| Peer-Reviewed

Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment

Received: 28 November 2015     Accepted: 5 December 2015     Published: 22 December 2015
Views:       Downloads:
Abstract

Reliability assessment is one of the necessary and critical parts in structural design under uncertainties. The methods for structural reliability assessment aim at evaluating the probability of limit state by considering the fluctuation of acting loads, variation of structural component or system, and complexity of operating environment. Latin Hypercube sampling (LHS) method as advanced Monte Carlo simulation (MCS) has higher efficiency in sampling. It will be chosen and applied in this paper in order to obtain an effective database for building Kriging surrogate models. In this paper, we propose an effective method to have reliability assessment by Latin Hypercube sampling based Kriging surrogate models. This method keeps the certain level of accuracy in prediction of the response of a structural finite element model or other explicit mathematical functions.

Published in Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 6)
DOI 10.11648/j.sjams.20150306.16
Page(s) 263-274
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Latin Hypercube Sampling, Kriging Models, Reliability Assessment

References
[1] Donald L. Phillips, Danny G. Mark. Spatial uncertainty analysis: propagation of interpolation errors in spatially distributed models. Ecological Modelling, Volume 91, Issues 1–3, 15 November 1996, Pages 213-229.
[2] L. Goel, R. Billinton. Monte Carlo simulation applied to distribution feeder reliability evaluation. Electric Power Systems Research, Volume 29, Issue 3, May 1994, Pages 193-202.
[3] R.E. Melchers. Importance sampling in structural systems. Structural Safety, Volume 6, Issue 1, July 1989, Pages 3-10.
[4] L. Mark Berliner, Christopher K. Wikle. Approximate importance sampling Monte Carlo for data assimilation. Physica D: Nonlinear Phenomena, Volume 230, Issues 1–2, June 2007, Pp 37-49.
[5] P. Beaurepaire, H. A. Jensen, G. I. Schuëller, M. A. Valdebenito. Reliability-based optimization using bridge importance sampling. Probabilistic Engineering Mechanics, Volume 34, October 2013, Pp 48-57.
[6] Munoz Zuniga Miguel, Garnier Josselin, Remy Emmanuel. An original sensitivity statistic within a new adaptive accelerated Monte-Carlo method. Procedia - Social and Behavioral Sciences, Volume 2, Issue 6, 2010, Pages 7712-7713.
[7] Yaning Liu, M. Yousuff Hussaini, Giray Ökten. Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives. Applied Numerical Mathematics, Volume 72, October 2013, Pages 160-171.
[8] Michael D. Shields, Kirubel Teferra, Adam Hapij, Raymond P. Daddazio. Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification. Reliability Engineering & System Safety, Volume 142, October 2015, Pp 310-325.
[9] Stein M. Large sample properties of simulations using Latin hypercube sampling. Technometrics 1987.
[10] Owen A. A central limit theorem for Latin hypercube sampling. J. R. Stat Soc B 1992, 54(2): 541-51.
[11] Huntington D. Improvements to and limitations of Latin hypercube sampling. Probabilistic Engineering Mechanics, 1998, 13(4): 245-253.
[12] Stocki R. A study on algorithms for optimization of Latin hybercubes. J Stat Plan Inference 2006, 136(9): 3231-3247.
[13] Iman R. A distribution-free approach to inducing rank correlation among input variables. Common Stat: Simul Comput 1982: 11(3):3 11-334.
[14] Florian A. An efficient sampling scheme: updated Latin hypercube sampling. Probabilistic Engineering Mechanics, 1992, 7: 123-130.
[15] Cioppa T, Lucas T. Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 2007, 49(1), 45-55.
[16] Novak D. Correlation control in small-sample Monte Carlo type simulations i: a simulated annealing approach. Probab Eng Mech 2009, 24, 452-462.
[17] B. Gaspar, A. P. Teixeira, C. Guedes Soares. Assessment of the efficiency of Kriging surrogate models for structural reliability analysis. Probabilistic Engineering Mechanics, Volume 37, July 2014, Pages 24-34.
[18] M. Zakerifar, W. E. Biles and G. W. Evans. Kriging metamodeling in multi-objective simulation optimization. 2115-2122, 2009.
[19] Van Beers, W. C. M., J. P. C. Kleijnen. 2003. Kriging for Interpolation in Random Simulation. Journal of the Operational Research So-ciety, No. 54: 255-262.
[20] G. Matheron. Principles of geo-statistics. Economic Geology, 58(8)(1963), pp 1243-1266.
[21] J. Sacks, S. B. Schiller, W. Welch. Designs for computer experiment. Technometrics, 31(1) (1989), pp 41-47.
[22] M. Handcock, M. Stein. A Bayesian analysis of kriging. Technometrics, 35(3) (1993), pp 403-410.
[23] Van Beers, J. P. C. Kleijnen. Customized sequential designs for random simulation experiments: Kriging metamodeling and bootstrapping. European Journal of Operational Research, 186(3) 2008, pp. 1099-1113.
[24] Aleš Florian. An efficient sampling scheme: Updated Latin Hypercube Sampling. Probabilistic Engineering Mechanics, Volume 7, Issue 2, 1992, Pages 123-130.
[25] Michael D. Shields, Kirubel Teferra, Adam Hapij, Raymond P. Daddazio. Refined Stratified Sampling for efficient Monte Carlo based uncertainty quantification. Reliability Engineering and System Safety 142 (2015) 310-325.
[26] B. Gaspar, A. P. Teixeira, C. Guedes Soares. Assessment of the efficiency of Kriging surrogate models for structural reliability analysis. Probabilistic Engineering Mechanics, Volume 37, July 2014, Pages 24-34.
Cite This Article
  • APA Style

