Skip to main content
SpringerLink
Log in

An active learning kriging model for hybrid reliability analysis with both random and interval variables

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

Abstract

Hybrid reliability analysis (HRA) with both random and interval variables is investigated in this paper. Firstly, it is figured out that a surrogate model just rightly predicting the sign of performance function can meet the requirement of HRA in accuracy. According to this idea, a methodology based on active learning Kriging (ALK) model named ALK-HRA is proposed. When constructing the Kriging model, the presented method only finely approximates the performance function in the region of interest: the region where the sign tends to be wrongly predicted. Based on the constructed Kriging model, Monte Carlo Simulation (MCS) is carried out to estimate both the lower and upper bounds of failure probability. ALK-HRA is accurate enough with calling the performance function as few times as possible. Four numerical examples and one engineering application are investigated to demonstrate the performance of the proposed method.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  • Au S, Papadimitriou C, Beck J (1999) Reliability of uncertain dynamical systems with multiple design points. Struct Saf 21:113–133

    Article  Google Scholar 

  • Balesdent M, Morio J, Marzat J (2013) Kriging-based adaptive importance sampling algorithms for rare event estimation. Struct Saf 44:1–10

    Article  Google Scholar 

  • Bect J, Ginsbourger D, Li L et al (2012) Sequential design of computer experiments for the estimation of a probability of failure. Stat Comput 22:773–793

    Article  MATH  MathSciNet  Google Scholar 

  • Bichon B, Eldred M, Swiler L et al (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46:2459–2468

    Article  Google Scholar 

  • Bichon B, McFarland J, Mahadevan S (2011) Efficient surrogate models for reliability analysis of systems with multiple failure modes. Reliab Eng Syst Saf 96:1386–1395

    Article  Google Scholar 

  • Du X (2007) Interval reliability analysis. In: Proceedings of the ASME 2007 Design Engineering Technical Conference and Computers and Information in Engineering Conference, Las Vegas, Nevada, USA

  • Du X (2008) Unified uncertainty analysis by the first order reliability method. J Mech Design (ASME) 130:1401–1410

    Google Scholar 

  • Dubourg V, Sudret B, Bourinet J-M (2011) Reliability-based design optimization using kriging surrogates and subset simulation. Struct Multidiscip Optim 44:673–690

    Article  Google Scholar 

  • Dumasa A, Echard B, Gaytona N et al (2013) AK-ILS: an active learning method based on kriging for the inspection of large surfaces. Precis Eng 37:1–9

    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 33:145–154

    Article  Google Scholar 

  • Echard B, Gayton N, Lemaire M 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 

  • Elishakoff I (1995a) Essay on uncertainties in elastic and viscoelastic structures: from A M. Freudenthal’s criticisms to modern convex modeling. Comput Struct 56:871–895

    Article  MATH  Google Scholar 

  • Elishakoff I (1995b) Discussion on: a non-probabilistic concept of reliability. Struct Saf 17:195–199

    Article  Google Scholar 

  • Elishakoff I (1999) Are probabilistic and anti-optimization approaches compatible? whys and hows in uncertainty modelling: probability, fuzziness and antioptimization. Springer, New York

    Google Scholar 

  • Gablonsky J (1998) Implementation of the DIRECT Algorithm. Center for Research in Scientific Computation, Technical Rept. CRSC-TR98-29, North Carolina State Univ, Raleigh, NC, Aug

  • Guo J, Du X (2009) Reliability sensitivity analysis with random and interval variables. Int J Numer Methods Eng 78:1585–1617

    Article  MATH  MathSciNet  Google Scholar 

  • Guo S, Lu Z (2002) Hybrid probabilistic and non-probabilistic model of structural reliability. Chinese J Mech Strength 24:524–526

    Google Scholar 

  • Huang B, Du X (2008) Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation. Reliab Eng Syst Saf 93:325–336

    Article  Google Scholar 

  • Jiang C, Lu G, Han X et al (2012) A new reliability analysis method for uncertain structures with random and interval variables. Int J Mech Mater Des 8:169–182

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  • Lophaven S, Nielsen H, Sondergaard J (2002) DACE, a matlab Kriging toolbox, version 2.0. Tech. Rep. IMM-TR-2002-12; Technical University of Denmark.

  • Luo Y, Kang Z, Alex L (2009) Structural reliability assessment based on probability and convex set mixed model. Comput Struct 87:1408–1415

    Article  Google Scholar 

  • Luo X, Li X, Zhou J et al (2012) A Kriging-based hybrid optimization algorithm for slope reliability analysis. Struct Saf 34:401–406

    Article  Google Scholar 

  • Möller B, Beer M (2008) Engineering computation under uncertainty - capabilities of non-traditional models. Comput Struct 86:1024–41

    Article  Google Scholar 

  • Picheny V, Ginsbourger D, Roustant O et al (2010) Adaptive designs of experiments for accurate approximation of a target region. J Mech Design 132:071008

    Article  Google Scholar 

  • Qin Q, Lin D, Mei G et al (2006) Effects of variable transformations on errors in FORM results. Reliab Eng Syst Safe 91:112–118

    Article  Google Scholar 

  • Qiu Z, Elishakoff I (2001) Anti-optimization technique-a generalization of interval analysis for nonprobabilistic treatment of uncertainty. Chaos Soliton Fract 12:1747–1759

    Article  MATH  MathSciNet  Google Scholar 

  • Qiu Z, Wang J (2010) The interval estimation of reliability for probabilistic and non-probabilistic hybrid structural system. Eng Fail Anal 17:1142–1154

    Article  Google Scholar 

  • Ranjan P, Bingham D, Michailidis G (2008) Sequential experiment design for contour estimation from complex computer codes. Technometrics 50:527–541

    Article  MathSciNet  Google Scholar 

  • Sharma G, Martin J (2009) MATLAB®: a language for parallel computing. Int J Parallel Prog 37(1):3–36

    Article  MATH  Google Scholar 

  • Wang J, Qiu Z (2010) The reliability analysis of probabilistic and interval hybrid structural system. Appl Math Model 34:3648–3658

    Article  MATH  MathSciNet  Google Scholar 

  • Wang X, Qiu Z, Elishakoff I (2008) Non-probabilistic set-theoretic model for structural safety measure. Acta Mech 198:51–64

    Article  MATH  Google Scholar 

  • Wang P, Lu Z, Tang Z (2013) An application of the Kriging method in global sensitivity analysis with parameter uncertainty. Appl Math Model 37:6543–6555

    Article  MathSciNet  Google Scholar 

  • Wei P, Lu Z, Hao W et al (2012) Efficient sampling methods for global reliability sensitivity analysis. Comput Phys Commun 183:1728–1743

    Article  MATH  MathSciNet  Google Scholar 

  • Xiao N, Huang H, Wang Z et al (2012) Unified uncertainty analysis by the mean value first order saddlepoint approximation. Struct Multidisc Optim 46:803–812

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work is supported by the Aerospace Support Fund (NBXW0001) and Foundation Research Funds of Northwestern Polytechnical University (JCY20130123).

Author information

Authors and Affiliations

  1. Institute of Aircraft Reliability Engineering Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, People’s Republic of China

    Xufeng Yang, Yongshou Liu, Yi Gao, Yishang Zhang & Zongzhan Gao

Authors
  1. Xufeng Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongshou Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yishang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zongzhan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongshou Liu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Liu, Y., Gao, Y. et al. An active learning kriging model for hybrid reliability analysis with both random and interval variables. Struct Multidisc Optim 51, 1003–1016 (2015). https://doi.org/10.1007/s00158-014-1189-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-014-1189-5

Keywords

Search

Navigation