Startseite A Novel Reliability Analysis Method for Turbine Discs with the Mixture of Fuzzy and Probability-Box Variables
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A Novel Reliability Analysis Method for Turbine Discs with the Mixture of Fuzzy and Probability-Box Variables

  • Xiaoqiang Zhang , Huiying Gao , Yan-Feng Li und Hong-Zhong Huang EMAIL logo
Veröffentlicht/Copyright: 24. August 2018
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Abstract

Fuzzy and probability-box (p-box) variables exit widely in aerospace engineering. To evaluate the reliability of turbine discs under the mixture of these two types of variables and guarantee safety, the critical point lies in how to deal with the fuzzy variables. In this paper, a novel method based on equivalent transformation of entropy and saddlepoint approximation (SPA) is proposed to estimate the reliability of turbine discs with the mixture of fuzzy and p-box variables. The advantage of the proposed method is that it can transform fuzzy variables whose memberships are non-normal into normal random variables through entropy invariability; meanwhile, using the SPA, the required sample size and corresponding computational cost decreases greatly. An example is used to illustrate the proposed method and a comparison is also made with the interval Monte Carlo simulation (IMCS). The results indicate that the proposed method is promising and has higher efficiency with almost the same accuracy.

Acknowledgements

This research was supported by the National Natural Science Foundation of China under contract number 51775090, the Fundamental Research Funds for the Central Universities under contract numbers ZYGX2014Z010 and SKLMT-KFKT-201601.

References

1. Li C, Mahadevan S. Relative contributions of aleatory and epistemic uncertainty sources in time series prediction. Int J Fatigue. 2016;82:474–86.10.1016/j.ijfatigue.2015.09.002Suche in Google Scholar

2. Huang HZ, Huang CG, Peng Z, Li YF, Yin H. Fatigue life prediction of fan blade using nominal stress method and cumulative fatigue damage theory. Int J Turbo Jet Engines. DOI:https://doi.org/10.1515/tjj-2017-0015 Suche in Google Scholar

3. Zheng B, Huang HZ, Guo W, Li YF, Mi J. Fault diagnosis method based on supervised particle swarm optimization classification algorithm. Intell Data Anal. 2018;22:191–210.10.3233/IDA-163392Suche in Google Scholar

4. Davis JP, Hall JW. A software-supported process for assembling evidence and handling uncertainty in decision-making. Decis Support Syst. 2003;35:415–33.10.1016/S0167-9236(02)00117-3Suche in Google Scholar

5. Zadeh LA. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1999;100:9–34.10.1016/S0165-0114(99)80004-9Suche in Google Scholar

6. Klir GJ. Generalized information theory: aims, results, and open problems. Reliab Eng Syst Saf. 2004;85:21–38.10.1016/j.ress.2004.03.003Suche in Google Scholar

7. Mi J, Li YF, Peng W, Huang HZ. Reliability analysis of complex multi-state system with common cause failure based on evidential networks. Reliab Eng Syst Saf. 2018;174:71–81.10.1016/j.ress.2018.02.021Suche in Google Scholar

8. Hurtado JE, Alvarez DA, Ramírez J. Fuzzy structural analysis based on fundamental reliability concepts. Comput Struct. 2012;112:183–92.10.1016/j.compstruc.2012.08.004Suche in Google Scholar

9. Jiang C, Han X, Lu GY, Liu J, Zhang Z, Bai YC. Correlation analysis of non-probabilistic convex model and corresponding structural reliability technique. Comput Meth Appl Mech Eng. 2011;200:2528–46.10.1016/j.cma.2011.04.007Suche in Google Scholar

10. Luo Y, Kang Z, Li A. Structural reliability assessment based on probability and convex set mixed model. Comput Struct. 2009;87:1408–15.10.1016/j.compstruc.2009.06.001Suche in Google Scholar

11. Kang Z, Luo Y. Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Comput Meth Appl Mech Eng. 2009;198:3228–38.10.1016/j.cma.2009.06.001Suche in Google Scholar

12. Li YF, Mi J, Liu Y, Yang YJ, Huang HZ. Dynamic fault tree analysis based on continuous-time Bayesian networks under fuzzy numbers. Proc Inst Mech Eng Part O J Risk Reliab. 2015;229:530–41.10.1177/1748006X15588446Suche in Google Scholar

13. Penmetsa RC, Grandhi RV. Efficient estimation of structural reliability for problems with uncertain intervals. Comput Struct. 2002;80:1103–12.10.2514/6.2001-1648Suche in Google Scholar

