SpringerLink
Log in

An adaptive ensemble of surrogate models based on hybrid measure for reliability analysis

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

Abstract

When dealing with complex reliability problems, the classical ensemble of surrogate models (CESM) has better ability of prediction and generalization than the individual surrogate model. However, since the CESM only considers the global errors of the sample set, the prediction results of the sample points far away from the region where most of the samples gather might not be so accurate, and the fitting accuracy of the limit state function will also be affected when the sample points are sparse. In view of the above situation, this paper proposes an adaptive ensemble of surrogate models based on hybrid measure (AESMHM), which comprehensively considers the global errors and local errors. The global weight matrix is modified by the local weight matrix of representative sample points to obtain the hybrid weight of each surrogate model. Through the discussion of four examples, it can be proved that AESMHM can not only improve the prediction accuracy of the whole sample points, but also have higher computational efficiency. Finally, the reliability problem of a radome structure in composite material is solved efficiently by 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

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  • Acar E (2010) Various approaches for constructing an ensemble of metamodels using local measures. Struct Multidisc Optim 42(6):879–896

    Article  Google Scholar 

  • Acar E, Rais-Rohani M (2009) Ensemble of metamodels with optimized weight factors. Struct Multidisc Optim 37(3):279–294

    Article  Google Scholar 

  • Bichon BJ, Eldred MS, Swiler LP (2008) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46(10):2459–2468

    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 

  • Chang CC, Lin CJ (2007) LIBSVM: a library for support vector machines. ACM Trans Intell Syst Technol 2(3):1–27

    Article  Google Scholar 

  • Cheng K, Lu Z (2020) Structural reliability analysis based on ensemble learning of surrogate models. Struct Saf 83:101905

    Article  Google Scholar 

  • Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20(3):273–297

    Article  MATH  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 

  • Erfani SM, Rajasegarar S, Karunasekera S, Leckie C (2016) High-dimensional and large-scale anomaly detection using a linear one-class SVM with deep learning. Pattern Recognit 58:121–134

    Article  Google Scholar 

  • Feng K, Lu Z, Pang C, Yun W (2018) Efficient numerical algorithm of profust reliability analysis: an application to wing box structure. Aerosp Sci Technol 80:203–211

    Article  Google Scholar 

  • Goel T, Haftka RT, Wei S, Queipo NV (2007) Ensemble of surrogates. Struct Multidisc Optim 33(3):199–216

    Article  Google Scholar 

  • Gunst RF, Myers RH, Montgomery DC (1996) Response surface methodology: process and product optimization using designed experiments. Technometrics 38(3):285

    Article  Google Scholar 

  • Gutmann HM (2001) A radial basis function method for global optimization. J Glob Optim 19(3):201–227

    Article  MathSciNet  MATH  Google Scholar 

  • Hardy RL (1971) Multiquadric equations of topography and other irregular surfaces. J Geophys Res 76(8):1905–1915

    Article  Google Scholar 

  • Hasofer AM, Lind NC (1974) Exact and invariant second moment code format. J Eng Mech 100(1):111–121

    Google Scholar 

  • Helton JC, Davis FJ (2002) Sampling-based methods for uncertainty and sensitivity analysis. Risk Anal 22(3):591–622

    Article  Google Scholar 

  • Hu C, Youn BD, Yoon H (2012) An adaptive dimension decomposition and reselection method for reliability analysis. Struct Multidisc Optim 47(3):423–440

    Article  MathSciNet  MATH  Google Scholar 

  • Huntington DE, Lyrintzis CS (1998) Improvements to and limitations of latin hypercube sampling. Probab Eng Mech 13(4):245–253

    Article  Google Scholar 

  • Hurtado JE, Alverez DA (2001) Neural-network-based reliability analysis: a comparative study. Comput Methods Appl Mech Eng 191(1/2):113–132

    Article  Google Scholar 

  • James KE, White RF, Kraemer HC (2010) Repeated split sample validation to assess logistic regression and recursive partitioning: an application to the prediction of cognitive impairment. Stat Med 24(19):3019–3035

    Article  MathSciNet  Google Scholar 

  • ** R, Simpson TW (2001) Comparative studies of metamodeling techniques under multiple modeling criteria. Struct Multidisc Optim 23(1):1–13

    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  MATH  Google Scholar 

  • Kaw A (2005) Mechanics of composite materials. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  • Kiureghian AD (2000) The geometry of radom vibrations and solutions by FORM and SORM. Probab Eng Mech 15(1):81–90

    Article  Google Scholar 

  • Krige DG (1952) A statistical analysis of some borehole values in the orange free state goldfield. J Chem Metall Soc S Afr 53:47–64

    Google Scholar 

  • Lee Y, Choi DH (2014) Pointwise ensemble of meta-models using v nearest points cross-validation. Struct Multidisc Optim 50(3):383–394

    Article  Google Scholar 

  • Liu Y, Li L (2020) Global reliability sensitivity analysis based on state dependent parameter method and efficient sampling techniques. Aerosp Sci Technol 99:105740

    Article  Google Scholar 

  • Liu PF, Zheng JY (2010) Recent developments on damage modeling and finite element analysis for composite laminates: a review. Mater Des 31(8):3825–3834

    Article  Google Scholar 

  • Lophaven SN, Nielsen HB, Sndergaard J (2002) DACE—a MATLAB kriging toolbox. Technical report IMM-TR-2002-12, Technical University of Denmark

