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An improved Kriging-based approach for system reliability analysis with multiple failure modes

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Abstract

Reliability analysis with multiple failure modes is needed because more than one failure mode exists in many engineering applications. Kriging-based surrogate model is widely adopted for component reliability analysis because of its high computational efficiency. Compared with Kriging-based component reliability analysis, selecting the sample points that affect the system performance is more difficult than that of a single failure mode in system reliability analysis. Therefore, how to select suitable sample points is a key problem in system reliability analysis. Meanwhile, reducing the number of calls to the performance functions is challenging, especially for systems with time-consuming performance functions. In this paper, an improved Kriging-based system reliability analysis approach is proposed based on the two strategies. In strategy 1, the initial sample points are determined by considering only two different cases: (a) the candidate samples are selected from the safe regions only for series systems; (b) the candidate samples are selected from the failure regions only for parallel systems. Therefore, samples having little contributions to the composite performance function are avoided. In strategy 2, the sample points determined in strategy 1 will be further optimized by interpolating. From comparisons with three reported methods in numerical examples, the efficiency and accuracy of the proposed method are illustrated.

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References

  1. Gandoman FH, Ahmadi A, Bossche PV, Mierlo JV, Omar N et al (2019) Status and future perspectives of reliability assessment for electric vehicles. Reliab Eng Syst Saf 183:1–16

    Article  Google Scholar 

  2. Tu B, Fang Z, Dong Y, Frangopol DM (2017) Time-variant reliability analysis of widened deteriorating prestressed concrete bridges considering shrinkage and creep. Eng Struct 153:1–16

    Article  Google Scholar 

  3. Zhang D, Han X (2020) Kinematic reliability analysis of robotic manipulator”. J Mech Des N Y 142(4):044502

    Article  Google Scholar 

  4. Palacios JA, Ganesan R (2019) Reliability evaluation of carbonnanotube-reinforced-polymer composites based on multiscale finite element model. Compos Struct 229:111381

    Article  Google Scholar 

  5. Zhao H, Li S, Ru Z (2017) Adaptive reliability analysis based on a support vector machine and its application to rock engineering. Appl Math Model 44:508–522

    Article  Google Scholar 

  6. Guimaraes H, Matos JC, Henriques AA (2018) An innovative adaptive sparse response surface method for structural reliability analysis. Struct Saf 73:12–28

    Article  Google Scholar 

  7. Marelli S, Sudret B (2018) An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis. Struct Saf 75:67–74

    Article  Google Scholar 

  8. Marugan AP, Chacón AMP, Márquez FPG (2019) Reliability analysis of detecting false alarms that employ neural networks: a real case study on wind turbines. Reliab Eng Syst Saf 191:106574

    Article  Google Scholar 

  9. Zhang D, Zhang N, Ye N, Fang J, Han X (2020) Hybrid learning algorithm of radial basis function networks for reliability analysis. IEEE Trans Reliab. https://doi.org/10.1109/TR.2020.3001232

    Article  Google Scholar 

  10. Wan L, Chen H, Ouyang L, Chen Y (2020) A new ensemble modeling approach for reliability-based design optimization of flexure-based bridge-type amplification mechanisms. Int J Adv Manuf Technol 106(1–2):47–63

    Article  Google Scholar 

  11. Feng J, Liu L, Wu D, Li G, Beer M, Gao W (2019) Dynamic reliability analysis using the extended support vector regression (X-SVR). Mech Syst Signal Process 126:368–391

    Article  Google Scholar 

  12. 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 

  13. Zhou CN, Xiao NC, Zuo MJ, Huang X (2020) Ak-pdf: an active learning method combining kriging and probability density function for efficient reliability analysis. Proc Inst Mech Eng O J Risk Reliab 234(3):536–549

    Google Scholar 

  14. Xiao NC, Zuo MJ, Zhou CN (2018) A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis. Reliab Eng Syst Saf 169:330–338

    Article  Google Scholar 

  15. Fauriat W, Gayton N (2014) AK-SYS: an adaptation of the AK-MCS method for system reliability. Reliab Eng Syst Saf 123:137–144

    Article  Google Scholar 

  16. Yang X, Liu Y, Mi C, Tang C (2018) System reliability analysis through active learning kriging model with truncated candidate region. Reliab Eng Syst Saf 169:235–241

