design optimization by PSO-t-IRS: A methodology incorporating a particle swarm optimization algorithm and an enhanced instantaneous response surface," Reliability Engineering and System Safety, Elsevier, vol. 191(C).
    5. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    6. Wang, Zeyu & Shafieezadeh, Abdollah, 2019. "REAK: Reliability analysis through Error rate-based Adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 33-45.
    7. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    8. Aven, Terje, 2016. "Risk assessment and risk management: Review of recent advances on their foundation," European Journal of Operational Research, Elsevier, vol. 253(1), pages 1-13.
    9. 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.
    10. Gaspar, B. & Teixeira, A.P. & Guedes Soares, C., 2017. "Adaptive surrogate model with active refinement combining Kriging and a trust region method," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 277-291.
    11. Yang, Xufeng & Liu, Yongshou & Mi, Caiying & Tang, Chenghu, 2018. "System reliability analysis through active learning Kriging model with truncated candidate region," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 235-241.
    12. Chen, Weidong & Xu, Chunlong & Shi, Yaqin & Ma, Jingxin & Lu, Shengzhuo, 2019. "A hybrid Kriging-based reliability method for small failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 31-41.
    13. Wen, Zhixun & Pei, Haiqing & Liu, Hai & Yue, Zhufeng, 2016. "A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 170-179.
    14. 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.
    15. Wang, Zeyu & Shafieezadeh, Abdollah, 2020. "Real-time high-fidelity reliability updating with equality information using adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yanbo Song & Xiaoyue Wang, 2022. "Reliability Analysis of the Multi-State k -out-of- n : F Systems with Multiple Operation Mechanisms," Mathematics, MDPI, vol. 10(23), pages 1-16, December.
    2. Zhuang, Liangliang & Xu, Ancha & Pang, Jihong, 2021. "Product reliability analysis based on heavily censored interval data with batch effects," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    3. Jakeman, John D. & Kouri, Drew P. & Huerta, J. Gabriel, 2022. "Surrogate modeling for efficiently, accurately and conservatively estimating measures of risk," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    4. Xiao, Ning-Cong & Yuan, Kai & Zhan, Hongyou, 2022. "System reliability analysis based on dependent Kriging predictions and parallel learning strategy," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    5. Jiang, Chen & Yan, Yifang & Wang, Dapeng & Qiu, Haobo & Gao, Liang, 2021. "Global and local Kriging limit state approximation for time-dependent reliability-based design optimization through wrong-classification probability," Reliability Engineering and System Safety, Elsevier, vol. 208(C).
    6. Qian, Hua-Ming & Li, Yan-Feng & Huang, Hong-Zhong, 2021. "Time-variant system reliability analysis method for a small failure probability problem," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    7. Ma, Yuan-Zhuo & Zhu, Yi-Chen & Li, Hong-Shuang & Nan, Hang & Zhao, Zhen-Zhou & Jin, Xiang-Xiang, 2022. "Adaptive Kriging-based failure probability estimation for multiple responses," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    8. Jingkui Li & Wenqi Liu & Yan Zhou & Zhandong Li, 2023. "An active learning Kriging-based method combining the weight information entropy function and the adaptive candidate sample pool," Journal of Risk and Reliability, , vol. 237(4), pages 741-751, August.
    9. Teixeira, Rui & Martinez-Pastor, Beatriz & Nogal, Maria & O’Connor, Alan, 2021. "Reliability analysis using a multi-metamodel complement-basis approach," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    10. Zhang, Chi & Shafieezadeh, Abdollah, 2022. "Simulation-free reliability analysis with active learning and Physics-Informed Neural Network," Reliability Engineering and System Safety, Elsevier, vol. 226(C).
    11. He, Jingran & Gao, Ruofan & Chen, Jianbing, 2022. "A sparse data-driven stochastic damage model for seismic reliability assessment of reinforced concrete structures," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    12. Wang, Zeyu & Shafieezadeh, Abdollah & Xiao, Xiong & Wang, Xiaowei & Li, Quanwang, 2022. "Optimal monitoring location for tracking evolving risks to infrastructure systems: Theory and application to tunneling excavation risk," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    13. Perrin, G., 2021. "Point process-based approaches for the reliability analysis of systems modeled by costly simulators," Reliability Engineering and System Safety, Elsevier, vol. 214(C).

    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. Wang, Zeyu & Shafieezadeh, Abdollah, 2020. "Real-time high-fidelity reliability updating with equality information using adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. 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.
    3. Zhang, Xufang & Wang, Lei & Sørensen, John Dalsgaard, 2019. "REIF: A novel active-learning function toward adaptive Kriging surrogate models for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 440-454.
    4. Cheng, Kai & Lu, Zhenzhou, 2021. "Adaptive Bayesian support vector regression model for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    5. Zhang, Jinhao & Gao, Liang & Xiao, Mi, 2020. "A composite-projection-outline-based approximation method for system reliability analysis with hybrid uncertainties," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Wang, Jinsheng & Xu, Guoji & Li, Yongle & Kareem, Ahsan, 2022. "AKSE: A novel adaptive Kriging method combining sampling region scheme and error-based stopping criterion for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    7. Wang, Jian & Sun, Zhili & Cao, Runan, 2021. "An efficient and robust Kriging-based method for system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    8. 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.
    9. Jiang, Chen & Qiu, Haobo & Gao, Liang & Wang, Dapeng & Yang, Zan & Chen, Liming, 2020. "EEK-SYS: System reliability analysis through estimation error-guided adaptive Kriging approximation of multiple limit state surfaces," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    10. 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).
    11. Zhou, Yicheng & Lu, Zhenzhou & Yun, Wanying, 2020. "Active sparse polynomial chaos expansion for system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 202(C).
    12. Zhang, Yu & Dong, You & Xu, Jun, 2023. "An accelerated active learning Kriging model with the distance-based subdomain and a new stopping criterion for reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    13. 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.
    14. Teixeira, Rui & Nogal, Maria & O’Connor, Alan & Martinez-Pastor, Beatriz, 2020. "Reliability assessment with density scanned adaptive Kriging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    15. Yuan, Kai & Xiao, Ning-Cong & Wang, Zhonglai & Shang, Kun, 2020. "System reliability analysis by combining structure function and active learning kriging model," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    16. Saraygord Afshari, Sajad & Enayatollahi, Fatemeh & Xu, Xiangyang & Liang, Xihui, 2022. "Machine learning-based methods in structural reliability analysis: A review," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    17. Chen, Weidong & Xu, Chunlong & Shi, Yaqin & Ma, Jingxin & Lu, Shengzhuo, 2019. "A hybrid Kriging-based reliability method for small failure probabilities," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 31-41.
    18. Jing, Zhao & Chen, Jianqiao & Li, Xu, 2019. "RBF-GA: An adaptive radial basis function metamodeling with genetic algorithm for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 189(C), pages 42-57.
    19. Yang, Seonghyeok & Lee, Mingyu & Lee, Ikjin, 2023. "A new sampling approach for system reliability-based design optimization under multiple simulation models," Reliability Engineering and System Safety, Elsevier, vol. 231(C).
    20. Yang, Seonghyeok & Jo, Hwisang & Lee, Kyungeun & Lee, Ikjin, 2022. "Expected system improvement (ESI): A new learning function for system reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 222(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:eee:reensy:v:196:y:2020:i:c:s0951832018310858. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    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.