Uncertainty Propagation Combining Robust Condensation and Generalized Polynomial Chaos Expansion

  • K. Chikhaoui
  • N. Kacem
  • N. Bouhaddi
  • M. Guedri
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Among probabilistic uncertainty propagation methods, the generalized Polynomial Chaos Expansion (gPCE) has recently shown a growing emphasis. The numerical cost of the non-intrusive regression method used to compute the gPCE coefficient depends on the successive Latin Hypercube Sampling (LHS) evaluations, especially for large size FE models, large number of uncertain parameters, presence of nonlinearities and when using iterative techniques to compute the dynamic responses. To overcome this issue, the regression technique is coupled with a robust condensation method adapted to the Craig-Bampton component mode synthesis approach leading to computational cost reduction without significant loss of accuracy. The performance of the proposed method and its comparison to the LHS simulation are illustrated by computing the time response of a structure composed of several coupled-beams containing localized nonlinearities and stochastic design parameters.


Robustness Uncertainty Generalized polynomial chaos expansion Component mode synthesis Metamodel 


  1. 1.
    Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81:23–69CrossRefGoogle Scholar
  2. 2.
    Xiu D, Karniadakis GE (2002) The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM J Sci Comput 24(2):619–644CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Berveiller M (2005) Eléments finis stochastiques : Approches intrusive et non intrusive pour des analyses de fiabilité, Ph.D. thesis. Université BLAISE PASCAL - Clermont II, AubièreGoogle Scholar
  4. 4.
    Blatman G, Sudret B (2010) An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis. Probab Eng Mech 25:183–197CrossRefGoogle Scholar
  5. 5.
    Craig RR Jr, Bampton MCC (1968) Coupling of substructures for dynamic analyses. AIAA J 6(7):1303–1319Google Scholar
  6. 6.
    Lombard JP (1999) Contribution à la réduction des modèles éléments finis par synthèse modale, Ph.D. thesis. Université de Franche-Comté, FranceGoogle Scholar
  7. 7.
    Bouazizi ML, Guedri M, Bouhaddi N (2006) Robust component modal synthesis method adapted to the survey of the dynamic behavior of structures with localized nonlinearities. Mech Syst Signal Process 20:131–157CrossRefGoogle Scholar
  8. 8.
    Guedri M, Bouhaddi N, Majed R (2006) Reduction of the stochastic finite element models using a robust dynamic condensation method. J Sound Vib 297:123–45CrossRefGoogle Scholar
  9. 9.
    Maute K, Weickum G, Eldred M (2009) A reduced-order stochastic finite element approach for design optimization under uncertainty. Struct Saf 31:450–459CrossRefGoogle Scholar
  10. 10.
    Afonso SMB, Motta RS (2013) Structural optimization under uncertainties considering reduced-order modeling, 10th world congress on structural and multidisciplinary optimization, Orlando, 19–24 May 2013Google Scholar
  11. 11.
    Hemez FM, Doebling SW (2003) From shock response spectrum to temporal moments and vice-versa, international modal analysis conference (IMAC-XXI), Kissimmee, 3–6 Feb 2003Google Scholar

Copyright information

© The Society for Experimental Mechanics, Inc. 2015

Authors and Affiliations

  • K. Chikhaoui
    • 1
    • 2
  • N. Kacem
    • 1
  • N. Bouhaddi
    • 1
  • M. Guedri
    • 2
  1. 1.FEMTO-ST Institute, UMR 6174, Applied Mechanics LaboratoryUniversity of Franche-ComtéBesançonFrance
  2. 2.National High School of Engineers of Tunis (ENSIT)University of TunisTunisTunisia

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