    Liu Chu, Eduardo Souza De Cursi, Abdelkhalak El Hami, Mohamed Eid. (2015). Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment. Science Journal of Applied Mathematics and Statistics, 3(6), 263-274. https://doi.org/10.11648/j.sjams.20150306.16

    Copy | Download

    ACS Style

    Liu Chu; Eduardo Souza De Cursi; Abdelkhalak El Hami; Mohamed Eid. Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment. Sci. J. Appl. Math. Stat. 2015, 3(6), 263-274. doi: 10.11648/j.sjams.20150306.16

    Copy | Download

    AMA Style

    Liu Chu, Eduardo Souza De Cursi, Abdelkhalak El Hami, Mohamed Eid. Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment. Sci J Appl Math Stat. 2015;3(6):263-274. doi: 10.11648/j.sjams.20150306.16

    Copy | Download

  • @article{10.11648/j.sjams.20150306.16,
      author = {Liu Chu and Eduardo Souza De Cursi and Abdelkhalak El Hami and Mohamed Eid},
      title = {Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {3},
      number = {6},
      pages = {263-274},
      doi = {10.11648/j.sjams.20150306.16},
      url = {https://doi.org/10.11648/j.sjams.20150306.16},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150306.16},
      abstract = {Reliability assessment is one of the necessary and critical parts in structural design under uncertainties. The methods for structural reliability assessment aim at evaluating the probability of limit state by considering the fluctuation of acting loads, variation of structural component or system, and complexity of operating environment. Latin Hypercube sampling (LHS) method as advanced Monte Carlo simulation (MCS) has higher efficiency in sampling. It will be chosen and applied in this paper in order to obtain an effective database for building Kriging surrogate models. In this paper, we propose an effective method to have reliability assessment by Latin Hypercube sampling based Kriging surrogate models. This method keeps the certain level of accuracy in prediction of the response of a structural finite element model or other explicit mathematical functions.},
     year = {2015}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Application of Latin Hypercube Sampling Based Kriging Surrogate Models in Reliability Assessment
    AU  - Liu Chu
    AU  - Eduardo Souza De Cursi
    AU  - Abdelkhalak El Hami
    AU  - Mohamed Eid
    Y1  - 2015/12/22
    PY  - 2015
    N1  - https://doi.org/10.11648/j.sjams.20150306.16
    DO  - 10.11648/j.sjams.20150306.16
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
    JO  - Science Journal of Applied Mathematics and Statistics
    SP  - 263
    EP  - 274
    PB  - Science Publishing Group
    SN  - 2376-9513
    UR  - https://doi.org/10.11648/j.sjams.20150306.16
    AB  - Reliability assessment is one of the necessary and critical parts in structural design under uncertainties. The methods for structural reliability assessment aim at evaluating the probability of limit state by considering the fluctuation of acting loads, variation of structural component or system, and complexity of operating environment. Latin Hypercube sampling (LHS) method as advanced Monte Carlo simulation (MCS) has higher efficiency in sampling. It will be chosen and applied in this paper in order to obtain an effective database for building Kriging surrogate models. In this paper, we propose an effective method to have reliability assessment by Latin Hypercube sampling based Kriging surrogate models. This method keeps the certain level of accuracy in prediction of the response of a structural finite element model or other explicit mathematical functions.
    VL  - 3
    IS  - 6
    ER  - 

    Copy | Download

Author Information
  • Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, Rouen, France

  • Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, Rouen, France

  • Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, Rouen, France

  • Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, Rouen, France

  • Sections