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Dynamic reliability analysis model for structure with both random and interval uncertainties

  • Yan Shi
  • Zhenzhou LuEmail author
Article

Abstract

Aiming at analyzing the safety of the dynamic structure involving both input random variables and the interval ones, a new dynamic reliability analysis model is presented by constructing a second level limit state function. Two steps are involved in the construction of the dynamic reliability model. In the first step, the non-probabilistic reliability index is firstly extended to the dynamic structure, in which the uncertainties of interval inputs can be analyzed by fixing random inputs and time parameter. In the second step, the second level limit state function is constructed by considering the fact that the non-probabilistic reliability index larger than one corresponds to the safe state, in which the uncertainties of random inputs are taken into account. Generally, the actual reliability of dynamic structure with both random and interval inputs is an interval variable, and theoretic analysis illustrates that the proposed reliability is equivalent to the lower bound of the actual reliability, which can provide an efficient way for measuring the safety of dynamic structure. For estimating the proposed reliability, a double-loop optimization algorithm combined with Monte Carlo Simulation as well as the active learning Kriging method is established. Several examples involving a cylindrical pressure vessel, an automobile front axle and a planar 10-bar structure are introduced to illustrate the validity and significance of the established reliability model and the efficiency and accuracy of the proposed solving procedure.

Keywords

Dynamic reliability analysis Hybrid input variables Non-probabilistic reliability index Kriging surrogate 

Notes

Acknowledgements

This work was supported by the Natural Science Foundation of China (Grants 51475370 and 51775439).