    Article  Google Scholar 

  17. Jiang C, Qiu H, Yang Z, Chen L, Gao L, Li P (2019) A general failure-pursuing sampling framework for surrogate-based reliability analysis. Reliab Eng Syst Saf 183:47–59

    Article  Google Scholar 

  18. Xiao M, Zhang J, Gao L (2020) A system active learning Kriging method for system reliability-based design optimization with a multiple response model. Reliab Eng Syst Saf 199:106935

    Article  Google Scholar 

  19. Yi J, Zhou Q, Cheng Y, Liu J (2020) Efficient adaptive Kriging-based reliability analysis combining new learning function and error-based stopping criterion. Struct Multidiscipl Optim 62(5):2517–2536

  20. 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 Methods Appl Mech Eng 372:113336

    Article  MathSciNet  Google Scholar 

  21. Yun W, Lu Z, Zhou Y, Jiang X (2019) Ak-sysi: an improved adaptive kriging model for system reliability analysis with multiple failure modes by a refined u learning function. Struct Multidiscip Optim 59(1):263–278

    Article  MathSciNet  Google Scholar 

  22. Xiao NC, Yuan K, Zhou CN (2020) Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables. Comput Methods Appl Mech Eng 359:112649

  23. Gong C, Zhou W (2018) Importance sampling-based system reliability analysis of corroding pipelines considering multiple failure modes. Reliab Eng Syst Saf 169:199–208

    Article  Google Scholar 

  24. Fisher RA (1936) Design of experiments. Br Med J. https://doi.org/10.1136/bmj.1.3923.554-a

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Krige DG (1951) A statistical approach to some basic mine valuation problems on the Witwatersrand. J S Afr Inst Min Metall 52(6):119–139

    Google Scholar 

  27. Kiš IM (2016) Comparison of Ordinary and Universal Kriging interpolation techniques on a depth variable (a case of linear spatial trend), case study of the Šandrovac Field. Rudarsko Geološko Naftni Zbornik. https://doi.org/10.17794/rgnzbornik.v31i2.3862

  28. Oliver MA, Webster R (1990) Kriging: a method of interpolation for geographical information systems. Int Geogr Inf Syst 4(3):313–332

    Article  Google Scholar 

  29. Zhang J, Xiao M, Gao L, Fu J (2018) A novel projection outline based active learning method and its combination with Kriging metamodel for hybrid reliability analysis with random and interval variables. Comput Methods Appl Mech Eng 341:32–52

    Article  MathSciNet  Google Scholar 

  30. Xiao M, Zhang J, Gao L, Lee S, Eshghi AT (2019) An efficient Kriging-based subset simulation method for hybrid reliability analysis under random and interval variables with small failure probability. Struct Multidiscip Optim 59(6):2077–2092

    Article  MathSciNet  Google Scholar 

  31. Jiang C, Qiu HB, Li XK, Chen ZZ, Gao L, Li PG (2020) Iterative reliable design space approach for efficient reliability-based design optimization. Eng Comput 36(1):151–169

    Article  Google Scholar 

  32. Perrin G (2016) Active learning surrogate models for the conception of systems with multiple failure modes. Reliab Eng Syst Saf 149:130–136

    Article  Google Scholar 

  33. Sacks J, Schiller SB, Welch WJ (1989) Designs for computer experiments. Technometrics 31(1):41–47

    Article  MathSciNet  Google Scholar 

  34. Lophaven SN, Nielsen HB, Søndergaard J (2002) DACE—a matlab kriging toolbox. Version 2.0

  35. Kaymaz I (2005) Application of kriging method to structural reliability problems. Struct Saf 27(2):133–151

    Article  Google Scholar 

  36. Zhang L, Lu Z, Wang P (2015) Efficient structural reliability analysis method based on advanced kriging model. Appl Math Model 39(2):781–793

    Article  MathSciNet  Google Scholar 

  37. Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13(4):455–492

    Article  MathSciNet  Google Scholar 

  38. Cui JD, Shen XL (2018) The finite element method programming and application. CHN Arch Bldg Press, Beijing

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51975105 and 51537010), and the Sichuan Science and Technology Program under Grant No. 2020YJ0030.

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Correspondence to Ning-Cong Xiao.

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Zhou, C., Xiao, NC., Zuo, M.J. et al. An improved Kriging-based approach for system reliability analysis with multiple failure modes. Engineering with Computers 38 (Suppl 3), 1813–1833 (2022). https://doi.org/10.1007/s00366-021-01349-z

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