Skip to main content
SpringerLink
Log in

Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

The failure probability-based global sensitivity is proposed to evaluate the influence of input variables on the failure probability. But for the problem that the distribution parameters of variables are uncertain due to the lack of data or acknowledgement, if the original failure probability-based global sensitivity is employed to evaluate the influences of different uncertainty sources directly, the computational cost will be prohibitive. To address this issue, this work proposes the novel predictive failure probability (PFP) based on global sensitivity. By separating the overall uncertainty of variables into inherent uncertainty and distribution parameter uncertainty, the PFP can be evaluated by a single loop with equivalent transformation. Then, the PFP based global sensitivities with respect to (w.r.t) the overall uncertainty, inherent uncertainty and distribution parameter uncertainty are proposed, respectively, and their relationships are discussed, which can be used to measure the influences of different uncertainty sources. To compute those global sensitivities efficiently, the Monte Carlo method and Kriging-based method are employed for comparison. Several examples including two numerical examples and three engineering practices are investigated to validate the reasonability and efficiency 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
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

References

  1. Fort JC, Klein T, Rachdi N (2016) New sensitivity analysis subordinated to contrast. Commun Stat Theory Methods 45(15):4349–4364

    Article  MathSciNet  MATH  Google Scholar 

  2. Andrea S (2002) Sensitivity analysis for importance assessment. Risk Anal 22:579–590

    Article  Google Scholar 

  3. Dellino G, Meloni C (2015) Uncertainty management in simulation-optimization of complex systems: algorithms and applications. Oper Res 59:101–122

    MATH  Google Scholar 

  4. Wei P, Lu Z, Song S (2015) Variable importance analysis: a comprehensive review. Reliab Eng Syst Saf 142:399–432

    Article  Google Scholar 

  5. Saltelli A, Tarantola S, Campolongo F et al (2004) Sensitivity analysis in practice: a guide to assessing scientific models. J R Stat Soc Ser A 101:398–399

    MATH  Google Scholar 

  6. Helton JC, Johnson JD, Sallaberry CJ et al (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91:1175–1209

    Article  Google Scholar 

  7. Storlie CB, Swiler LP, Helton JC et al (2009) Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models. Reliab Eng Syst Saf 94:1735–1763

    Article  Google Scholar 

  8. Song S, Wang L (2021) A novel global sensitivity measure based on probability weighted moments. Symmetry 13(1):90

    Article  Google Scholar 

  9. Kala Z (2021) Global sensitivity analysis of quantiles: new importance measure based on superquantiles and subquantiles. Symmetry 13(2):263

    Article  Google Scholar 

  10. Molkenthin C, Scherbaum F, Griewank A et al (2017) Derivative-based global sensitivity analysis: upper bounding of sensitivities in seismic-hazard assessment using automatic differentiation. Bull Seismol Soc Amer 107(2):984–1004

    Article  Google Scholar 

  11. Li L, Lu Z, Chen C (2016) Moment-independent importance measure of correlated input variable and its state dependent parameter solution. Aerosp Sci Technol 48:281–290

    Article  Google Scholar 

  12. Morris MD (2012) Factorial sampling plans for preliminary computational experiments. Technometrics 33(2):161–174

    Article  Google Scholar 

  13. Xiao S, Lu Z, Xu L (2016) A new effective screening design for structural sensitivity analysis of failure probability with the epistemic uncertainty. Reliab Eng Syst Saf 156:1–14

    Article  Google Scholar 

  14. Saltelli A, Marivoet J (1990) Non-parametric statistics in sensitivity analysis for model output: a comparison of selected techniques. Reliab Eng Syst Saf 28(2):229–253

    Article  Google Scholar 

  15. Borgonovo E (2007) A new uncertainty importance measure. Reliab Eng Syst Saf 92(6):771–784

    Article  Google Scholar 

  16. Borgonovo E, Tarantola S, Plischke E et al (2014) Transformations and invariance in the sensitivity analysis of computer experiments. J R Stat Soc Ser B 76:925–947

    Article  MathSciNet  MATH  Google Scholar 

  17. Castaings W, Borgonovo E, Morris MD et al (2012) Sampling strategies in density-based sensitivity analysis. Environ Modell Softw 38:13–26

