Skip to main content
SpringerLink
Log in

Invariance problem in structural non-probabilistic reliability index

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

Abstract

The non-probabilistic reliability index has been extensively used to evaluate the safety degree of structures with limited experiment data. By dealing the uncertain parameters of structures with the ellipsoidal model, this paper investigates the invariance problem in the non-probabilistic reliability index. A prerequisite of the existence of the invariance problem is first given. An investigation of whether the two non-probabilistic first order reliability methods, namely the mean-value and design-point methods, encounter the same problem is then presented. A comparison of the precision of these two methods is further conducted through three numerical examples, and based on which some significant phenomena are summarized.

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. Y. Ben-Haim and I. Elishakoff, Convex Models of Uncertainties in Applied Mechanics, Elsevier Science Publisher, Amsterdam, Netherlands (1990).

    MATH  Google Scholar 

  2. X. J. Wang, I. Elishakoff and Z. P. Qiu, Experimental data have to decide which of the nonprobabilistic uncertainty descriptions—convex modeling or interval analysis—to utilize, Journal Applied Mechanics, 75(4) (2008) 041018.

    Article  Google Scholar 

  3. Y. T. Zhou, C. Jiang and X. Han, Interval and subinterval analysis methods of the structural analysis and their error estimations, International Journal of Computational Methods, 3 (2011) 229–244.

    Article  MathSciNet  Google Scholar 

  4. Y. S. Liu, X. J. Wang and L. Wang, Interval uncertainty analysis for static response of structures using radial basis functions, Applied Mathematical Modelling, 69 (2019) 425–440.

    Article  MathSciNet  Google Scholar 

  5. L. P. Zhu, I. Elishakoff and J. H. Starnes, Derivation of multidimensional ellipsoidal convex model for experimental data, Mathematical and Computer Modelling, 24 (1996) 103–114.

    Article  MathSciNet  Google Scholar 

  6. C. Jiang, X. Han, G. Y. Lu, J. Liu, Z. Zhang and Y. C. Bai, Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique, Computer Methods in Applied Mechanics and Engineering, 200 (2011) 2528–2546.

    Article  Google Scholar 

  7. Z. Kang and W. B. Zhang, Construction and application of an ellipsoidal convex model using a semi-definite programming formulation from measured data, Computer Methods in Applied Mechanics and Engineering, 300 (2016) 461–489.

    Article  MathSciNet  Google Scholar 

  8. L. X. Cao, J. Liu, L. Xie, C. Jiang and R. G. Bi, Non-probabilistic polygonal convex set model for structural uncertainty quantification, Applied Mathematical Modelling, 89 (2021) 504–518.

    Article  MathSciNet  Google Scholar 

  9. B. Y. Ni, I. Elishakoff, C. Jiang, C. M. Fu and X. Han, Generalization of the super ellipsoid concept and its application in mechanics, Applied Mathematical Modelling, 40 (2016) 9427–9444.

    Article  MathSciNet  Google Scholar 

  10. Y. Ben-Haim, A non-probabilistic measure of reliability of linear systems based on expansion of convex models, Structural Safety, 17 (1995) 91–109.

    Article  Google Scholar 

  11. Y. Ben-Haim, Robust reliability of structures, Advances in Applied Mechanics, 33 (1997) 1–41.

    Article  Google Scholar 

  12. Z. P. Qiu, P. C. Mueller and A. Frommer, The new nonprobabilistic criterion of failure for dynamical systems based on convex models, Mathematical and Computer Modelling, 40 (2004) 201–215.

    Article  MathSciNet  Google Scholar 

  13. I. Elishakoff, Discussion on: a non-probabilistic concept of reliability, Structural Safety, 17 (1995) 195–199.

    Article  Google Scholar 

  14. S. X. Guo, Z. Z. Lu and Y. S. Feng, A non-probabilistic model of structural reliability based on interval analysis, Chinese Journal of Computational Mechanics, 18 (2001) 56–60.

    Google Scholar 

  15. T. Jiang, J. J. Chen and Y. L. Xu, A semi-analytic method for calculating non-probabilistic reliability index based on interval models, Applied Mathematical Modelling, 31 (2007) 1362–1370.

    Article  Google Scholar 

  16. X. Y. Chen, C. Y. Tang, C. P. Tsui and J. P. Fan, Modified scheme based on semi-analytic approach for computing non-probabilistic reliability index, Acta Mechanica Solida Sinica, 23 (2010) 115–123.