14. Bae HR, Grandhi RV, Canfield RA. Epistemic uncertainty quantification techniques including evidence theory for large-scale structures. Comput Struct. 2004;82:1101–12.10.1016/j.compstruc.2004.03.014Suche in Google Scholar

15. Helton JC, Johnson JD, Oberkampf WL, Storlie CB. A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Comput Meth Appl Mech Eng. 2007;196:3980–98.10.1016/j.cma.2006.10.049Suche in Google Scholar

16. Hofer E, Kloos M, Krzykacz-Hausmann B, Peschke J, Woltereck M. An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties. Reliab Eng Syst Saf. 2002;77:229–38.10.1016/S0951-8320(02)00056-XSuche in Google Scholar

17. Youn BD, Choi KK, Du L, Gorsich D. Integration of possibility-based optimization and robust design for epistemic uncertainty. J Mech Des. 2007;129:876–82.10.1115/1.2717232Suche in Google Scholar

18. Jakeman J, Eldred M, Xiu D. Numerical approach for quantification of epistemic uncertainty. J Comput Phys. 2010;229:4648–63.10.1016/j.jcp.2010.03.003Suche in Google Scholar

19. Möller B, Graf W, Beer M. Fuzzy structural analysis using α-level optimization. Comput Mech. 2000;26:547–65.10.1007/s004660000204Suche in Google Scholar

20. Bagheri M, Miri M, Shabakhty N. Fuzzy reliability analysis using a new alpha level set optimization approach based on particle swarm optimization. J Intell Fuzzy Syst. 2016;30:235–44.10.3233/IFS-151749Suche in Google Scholar

21. Li XY, Huang HZ, Li YF. Reliability Analysis of phased mission system with non-exponential and partially repairable components. Reliab Eng Syst Saf. 2018;175:119–27.10.1016/j.ress.2018.03.008Suche in Google Scholar

22. Yang X, Liu Y, Zhang Y, Yue Z. Hybrid reliability analysis with both random and probability-box variables. Acta Mech. 2015;226:1341–57.10.1007/s00707-014-1252-8Suche in Google Scholar

23. Xiao NC, Li YF, Yu L, Wang Z, Huang HZ. Saddlepoint approximation-based reliability analysis method for structural systems with parameter uncertainties. Proc Inst Mech Eng Part O J Risk Reliab. 2014;228:529–40.10.1177/1748006X14537619Suche in Google Scholar

24. Beer M. Fuzzy probability theory. In: Encyclopedia of complexity and systems science. Editors: Robert A. Meyers, New York: Springer, 2009.10.1007/978-0-387-30440-3_237Suche in Google Scholar

25. Krätschmer V. A unified approach to fuzzy random variables. Fuzzy Sets Syst. 2001;123:1–9.10.1016/S0165-0114(00)00038-5Suche in Google Scholar

26. Crespo LG, Kenny SP, Giesy DP. Reliability analysis of polynomial systems subject to p-box uncertainties. Mech Syst Signal Process. 2013;37:121–36.10.1016/j.ymssp.2012.08.012Suche in Google Scholar

27. Hurtado JE, Alvarez DA, Paredes JA. Interval reliability analysis under the specification of statistical information on the input variables. Struct Saf. 2017;65:35–48.10.1016/j.strusafe.2016.12.005Suche in Google Scholar

28. Corder GW, Foreman DI. Nonparametric statistics: a step-by-step approach. Hoboken: John Wiley & Sons, 2014.Suche in Google Scholar

29. Smith JE. Generalized Chebychev inequalities: theory and applications in decision analysis[J]. Oper Res. 1995;43:807–25.10.1287/opre.43.5.807Suche in Google Scholar

30. Du X, Sudjianto A. First-order saddlepoint approximation for reliability analysis. AIAA J. 2004;42:1199–207.10.2514/6.2004-4355Suche in Google Scholar

31. Yuen KV, Wang J, Au SK. Application of saddlepoint approximation in reliability analysis of dynamic systems. Earthquake Eng Eng Vib. 2007;6:391–400.10.1007/s11803-007-0773-8Suche in Google Scholar

32. Huang B, Du X. Probabilistic uncertainty analysis by mean-value first order saddlepoint approximation. Reliab Eng Syst Saf. 2008;93:325–36.10.1016/j.ress.2006.10.021Suche in Google Scholar