    Article  Google Scholar 

  18. Gamboa F, Klein T, Lagnoux A (2018) Sensitivity analysis based on cramer-von mises distance. SIAM/ASA J Uncertain Quantif 6(2):522–548

    Article  MathSciNet  MATH  Google Scholar 

  19. Liu Q, Homma T (2012) A new importance measure for sensitivity analysis. Taylor & Francis Group 47(1):53–61

    Google Scholar 

  20. Lemaître P, Sergienko E, Arnaud A et al (2015) Density modification-based reliability sensitivity analysis. J Stat Comput Simul 85:1200–1223

    Article  MathSciNet  MATH  Google Scholar 

  21. Wei P, Lu Z, Wu D et al (2013) Moment-independent regional sensitivity analysis: application to an environmental model. Environ Modell Softw 47:55–63

    Article  Google Scholar 

  22. Greegar G, Manohar CS (2015) Global response sensitivity analysis using probability distance measures and generalization of Sobol’s analysis. Probabilistic Eng Mech 41:21–33

    Article  Google Scholar 

  23. Stefanak J, Kala Z, Mica L et al (2018) Global sensitivity analysis for transformation of Hoek-Brown failure criterion for rock mass. J Civ Eng Manag 24(3–5):390–398

    Article  Google Scholar 

  24. Mahmoudi E, Holter R, Georgieva R, Konig M, Schanz T (2019) On the global sensitivity analysis methods in geotechnical engineering: a comparative study on a rock salt energy storage. Int J Civ Eng 17:131–143

    Article  Google Scholar 

  25. Pitchai P, Jha NK, Nair RG, Guruprasad PJ (2021) A coupled framework of variational asymptotic method based homogenization technique and Monte Carlo approach for the uncertainty and sensitivity analysis of unidirectional composites. Compos Struct 263:113656

    Article  Google Scholar 

  26. Ma YZ, Li HS, Zhao ZZ (2021) Reliability sensitivity analysis of thermal protection system. Struct Multidiscip Optim. https://doi.org/10.1007/s00158-021-02909-z

    Article  Google Scholar 

  27. Yang Z, Unsong P, Zhao H (2020) Reliability sensitivity analysis of stochastic resonance failure of vehicle drum brake. ICECTT. https://doi.org/10.1109/ICECTT50890.2020.00011

    Article  Google Scholar 

  28. Kala Z (2020) Sensitivity analysis in probabilistic structural design: a comparison of selected techniques. Sustainability 12(11):4788

    Article  Google Scholar 

  29. Cui LJ, Lu ZZ, Zhao XP (2010) Moment-independent importance measure of basic random variable and its probability density evolution solution. Sci China Technol Sci 53:1138–1145

    Article  MATH  Google Scholar 

  30. Li L, Lu Z, Jun F et al (2012) Moment-independent importance measure of basic variable and its state dependent parameter solution. Struct Saf 38:40–47

    Article  Google Scholar 

  31. Xiao S, Lu Z (2017) Structural reliability sensitivity analysis based on classification of model output. Aerosp Sci Technol 71:52–61

    Article  Google Scholar 

  32. Wei P, Lu Z, Yuan X (2013) Monte Carlo simulation for moment-independent sensitivity analysis. Reliab Eng Syst Saf 110:60–67

    Article  Google Scholar 

  33. Wei P, Lu Z, Hao W et al (2012) Efficient sampling methods for global reliability sensitivity analysis. Comput Phys Commun 183(8):1728–1743

    Article  MathSciNet  MATH  Google Scholar 

  34. Merz B, Thieken AH (2005) Separating natural and epistemic uncertainty in flood frequency analysis. J Hydrol 309:114–132

    Article  Google Scholar 

  35. Helton JC (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1–10

    Article  Google Scholar 

  36. Eldred MS, Swiler LP, Tang G (2011) Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation. Reliab Eng Syst Saf 96:1092–1113

    Article  Google Scholar 

  37. Helton JC, Oberkampf WL (2004) Alternative representations of epistemic uncertainty. Reliab Eng Syst Saf 85:1–10

    Article  Google Scholar 

  38. Sun S, Fu G, Djordjevic S et al (2012) Separating aleatory and epistemic uncertainties: probabilistic sewer flooding evaluation using probability box. J Hydrol 420:360–372

