IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v157y2017icp152-165.html
   My bibliography  Save this article

LIF: A new Kriging based learning function and its application to structural reliability analysis

Author

Listed:
  • Sun, Zhili
  • Wang, Jian
  • Li, Rui
  • Tong, Cao

Abstract

The main task of structural reliability analysis is to estimate failure probability of a studied structure taking randomness of input variables into account. To consider structural behavior practically, numerical models become more and more complicated and time-consuming, which increases the difficulty of reliability analysis. Therefore, sequential strategies of design of experiment (DoE) are raised. In this research, a new learning function, named least improvement function (LIF), is proposed to update DoE of Kriging based reliability analysis method. LIF values how much the accuracy of estimated failure probability will be improved if adding a given point into DoE. It takes both statistical information provided by the Kriging model and the joint probability density function of input variables into account, which is the most important difference from the existing learning functions. Maximum point of LIF is approximately determined with Markov Chain Monte Carlo(MCMC) simulation. A new reliability analysis method is developed based on the Kriging model, in which LIF, MCMC and Monte Carlo(MC) simulation are employed. Three examples are analyzed. Results show that LIF and the new method proposed in this research are very efficient when dealing with nonlinear performance function, small probability, complicated limit state and engineering problems with high dimension.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:reensy:v:157:y:2017:i:c:p:152-165
    DOI: 10.1016/j.ress.2016.09.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832016304847
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2016.09.003?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. Dubreuil, S. & Berveiller, M. & Petitjean, F. & Salaün, M., 2014. "Construction of bootstrap confidence intervals on sensitivity indices computed by polynomial chaos expansion," Reliability Engineering and System Safety, Elsevier, vol. 121(C), pages 263-275.
    2. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    3. Bichon, Barron J. & McFarland, John M. & Mahadevan, Sankaran, 2011. "Efficient surrogate models for reliability analysis of systems with multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 96(10), pages 1386-1395.
    4. Alibrandi, Umberto, 2014. "A response surface method for stochastic dynamic analysis," Reliability Engineering and System Safety, Elsevier, vol. 126(C), pages 44-53.
    5. 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.
    6. Dellino, G. & Lino, P. & Meloni, C. & Rizzo, A., 2009. "Kriging metamodel management in the design optimization of a CNG injection system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2345-2360.
    7. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
    8. 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.
    9. Busby, Daniel, 2009. "Hierarchical adaptive experimental design for Gaussian process emulators," Reliability Engineering and System Safety, Elsevier, vol. 94(7), pages 1183-1193.
    10. Pedroni, N. & Zio, E. & Apostolakis, G.E., 2010. "Comparison of bootstrapped artificial neural networks and quadratic response surfaces for the estimation of the functional failure probability of a thermal–hydraulic passive system," Reliability Engineering and System Safety, Elsevier, vol. 95(4), pages 386-395.
    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. 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.
    2. 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.
    3. 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).
    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. Jian, Wang & Zhili, Sun & Qiang, Yang & Rui, Li, 2017. "Two accuracy measures of the Kriging model for structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 494-505.
    6. Ni, Pinghe & Li, Jun & Hao, Hong & Yan, Weimin & Du, Xiuli & Zhou, Hongyuan, 2020. "Reliability analysis and design optimization of nonlinear structures," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    7. Zhang, Jinhao & Xiao, Mi & Gao, Liang, 2019. "An active learning reliability method combining Kriging constructed with exploration and exploitation of failure region and subset simulation," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 90-102.
    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. 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).
    10. 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).
    11. Guo, Qing & Liu, Yongshou & Chen, Bingqian & Yao, Qin, 2021. "A variable and mode sensitivity analysis method for structural system using a novel active learning Kriging model," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    12. Xiong, Yifang & Sampath, Suresh, 2021. "A fast-convergence algorithm for reliability analysis based on the AK-MCS," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    13. 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).
    14. 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.
    15. Cao, Runan & Sun, Zhili & Wang, Jian & Guo, Fanyi, 2022. "A single-loop reliability analysis strategy for time-dependent problems with small failure probability," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    16. Zio, E., 2018. "The future of risk assessment," Reliability Engineering and System Safety, Elsevier, vol. 177(C), pages 176-190.
    17. Bansal, Sahil & Cheung, Sai Hung, 2017. "On the evaluation of multiple failure probability curves in reliability analysis with multiple performance functions," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 583-594.
    18. 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.
    19. Turati, Pietro & Pedroni, Nicola & Zio, Enrico, 2017. "Simulation-based exploration of high-dimensional system models for identifying unexpected events," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 317-330.
    20. Chengning Zhou & Ning-Cong Xiao & Ming J Zuo & Xiaoxu Huang, 2020. "AK-PDF: An active learning method combining kriging and probability density function for efficient reliability analysis," Journal of Risk and Reliability, , vol. 234(3), pages 536-549, June.

    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:157:y:2017:i:c:p:152-165. 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.