Skip to main content
SpringerLink
Log in

A double weighted stochastic response surface method for reliability analysis

  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The weighted stochastic response surface method (WSRSM) has been demonstrated to be effective in improving the accuracy of the estimation of statistical moments and probability of failure (PoF) upon the stochastic response surface method (SRSM). However, it has been noticed that the weighting method in WSRSM may have little and sometimes negative impact on PoF estimation especially in the cases of low PoF. To mitigate this issue, a new double weighted SRSM (DWSRSM) is proposed that the weights of sample points are determined based on their importance not only to regression but also to PoF estimation. Specifically, relatively larger weights are assigned to points closer to the failure surface, which significantly accounts for the accuracy of PoF estimation. Comparative studies show that DWSRSM outperforms WSRSM producing more accurate PoF estimation without incurring additional function evaluations. An application of DWSRSM to the rocket design further demonstrates its effectiveness for PoF estimation.

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

Similar content being viewed by others

References

  1. X. Du, A. Sudjianto and W. Chen, An integrated framework for optimization under uncertainty using inverse reliability strategy, ASME Journal of Mechanical Design, 126(4) (2004) 562–570.

    Article  Google Scholar 

  2. Z. P. Mourelatos and J. Liang, A methodology for tradingoff performance and robustness under uncertainty, ASME Journal of Mechanical Design, 128(4) (2006) 856–863.

    Article  Google Scholar 

  3. B. D Youn, K. K. Choi and K. Yi, Performance moment integration (PMI) method for quality assessment in reliability-based robust optimization, Mechanics Based Design of Structures and Machines, 33(2) (2005) 185–213.

    Article  Google Scholar 

  4. J. Tu and K. K. Choi, A new study on reliability-based design optimization, ASME Journal of Mechanical Design, 121(4) (1999) 557–564.

    Article  Google Scholar 

  5. M. Hohenbichler and Rackwitz, Improvement of secondorder reliability estimates by importance sampling, ASCE Journal of Engineering Mechanics, 114(12) (1988) 195–2199.

    Article  Google Scholar 

  6. S. S. Isukapalli, A. Roy and P. G. Georgopoulos, Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems, Risk Analysis, 18(3) (1998) 351–363.

    Article  Google Scholar 

  7. S. S. Isukapalli, Uncertainty analysis of transporttransformation models, Ph.D dissertation, The State University of New Jersey (1999).

  8. S. S. Isukapalli, A. Roy and P. G. Georgopoulos, Efficient sensitivity/uncertainty analysis using the combined stochastic Response surface method and automated differentiation: application to environmental and biological systems, Risk Analysis, 20(5) (2000) 591–602.

    Article  Google Scholar 

  9. X. Xiong, W. Chen, Y. Xiong and S. Yang, Weighted stochastic response surface method considering sample weights, Journal of Structural Multidisciplinary Optimization, 423(6) (2011) 837–849.

    Article  Google Scholar 

  10. S. Rahman and D. Wei, A univariate approximation at most probable point for higher-order reliability analysis, International Journal of Solids and Structures, 43(9) (2006) 2820–2839.

    Article  MATH  Google Scholar 

  11. F. Xiong, S. Greene, Y. Xiong, W. Chen and S. Yang, A new sparse grid based method for uncertainty propagation, Journal of Structural and Multidisciplinary Optimization, 41(3) (2010) 335–349.

    Article  MathSciNet  Google Scholar 

  12. H. P. Gavin and C. Y. Siu, High-order limit state functions in the response surface method for structural reliability analysis, Structural Safety, 30(2) (2006) 162–179.

    Article  Google Scholar 

  13. I. Kaymaza and C. McMahon, A response surface method based on weighted regression for structural reliability analysis, Probabilistic Engineering Mechanics, 20(1) (2005) 11–17.

    Article  Google Scholar 

  14. X. Nguyen, A. Sellier, F. Duprat and G. Pons, Adaptive response surface method based on a double weighted regression technique, Probabilistic Engineering Mechanics, 24(2) (2009) 135–143.

    Article  Google Scholar 

  15. C. M. Creveling, Tolerance design: A handbook for developing optimal specifications, Addison-Wesley, MA (1997).

    Google Scholar 

  16. S. Kim and S. Na, Response surface method using vector projected sampling points, Structural Safety, 19(1) (1997) 3–19.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Fenfen Xiong & Shuxing Yang

  2. School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, China

    Yu Liu

  3. Bank of America, Charlotte, NC, 28255, USA

    Ying Xiong

Authors
  1. Fenfen Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yu Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ying Xiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shuxing Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shuxing Yang.

Additional information

Recommended by Editor Maenghyo Cho

Fenfen Xiong is a faculty in School of Aerospace Engineering of Beijing Institute of Technology. Her research interests include multidisciplinary design optimization under uncertainty and flight vehicle design.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xiong, F., Liu, Y., Xiong, Y. et al. A double weighted stochastic response surface method for reliability analysis. J Mech Sci Technol 26, 2573–2580 (2012). https://doi.org/10.1007/s12206-012-0425-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-012-0425-4

Keywords

Search

Navigation