    Article  Google Scholar 

  39. Urbina A, Mahadevan S, Paez TL (2011) Quantification of margins and uncertainties of complex systems in the presence of aleatoric and epistemic uncertainty. Reliab Eng Syst Saf 96:1114–1125

    Article  Google Scholar 

  40. Wang P, Lu ZZ, Xiao SN (2017) A generalized separation for the variance contributions of input variables and their distribution parameters. Appl Math Model 47:381–399

    Article  MathSciNet  MATH  Google Scholar 

  41. Morio J (2011) Influence of input PDF parameters of a model on a failure probability estimation. Simul Model Pract Theory 19(10):2244–2255

    Article  Google Scholar 

  42. Krzykacz-Hausmann B (2006) An approximate sensitivity analysis of results from complex computer models in the presence of epistemic and aleatory uncertainties. Reliab Eng Syst Saf 91:1210–1218

    Article  Google Scholar 

  43. Hofer E, Kloos M, Krzykacz-Hausmann B et al (2002) An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties. Reliab Eng Syst Saf 77:229–238

    Article  Google Scholar 

  44. 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  MATH  Google Scholar 

  45. Wang P, Lu ZZ, Tang ZC (2013) Importance measure analysis with epistemic uncertainty and its moving least squares solution. Comput Math Appl 66(4):460–471

    Article  MathSciNet  MATH  Google Scholar 

  46. Sankararaman S, Mahadevan S (2011) Model validation under epistemic uncertainty. Reliab Eng Syst Saf 96:1232–1241

    Article  Google Scholar 

  47. Sankararaman S, Mahadevan S (2013) Separating the contributions of variability and parameter uncertainty in probability distributions. Reliab Eng Syst Saf 112:187–199

    Article  Google Scholar 

  48. Chabridon V, Balesdent M, Bourinet J-M et al (2017) Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment. Aerosp Sci Technol 69:526–537

    Article  Google Scholar 

  49. Chabridon V, Balesdent M, Perrin G, Morio J, Bourinet J-M, Gayton N (2018) Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty. Reliab Eng Syst Saf 178:164–178

    Article  Google Scholar 

  50. Chabridon V, Balesdent M, Perrin G et al (2021) Global reliability-oriented sensitivity analysis under distribution parameter uncertainty. Wiley, Hoboken

    Book  Google Scholar 

  51. Li G, Rabitz H (2012) General formulation of HDMR component functions with independent and correlated variables. J Math Chem 50(1):99–130

    Article  MathSciNet  MATH  Google Scholar 

  52. 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 

  53. 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 

  54. Bichon BJ, Eldred MS, Swiler LP et al (2012) Efficient global reliability analysis for nonlinear implicit performance functions. AIAA J 46:2459–2468

    Article  Google Scholar 

  55. Dumas A, Echard B, Gayton 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 

  56. Ishigami T, Homma T (1990) An importance quantification technique in uncertainty analysis for computer models, international symposium on uncertainty modeling & analysis. IEEE Xplore. https://doi.org/10.1109/ISUMA.1990.151285

    Article  Google Scholar 

  57. 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 70:1182–1197

    Article  MathSciNet  MATH  Google Scholar 

  58. Xiao NC, Zhan HY, Kai Y (2020) A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models. Comput Math Appl Mech Eng 372:113336

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51975473) and the Aviation Science Foundation for the Aviation Key Laboratory of Science and Technology on Life-support Technology (Grant No. 201929053001).

Author information

Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an, Shaanxi, People’s Republic of China

    Pan Wang, Chunyu Li, Fuchao Liu & Hanyuan Zhou

Authors
  1. Pan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fuchao Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hanyuan Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pan Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, P., Li, C., Liu, F. et al. Global sensitivity analysis of failure probability of structures with uncertainties of random variable and their distribution parameters. Engineering with Computers 38 (Suppl 5), 4367–4385 (2022). https://doi.org/10.1007/s00366-021-01484-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-021-01484-7

Keywords

Search

Navigation