References

  1. Abdelal, G.F., Abuelfoutouh, N., Hamdy, A.: Mechanical fatigue and spectrum analysis of small-statellite structure. Int. J. Mech. Mater. Des. 4(3), 265–278 (2008)CrossRefGoogle Scholar
  2. Abdelal, G.F., Cooper, J.E., Robotham, A.J.: Reliability assessment of 3D space frame structures applying stochastic finite element analysis. Int. J. Mech. Mater. Des. 9(1), 1–9 (2013)CrossRefGoogle Scholar
  3. Antonio, C.C., Hoffbauer, L.N.: Uncertainty propagation in inverse reliability-based design of composite structures. Int. J. Mech. Mater. Des. 6(1), 89–102 (2010)CrossRefGoogle Scholar
  4. Balu, A.S., Rao, B.N.: Explicit fuzzy analysis of systems with imprecise properties. Int. J. Mech. Mater. Des. 7(4), 283–289 (2017)CrossRefGoogle Scholar
  5. Ben-Haim, Y.: A non-probabilistic concept of reliability. Struct. Saf. 14(4), 227–245 (1994)CrossRefGoogle Scholar
  6. Ben-Haim, Y.: Discussion on the paper: a non-probabilistic concept of reliability. Struct. Saf. 17(3), 195–199 (1995)CrossRefGoogle Scholar
  7. Carneiro, G.N., Antonio, C.C.: Robustness and reliability of composite structures: effects of different sources of uncertainty. Int. J. Mech. Mater. Des. (2017).  https://doi.org/10.1007/s10999-017-9401-6 Google Scholar
  8. Chen, X., Yao, W., Zhao, Y.: An extended probabilistic method for reliability analysis under mixed aleatory and epistemic uncertainties with flexible intervals. Struct. Multidiscip. Optim. 54(6), 1641–1652 (2016)MathSciNetCrossRefGoogle Scholar
  9. Du, X.P., Sudjianto, A., Huang, B.Q.: Reliability-based design with the mixture of random and interval variables. J. Mech. Des. 127(6), 1068–1076 (2005)CrossRefGoogle Scholar
  10. Echars, B., Gayton, N., Lemaire, M.: AK-MCS: an active learning reliability method combining Kriging and Monte Carlo simulation. Struct. Saf. 33, 145–154 (2011)CrossRefGoogle Scholar
  11. Elishakoff, I.: Essay on uncertainties in elastic and viscoelastic structure: from A.M. Freudenthal’s criticisms to modern convex modeling. Comput. Struct. 56(6), 871–895 (1995)CrossRefzbMATHGoogle Scholar
  12. Geng, X.Y., Wang, X.J., Wang, L., et al.: Non-probabilistic time-dependent kinematic reliability assessment for function generation mechanisms with joint clearances. Mech. Mach. Theory 104, 202–221 (2016)CrossRefGoogle Scholar
  13. Guo, S.X., Lu, Z.Z.: Hybrid probabilistic and non-probabilistic model of structural reliability. J. Mech. Strength 24(4), 524–526 (2002)Google Scholar
  14. Guo, S.X., Lu, Z.Z., Feng, Y.S.: A non-probabilistic model of structural reliability based on interval analysis. Chin. J. Comput. Mech. 18, 56–60 (2001)Google Scholar
  15. Guo, S.X., Zhang, L., Li, Y.: Procedures for computing the non-probabilistic reliability index of uncertain in structures. Chin. J. Comput. Mech. 22, 227–231 (2002)Google Scholar
  16. Guo, J., Wang, Y., Zeng, S.: Nonintrusive-polynomial-chaos-based kinematic reliability analysis for mechanisms with mixed uncertainty. Adv. Mech. Eng. 6, 690985 (2015)CrossRefGoogle Scholar
  17. Hu, Z., Du, X.: Time-dependent reliability analysis with joint upcrossing rates. Struct. Multidiscip. Optim. 48(5), 893–907 (2013)MathSciNetCrossRefGoogle Scholar
  18. Huang, Z.L., Jiang, C., Zhou, Y.S., Zheng, J., Long, X.Y.: Reliability-based design optimization for problems with interval distribution parameters. Struct. Multidiscip. Optim. 55, 513–528 (2017)MathSciNetCrossRefGoogle Scholar
  19. Jiang, T., Chen, J.J., Jiang, P.G., et al.: A one-dimensional optimization algorithm for non-probabilistic reliability index. Eng. Mech. 24(7), 23–27 (2007)Google Scholar
  20. Jiang, C., Lu, G.Y., Han, X., et al.: A new reliability analysis method for uncertain structures with random and interval variables. Int. J. Mech. Mater. Des. 8, 169–182 (2012)CrossRefGoogle Scholar
  21. Jiang, C., Bi, R.G., Lu, G.Y., et al.: Structural reliability analysis using non-probabilistic convex model. Comput. Methods Appl. Mech. Eng. 254, 83–98 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  22. Jiang, C., Huang, X.P., Wei, X.P.: A time-variant reliability analysis method for structural systems based on stochastic process discretization. Int. J. Mech. Mater. Des. 13(2), 173–193 (2017)CrossRefGoogle Scholar
  23. Jiang, C., Zheng, J., Han, X.: Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: a review. Struct. Multidiscip. Optim. 57(6), 2485–2502 (2018)CrossRefGoogle Scholar
  24. Lemaire, M.: Structural Reliability. Wiley, London (2009)CrossRefGoogle Scholar
  25. Liu, J., Sun, X.S., Meng, X.H.: A novel shape function approach of dynamic load identification for the structures with interval uncertainty. Int. J. Mech. Mater. Des. 12(3), 375–386 (2016)CrossRefGoogle Scholar
  26. Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE-A MATLAB Kriging Toolbox. Technical University of Denmark, Kongens Lyngby (2002)Google Scholar
  27. Pang, H., Yu, T.X., Song, B.F.: Failure mechanism analysis and reliability assessment of an aircraft slat. Eng. Fail. Anal. 60, 261–279 (2016)CrossRefGoogle Scholar
  28. Qiu, Z.P., Mueller, P.C., Frommer, A.: The new non-probabilistic criterion of failure for dynamical systems based on convex models. Math. Comput. Model. 40, 201–215 (2004)CrossRefzbMATHGoogle Scholar
  29. Qiu, Z.P., Ma, L.H., Wang, X.J.: Non-probabilistic interval analysis method for dynamic response analysis of nonlinear systems with uncertainty. J. Sound Vib. 319, 531–540 (2009)CrossRefGoogle Scholar
  30. Shi, Y., Lu, Z.Z., Cheng, K., et al.: Temporal and spatial multi-parameter dynamic reliability and global reliability sensitivity analysis based on the extreme value moments. Struct. Multidiscip. Optim. 56(1), 117–129 (2017)MathSciNetCrossRefGoogle Scholar
  31. Sobol’, I.M.: On quasi-monte carlo integrations. Math. Comput. Simul. 47(2), 103–112 (1998)MathSciNetCrossRefGoogle Scholar
  32. Stampouloglou, I.H., Theotokoglou, E.E.: Investigation of the problem of a plane axisymmetric cylindrical tube under internal and external pressures. Int. J. Mech. Mater. Des. 3(1), 59–71 (2006)CrossRefGoogle Scholar
  33. Wu, J.L., Luo, Z., Zhang, N., Zhang, Y.Q.: A new uncertain analysis method and its application in vehicle dynamics. Mech. Syst. Signal Process. 50–51, 659–675 (2015)CrossRefGoogle Scholar
  34. Zheng, J., Luo, Z., Li, H., Jiang, C.: Robust topology optimization for cellular composites with hybrid uncertainties. Int. J. Numer. Meth. Eng. 115(6), 695–713 (2018)MathSciNetCrossRefGoogle Scholar
  35. Zou, L., Liu, X., Hu, X.L., et al.: Dynamic reliability of shock absorption rubber structure with probability-interval mixed uncertainty. Chin. J. Appl. Mech. 32(2), 197–204 (2015)Google Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of AeronauticsNorthwestern Polytechnical UniversityXi’anChina

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