  • Ma J, Theiler J, Perkins S (2003) Accurate on-line support vector regression. Neural Comput 15(11):2683–2703

    Article  MATH  Google Scholar 

  • Matheron G (1963) Principles of geostatistics. Econ Geol 58(8):1246–1266

    Article  Google Scholar 

  • Mertens S, Engel A (1997) Vapnik-chervonenkis dimension of neural networks with binary weights. Phys Rev E 55(4):4478–4488

    Article  Google Scholar 

  • Nogal M, Martinez-Pastor B, Rui T, O’Connor A (2020) Reliability analysis using a multi-metamodel complement-basis approach. Reliab Eng Syst Saf 205(19–20):107248

    Google Scholar 

  • Rackwitz R (2001) Reliability analysis—a review and some perspectives. Struct Saf 23(4):365–395

    Article  Google Scholar 

  • Rui T, Nogal M, O’Connor A (2020) Adaptive approaches in metamodel-based reliability analysis: a review. Struct Saf 89:102019

    Google Scholar 

  • Sacks J, Welch WJ, Wynn MHP (1989) [Design and analysis of computer experiments]: rejoinder. Stat Sci 4(4):433–435

    Google Scholar 

  • Schu Ee Ller GI, Pradlwarter HJ, Koutsourelakis PS (2004) A critical appraisal of reliability estimation procedures for high dimensions. Probab Eng Mech 19(4):463–474

    Article  Google Scholar 

  • Sciuva M, Lomario D (2003) A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure. Compos Struct 59(1):155–162

    Article  Google Scholar 

  • Shen GL, Hu GK, Lin B (2013) Mechanics of composite materials. Tsinghua University Press, Bei**g

    Google Scholar 

  • Spottswood SM, Palazotto AN (2001) Progressive failure analysis of a composite shell. Compos Struct 53(1):117–131

    Article  Google Scholar 

  • Sundar VS, Shields MD (2016) Surrogate-enhanced stochastic search algorithms to identify implicitly defined functions for reliability analysis. Struct Saf 62:1–11

    Article  Google Scholar 

  • Tarantola S, Becker W, Zeitz D (2012) A comparison of two sampling methods for global sensitivity analysis. Comput Phys Commun 183(5):1061–1072

    Article  MathSciNet  MATH  Google Scholar 

  • Trafalis TB, Gilbert RC (2006) Robust classification and regression using support vector machines. Eur J Oper Res 173(3):893–909

    Article  MathSciNet  MATH  Google Scholar 

  • Viana FA, Haftka RT, Steffen V Jr (2009) Multiple surrogates: how cross-validation errors can help us to obtain the best predictor. Struct Multidisc Optim 39(4):439–457

    Article  Google Scholar 

  • Viana F, Haftka RT, Watson LT (2013) Efficient global optimization algorithm assisted by multiple surrogate techniques. J Glob Optim 56(2):669–689

    Article  MATH  Google Scholar 

  • Wen Z, Pei H, Liu H, Yue Z (2016) A Sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability. Reliab Eng Syst Saf 153:170–179

    Article  Google Scholar 

  • Wilson G (1951) On the experimental attainment of optimum conditions. J R Stat Soc Ser B 13(1):1–45

    MathSciNet  MATH  Google Scholar 

  • Zhang J, Yue X, Qiu J, Zhang M, Wang X (2020) A unified ensemble of surrogates with global and local measures for global metamodelling. Eng Optim 1:1–22

    Google Scholar 

  • Zhang X, Lu Z, Cheng K (2021) AK-DS: an adaptive kriging-based directional sampling method for reliability analysis. Mech Syst Signal Process 156(15):107610

    Article  Google Scholar 

  • Zhao D, Xue DY (2011) A multi-surrogate approximation method for metamodeling. Eng Comput 27(2):139–153

    Article  Google Scholar 

  • Zhen H, Mahadevan S (2015) Global sensitivity analysis-enhanced surrogate (GSAS) modeling for reliability analysis. Struct Multidisc Optim 53(3):1–21

    MathSciNet  Google Scholar 

  • Zhou CC, Lu ZZ, Zhang F, Yue ZF (2015) An adaptive reliability method combining relevance vector machine and importance sampling. Struct Multidisc Optim 52(5):945–957

    Article  MathSciNet  Google Scholar 

  • Zhou CC, Li C, Zhang HL, Zhao HD, Zhou CP (2021) Reliability and sensitivity analysis of composite structures by an adaptive Kriging based approach. Compos Struct 278:114682

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. NSFC51975476), and the Natural Science Basic Research Program in Shaanxi (Grant No. 2020JM-135).

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Northwestern Polytechnical University, **’an, China

    Changcong Zhou, Hanlin Zhang, Qi Chang, **aokang Song & Chen Li

Authors
  1. Changcong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hanlin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qi Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. **aokang Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chen Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Changcong Zhou.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Replication of results

Code and data for replication can be provided upon request.

Additional information

Responsible Editor: Palaniappan Ramu

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

Zhou, C., Zhang, H., Chang, Q. et al. An adaptive ensemble of surrogate models based on hybrid measure for reliability analysis. Struct Multidisc Optim 65, 16 (2022). https://doi.org/10.1007/s00158-021-03129-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00158-021-03129-1

Keywords

Search

Navigation