    Article  Google Scholar 

  17. X. J. Wang, Z. P. Qiu and I. Elishakoff, Non-probabilistic set-theoretic model for structural safety measure, Acta Mechanica, 198 (2008) 51–64.

    Article  Google Scholar 

  18. R. X. Wang, X. J. Wang, L. Wang and X. J. Chen, Efficient computational method for the non-probabilistic reliability of linear structural systems, Acta Mechanica Solida Sinica, 29 (2016) 284–299.

    Article  Google Scholar 

  19. H. J. Cao and B. Y. Duan, Approach on the non-probabilistic reliability of structures based on uncertainty convex models, Chinese Journal of Computational Mechanics, 22 (2005) 546–549+578.

    Google Scholar 

  20. C. Jiang, G. Y. Lu, X. Han and R. G. Bi, Some important issues on first-order reliability analysis with non-probabilistic convex models, Journal of Mechanical Design, 136 (2014) 034501.

    Article  Google Scholar 

  21. X. J. Wang, L. Wang, I. Elishakoff and Z. P Qiu, Probability and convexity concepts are not antagonistic, Acta Mechanics, 219 (2011) 45–64.

    Article  Google Scholar 

  22. C. Jiang, R. G. Bi, G. Y. Lu and X. Han, Structural reliability analysis using non-probabilistic convex model, Computer Methods in Applied Mechanics and Engineering, 254 (2013) 83–98.

    Article  MathSciNet  Google Scholar 

  23. C. Jiang, Q. F. Zhang, X. Han, J. Liu and D. A. Hu, Multidimensional parallelepiped model-a new type of non-probabilistic convex model for structural uncertainty analysis, International Journal for Numerical Methods in Engineering, 103 (2015) 31–59.

    Article  MathSciNet  Google Scholar 

  24. C. Jiang, Q. F. Zhang, X. Han and Y. H. Qian, A non-probabilistic structural reliability analysis method based on a multidimensional parallelepiped convex mode, Acta Mechanica, 225 (2013) 383–395.

    Article  Google Scholar 

  25. S. X. Guo and Z. Z. Lu, A procedure of the analysis of non-probabilistic reliability of structural systems, Chinese Journal of Computational Mechanics, 19 (2002) 332–335.

    Google Scholar 

  26. X. J. Wang, L. Wang and Z. P. Qiu, Safety estimation of structural systems via interval analysis, Chinese Journal of Aeronautics, 26 (2013) 614–623.

    Article  Google Scholar 

  27. X. Z. Qiao, B. Wang, X. R. Fang and P. Liu, Non-probabilistic reliability bounds for series structural systems, International Journal of Computational Methods (2021) (to be published).

  28. O. Ditlevsen, Structural Reliability and the Invariance Problem, University of Waterloo Press, Waterloo, Canada (1973).

    Google Scholar 

  29. Z. P. Qiu, Convex Method based on Non-Probabilistic Set-theory and Its Application, National Defence Industry Press, Beijing, China (2005).

    Google Scholar 

  30. A. S. Nowak and K. R. Collins, Reliability of Structures, McGraw-Hill, New York, USA (2000).

    Google Scholar 

  31. Z. L. Hu and X. P. Du, Reliability methods for bimodal distribution with first-order approximation, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 5 (2019) 011005.

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by Research Program supported by the National Natural Science Foundation of China (Grant No. 51775427) and the Open Fund of Key Laboratory of Electronic Equipment Structure Design (Ministry of Education) in Xidian University, China.

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Xi’an University of Science and Technology, Xi’an, 710054, China

    Xinzhou Qiao, Linfan Song, Peng Liu & Xiurong Fang

  2. Key Laboratory of Electronic Equipment Structure Design, Ministry of Education, Xi’an, 710071, China

    Peng Liu

Authors
  1. Xinzhou Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Linfan Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiurong Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinzhou Qiao.

Additional information

Xinzhou Qiao is an Associate Professor at Xi’an University of Science and Technology, Xi’an, China. He received his Ph.D. in Mechanical Engineering from Xidian University, Xi’an, China, in 2009. His current research interests include uncertainty quantification, reliability analysis and reliability-based optimization design of structures.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiao, X., Song, L., Liu, P. et al. Invariance problem in structural non-probabilistic reliability index. J Mech Sci Technol 35, 4953–4961 (2021). https://doi.org/10.1007/s12206-021-1014-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-021-1014-1

Keywords

Search

Navigation