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Linear/Nonlinear Reduced-Order Substructuring for Uncertainty Quantification and Predictive Accuracy Assessment

  • Timothy Hasselman
  • George Lloyd
  • Ryan Schnalzer
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)

Abstract

Modal testing is routinely performed on space craft and launch vehicles to “verify” (calibrate and validate) analytical models. Large multi-component structures such as the Space Transportation System (STS) or “Space Shuttle,” and the newly proposed NASA Space Launch System (SLS), are impractical to test in their assembled configurations. Alternatively, substructure testing of these multi-component structures has been performed and used to calibrate/validate analytical models of the substructures, which are then assembled to analyze system response to applied loads. This paper describes a methodology applicable to uncertainty quantification (UQ) of reduced (modal) models of linear (or linearized) finite element models of substructures, as well as reduced (stochastic neural net (SNN)) models of nonlinear substructures, such as joints. The UQ at reduced substructure levels is propagated to higher levels of assembly by efficient means, enabling predictive accuracy assessment at the coupled system level. UQ is based entirely on comparisons on analysis and test data at the substructure level so that recourse to the specification and quantification of element-level random variables is not necessary. Examples are presented to illustrate the methodology.

Keywords

Uncertainty quantification Linear and nonlinear substructuring Reduced-order models component mode synthesis Stochastic neural networks Uncertainty propagation Predictive accuracy assessment 

Notes

Acknowledgements

This work has been supported by the Jet Propulsion Laboratory of Pasadena, California under a NASA STTR contract. The authors wish to thank Dr. Lee Peterson as COTR for his support and guidance on the project which addresses the quantification of margins and uncertainties (QMU) for integrated spacecraft systems. The authors also acknowledge the technical support provided by Dr. Thomas Paez who has contributed his expertise in probabilistic shock and vibration analysis, and has been very helpful in providing analytical models and software used in the numerical demonstrations.

References

  1. 1.
    Craig RR, Kurdila AJ (2006) Fundamentals of structural dynamics. Wiley, HobokenGoogle Scholar
  2. 2.
    Admire JR, Tinker ML, Ivey EW (1992) Mass-additive modal test method for verification of constrained structural models. In: Proceedings of the 10th international modal analysis conference, San Diego, CAGoogle Scholar
  3. 3.
    Gwinn KW, Lauffer JP, Miller AK (1988) Component mode synthesis using experimental modes enhanced by mass loading. In: Proceedings of the 6th international modal analysis conference, Kissimmee, FL, pp 1088–1093Google Scholar
  4. 4.
    Chandler KO, Tinker ML (1997) A general mass-additive method for component mode synthesis. In: Paper AIAA-97-1381, Proceedings of the 38th structures, structural dynamics and materials conference, Kissimmee, FL, pp 93–103Google Scholar
  5. 5.
    Hasselman TK, Lloyd GM, Red-Horse JR, Paez TL (2011) Quantification of margins and uncertainties (QMU) for integrated spacecraft system models, STTR Phase I Final Report, Report No. 11-744-1, ACTA Inc.Google Scholar
  6. 6.
    Hasselman TK (2001) Quantification of uncertainty in structural dynamic models. ASCE J Aerosp Eng 14(4):158–165Google Scholar
  7. 7.
    Guyan RJ (1965) Reduction of stiffness and mass matrices. AIAA J 3(2):380Google Scholar
  8. 8.
    Kammer D, Nimityongskul S (2011) Propagation of uncertainty in test/analysis correlation of substructured spacecraft. J Sound Vib 330: 1211–1224.Google Scholar
  9. 9.
    Lloyd G, Hasselman T, Paez T (2005) A proportional hazards neural network for performing reliability estimates and risk prognostics for mobile systems subject to stochastic covariates. In: Proceedings: ASME IMECE, Safety engineering and risk analysis/methods and tools for complex systems analysis, Orlando, FLGoogle Scholar
  10. 10.
    Bishop C (2000) Neural networks for pattern recognition. Oxford University Press, OxfordGoogle Scholar
  11. 11.
    Girosi F, Jones M, Poggio T (1995) Regularization theory and neural networks architectures. Neural Comput 7(2):219–269Google Scholar
  12. 12.
    Hasselman TK, Hart GC (1972) Modal analysis of random structural systems. J Eng Mech Div ASCE 98(EM3):561–579Google Scholar
  13. 13.
    Hasselman T, Chrostowski J (1994) Propagation of modeling uncertainty through structural dynamic models. Presented at the 35th AIAAASME/ASCE/AHS/ASC structures, structural dynamics and materials conference, Hilton Head, SC, 18–20 April 1994Google Scholar
  14. 14.
    Klema VC, Laub AJ (1980) The singular value decomposition; its computation and some applications. IEEE Trans Autom Control AC25(2):164–176.Google Scholar
  15. 15.
    Jackson JE (1991) A user’s guide to principal components. Wiley, New YorkGoogle Scholar
  16. 16.
    Iwan WD (1966) Distributed-element model for hysteresis and its steady state dynamic response. J Appl Mech 33(4):893–900. Trans. ASME, Vol. 88, Series E, DecGoogle Scholar

Copyright information

© The Society for Experimental Mechanics 2014

Authors and Affiliations

  • Timothy Hasselman
    • 1
  • George Lloyd
    • 1
  • Ryan Schnalzer
    • 1
  1. 1.ACTA IncorporatedTorranceUSA

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