33. Huang B, Du X, Lakshminarayana RE. A saddlepoint approximation based simulation method for uncertainty analysis. Int J Reliab Saf. 2006;1:206–24.10.1504/IJRS.2006.010698Suche in Google Scholar

34. Daniels HE. Saddlepoint approximations in statistics. Ann Math Stat. 1954;25:631–50.10.1214/aoms/1177728652Suche in Google Scholar

35. Lugannani R, Rice S. Saddle point approximation for the distribution of the sum of independent random variables. Adv Appl Probab. 1980;12:475–90.10.2307/1426607Suche in Google Scholar

36. Davison AC, Mastropietro D. Saddlepoint approximation for mixture models. Biometrika. 2009;96:479–86.10.1093/biomet/asp022Suche in Google Scholar

37. Li YF, Huang HZ, Liu Y, Xiao N, Li H. A new fault tree analysis method: fuzzy dynamic fault tree analysis. Eksploatacja i Niezawodnosc - Maintenance Reliab. 2012;14:208–14.Suche in Google Scholar

38. Shannon CE, Weaver W. The mathematical theory of communication. Urbana: University of Illinois Press, 1998.Suche in Google Scholar

39. Trillas E, Riera T. Entropies in finite fuzzy sets. Inf Sci. 1978;15:159–68.10.1016/0020-0255(78)90005-1Suche in Google Scholar

40. Brown CB. Entropy constructed probabilities. J Eng Mech Div. 1980;106:633–40.10.1061/JMCEA3.0002614Suche in Google Scholar

41. Kam TY, Brown CB. Updating parameters with fuzzy entropies. J Eng Mech. 1983;109:1334–43.10.1061/(ASCE)0733-9399(1983)109:6(1334)Suche in Google Scholar

42. Zadeh LA. Probability measures of fuzzy events. J Math Anal Appl. 1968;23:421–7.10.1016/0022-247X(68)90078-4Suche in Google Scholar

43. Feizabadi M, Jahromi AE. A new model for reliability optimization of series-parallel systems with non-homogeneous components. Reliab Eng Syst Saf. 2017;157:101–12.10.1016/j.ress.2016.08.023Suche in Google Scholar

44. Guo SX, Zhang L, Li Y. Procedures for computing the non-probabilistic reliability index of uncertain structures. Chin J Comput Mech. 2005;22:227–31.Suche in Google Scholar

45. Zhang H, Mullen RL, Muhanna RL. Interval Monte Carlo methods for structural reliability. Struct Saf. 2010;32:183–90.10.1016/j.strusafe.2010.01.001Suche in Google Scholar

Received: 2018-07-22
Accepted: 2018-08-09
Published Online: 2018-08-24
Published in Print: 2022-08-26

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Editorial
  3. Study on Global Aerodynamic Shape Optimization of Transonic Compressor Blade
  4. Original Research Articles
  5. The Migration of Corner Separation Flow in Multi-Channel Compressor Cascades at High Attack Angle
  6. Water Film Formation and Performance Effect on Compressor Stage in Water Injection Process
  7. A Novel Reliability Analysis Method for Turbine Discs with the Mixture of Fuzzy and Probability-Box Variables
  8. Numerical Study of Unsteady Pulsed Suction through Endwall Bleed Holes in a Highly Loaded Compressor Cascade
  9. A Study on Torsional Vibration Suppression Method for an Integrated Helicopter / Engine System
  10. Numerical Simulation of Supersonic Jet Control by Tabs with Slanted Perforation
  11. Effect of Gurney Flaps on the Aerodynamic Characteristics of NACA 0010 Cascades
  12. A Study on Nonlinear Model Predictive Control for Helicopter/Engine with Variable Rotor Speed Based on Linear Kalman Filter
  13. Performance Characteristic Modeling for 2D Compressor Cascades
  14. Numerical Investigation on Metrological Fidelity of a Shielded Thermocouple Probe and the Effects of Geometrical Parameters
  15. Experimental Study of Kerosene Ignition and Flame Stabilization in a Supersonic Combustor
  16. Metaheuristics Optimized Machine Learning Modelling of Environmental Exergo-Emissions for an Aero-Engine
  17. Nonlinear Model Predictive Control Strategy for Limit Management of Aero-Engines
  18. Numerical Investigation on the Cold Flow Field of a Typical Cavity-based Scramjet Combustor with Double Ramp Entry
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