Skip to main content
SpringerLink
Log in

An innovative DoE strategy of the kriging model for structural reliability analysis

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

An innovative strategy of the design of experiments (DoE) is proposed to reduce the number of calls of the performance function in the kriging-based structural reliability analysis procedure. Benefitting from the local uncertainty provided by the kriging model and the joint probability density function of performance function values of untried points derived in this research, the epistemic variance of the target failure probability is calculated approximately. The variance is treated as the accuracy measurement of the estimated failure probability. The next best point is defined as the untried point that can minimize the variance of failure probability in the sense of expectation which is computed by Gauss–Hermite quadrature. The basic idea of the proposed strategy is to refresh the current DoE by adding the next best point into it. The candidate points of the next best one are randomly generated by Markov chain Monte Carlo method from the kriging-based conditional distribution. A structural reliability analysis procedure is introduced to apply the proposed DoE strategy, whose stopping criterion is constructed mainly on the basis of the coefficient of variation of failure probability. To validate the efficiency of the proposed DoE strategy, three examples are analyzed in which there are explict and implict performance function. And, the analysis results demonstrate the outperformance of the innovative strategy.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Alibrandi U, Alani AM, Ricciardi G (2015) A new sampling strategy for SVM-based response surface for structural reliability analysis. Probab Eng Mech 41:1–12

    Article  Google Scholar 

  • Au S-K (2016) On MCMC algorithm for subset simulation. Probab Eng Mech 43:117–120

    Article  Google Scholar 

  • Au SK, Beck JL (2001) Estimation of small failure probabilities in high dimensions by subset simulation. Probab Eng Mech 16(4):263–277

    Article  Google Scholar 

  • Bae S, Park C, Kim NH (2018) Uncertainty quantification of reliability analysis under surrogate model uncertainty using Gaussian process. in ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2018, August 26, 2018 - August 29, 2018. American Society of Mechanical Engineers (ASME), Quebec City

  • Bichon BJ et al (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468

    Article  Google Scholar 

  • Blatman G, Sudret B (2008) Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach. CR Mec 336(6):518–523

    Article  Google Scholar 

  • Blatman G, Sudret B (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab Eng Mech 25(2):183–197

    Article  Google Scholar 

  • Bourinet JM, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343–353

    Article  Google Scholar 

  • Bucher C, Most T (2008) A comparison of approximate response functions in structural reliability analysis. Probab Eng Mech 23(2–3):154–163

    Article  Google Scholar 

  • Cornuet JM et al (2012) Adaptive multiple importance sampling. Scand J Stat 39(4):798–812

    Article  MathSciNet  Google Scholar 

  • Dubourg V, Sudret B, Deheeger F (2013) Metamodel-based importance sampling for structural reliability analysis. Probab Eng Mech 33:47–57

    Article  Google Scholar 

  • Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining kriging and Monte Carlo simulation. Struct Saf 33(2):145–154

    Article  Google Scholar 

  • Echard B et al (2013) A combined importance sampling and kriging reliability method for small failure probabilities with time-demanding numerical models. Reliab Eng Syst Saf 111:232–240

    Article  Google Scholar 

  • Gaspar B et al (2014) System reliability analysis by Monte Carlo based method and finite element structural models. J Offshore Mech Arct Eng Trans ASME 136(3):1–09

  • Gayton N, Bourinet JM, Lemaire M (2003) CQ2RS: a new statistical approach to the response surface method for reliability analysis. Struct Saf 25(1):99–121

    Article  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492

    Article  MathSciNet  Google Scholar 

  • Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 27(2):133–151

    Article  Google Scholar 

  • Kleijnen JPC (2009) Kriging metamodeling in simulation: a review. Eur J Oper Res 192(3):707–716

    Article  MathSciNet  Google Scholar 

  • Lv Z, Lu Z, Wang P (2015) A new learning function for kriging and its applications to solve reliability problems in engineering. Comput Math Appl 70(5):1182–1197

    Article  MathSciNet  Google Scholar 

  • Melchers RE (1990) Radial importance sampling for structural reliability. J Eng Mech ASCE 116(1):189–203

    Article  Google Scholar 

  • Pradlwarter HJ et al (2007) Application of line sampling simulation method to reliability benchmark problems. Struct Saf 29(3):208–221

    Article  Google Scholar 

  • Richard J-F, Zhang W (2007) Efficient high-dimensional importance sampling. J Econ 141(2):1385–1411

    Article  MathSciNet  Google Scholar 

  • Roussouly N, Petitjean F, Salaun M (2013) A new adaptive response surface method for reliability analysis. Probab Eng Mech 32:103–115

    Article  Google Scholar 

  • Schueremans L, Van Gemert D (2005) Benefit of splines and neural networks in simulation based structural reliability analysis. Struct Saf 27(3):246–261

    Article  Google Scholar 

  • Shimoyama K et al (2013) Updating kriging surrogate models based on the hypervolume indicator in multi-objective optimization. J Mech Des 135(9):094503

    Article  Google Scholar 

  • Sobol IM, Tutunnikov AV (1996) A variance reducing multiplier for Monte Carlo integrations. Math Comput Model 23(8–9):87–96

    Article  MathSciNet  Google Scholar 

  • Song H et al (2013) Adaptive virtual support vector machine for reliability analysis of high-dimensional problems. Struct Multidiscip Optim 47(4):479–491

    Article  MathSciNet  Google Scholar 

  • Sun Z et al (2017) LIF: a new kriging based learning function and its application to structural reliability analysis. Reliab Eng Syst Saf 157:152–165

    Article  Google Scholar 

  • Yang X et al (2015a) An active learning kriging model for hybrid reliability analysis with both random and interval variables. Struct Multidiscip Optim 51(5):1003–1016

    Article  MathSciNet  Google Scholar 

  • Yang X et al (2015b) Hybrid reliability analysis with both random and probability-box variables. Acta Mech 226(5):1341–1357

    Article  MathSciNet  Google Scholar 

  • Yu H, Gillot F, Ichchou M (2012) A polynomial chaos expansion based reliability method for linear random structures. Adv Struct Eng 15(12):2097–2111

    Article  Google Scholar 

  • Zhang H, Mullen RL, Muhanna RL (2010) Interval Monte Carlo methods for structural reliability. Struct Saf 32(3):183–190

    Article  Google Scholar 

  • Zhao YG, Ono T (1999) A general procedure for first/second-order reliability method (FORM/SORM). Struct Saf 21(2):95–112

    Article  Google Scholar 

Download references

Funding

The study was funded by National Science and Technology Major Project of China (Grant No. 2013ZX04011-011) and the National Defense Technology Foundation of China (Grant No. JSZL2015208B001).

Author information

Authors and Affiliations

  1. College of Mechanical and Automation, Northeastern University, No. 3-11, Wenhua Road, Heping District, Shenyang, People’s Republic of China

    Mingang Yin, Jian Wang & Zhili Sun

Authors
  1. Mingang Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhili Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mingang Yin.

Ethics declarations

Conflict of Interest

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Responsible Editor: Raphael Haftka

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, M., Wang, J. & Sun, Z. An innovative DoE strategy of the kriging model for structural reliability analysis. Struct Multidisc Optim 60, 2493–2509 (2019). https://doi.org/10.1007/s00158-019-02337-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-019-02337-0

Keywords

Search

Navigation