Skip to main content
SpringerLink
Log in
Book cover

Sensors, Instrumentation and Special Topics, Volume 6 pp 137–154Cite as

Optimal Selection of Artificial Boundary Conditions for Model Update and Damage Detection

  • Conference paper
  • First Online:

  • 1169 Accesses

Abstract

Sensitivity-based model error localization and damage detection is hindered by the relative differences in modal sensitivity magnitude among updating parameters. The method of artificial boundary conditions is shown to directly address this limitation, resulting in the increase of the number of updating parameters at which errors can be accurately localized. Using a single set of FRF data collected from a modal test, the artificial boundary conditions (ABC) method identifies experimentally the natural frequencies of a structure under test for a variety of different boundary conditions, without having to physically apply the boundary conditions, hence the term "artificial." The parameter-specific optimal ABC sets applied to the finite element model will produce increased sensitivities in the updating parameter, yielding accurate error localization and damage detection solutions. A method is developed for identifying the parameter-specific optimal ABC sets for updating or damage detection, and is based on the QR decomposition with column pivoting. Updating solution residuals, such as magnitude error and false error location, are shown to be minimized when the updating parameter set is limited to those corresponding to the QR pivot columns. The existence of an optimal ABC set for a given updating parameter is shown to be dependent on the number of modes used, and hence the method developed provides a systematic determination of the number of modes required for localization in a given updating parameter. These various concepts are demonstrated on a simple model with simulated test data.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. Lallement, J. Piranda, Localisation methods for parameter updating of finite element models in elastodynamics, 8th International Modal Analysis Conference. (1990) Orlando, Florida, USA. pp. 579-585.

    Google Scholar 

  2. W. D'Ambrogio, A. Fregolent, Dynamic model updating using virtual antiresonances, Shock and Vibration, 11 (2004) 351-363.

    Google Scholar 

  3. J.E. Mottershead, On the zeros of structural frequency response functions and their sensitivities, Mechanical Systems and Signal Processing. 12(5) (1998) 591-597.

    Article  Google Scholar 

  4. W. D'Ambrogio, A. Fregolent, The use of antiresonances for robust model updating, Journal of Sound and Vibration 236(2) (2000) 227-243.

    Article  Google Scholar 

  5. K. Jones, J. Turcotte, Finite element model updating using antiresonant frequencies. Journal of Sound and Vibration 252(4) (2002) 717-727.

    Article  Google Scholar 

  6. W. D'Ambrogio, A. Fregolent, Results obtained by minimizing natural frequency and antiresonance errors of a beam model, Mechanical Systems and Signal Processing 17(1) (2003) 29-37.

    Article  Google Scholar 

  7. D. Hanson, T.P. Waters, D.J. Thompson, R.B. Randall, R.A.J. Ford, The role of anti-resonance frequencies from operational modal analysis in finite element model updating, Mechanical Systems and Signal Processing 21 (2007) 74-97.

    Article  Google Scholar 

  8. S. Li, S. Shelley, and D. Brown, Perturbed boundary condition testing, Proceedings of the 13th International Modal Analysis Conference, Vol. 1 (1995) 902-907.

    Google Scholar 

  9. B.K. Wada, C.P. Kui, R.J. Glaser, Extension of ground-based testing for large space structures, Journal of Spacecraft, Vol. 23 No. 2 (1986) 184-188.

    Article  Google Scholar 

  10. B.K. Wada, C.P. Kuo, R.J. Glaser, Multiple boundary condition tests (MBCT) for verification of large space structures, AIAA Paper 86-0905 (1986).

    Google Scholar 

  11. C.P. Kuo, B.K. Wada, System identification of a truss type space structure using the multiple boundary condition test (MBCT) method, AIAA Paper 87-0746 (1987).

    Google Scholar 

  12. C.P. Kuo, B.K. Wada, Multiple boundary condition test (MBCT): Identification with mode shapes, AIAA Paper 88-2353. (1988).

    Google Scholar 

  13. J. H. Gordis, Artificial boundary conditions for model updating and damage detection, journal of mechanical systems and signal processing, Vol. 13, No. 3 (1999) 437-448.

    Article  Google Scholar 

  14. J. H. Gordis, Omitted coordinate systems and artificial constraints in spatially incomplete identification.” Int. J. Anal. Exp. Modal Anal, Vol. 11 No. 1-2. (1996) 83-95.

    Google Scholar 

  15. J. H. Gordis, Spatial, frequency domain updating of linear, structural dynamic models, Proceedings of the 34th AIAA/ASME/ASCE/AHS/ACS Structures, Structural Dynamics, and Materials Conference, (1992) 3050-3058.

    Google Scholar 

  16. J. H. Gordis, An Analysis of the Improved Reduced System Model Reduction Procedure,” Int. J. Anal. Exp. Modal Anal, Vol. 9 No. 4 (1994) 269-285.

    Google Scholar 

  17. J. H. Gordis, An exact formulation for structural dynamic model error localization, Int. J. Anal. Exp. Modal Anal, Vol. 10 No. 1 (1995) 19-33.

    Google Scholar 

  18. E.J. Berman, M.S. Allen, D.C. Kammer, R.L. Mayes, Probabilistic investigation of sensitivities of advanced test-analysis model correlation methods, Journal of Sound and Vibration. 329(2010) 2516-2531.

    Article  Google Scholar 

  19. Z.Tu, Y. Lu, FE model updating using artificial boundary conditions with genetic algorithms, Computers and Structures, Vol. 86 (2008) 714-727.

    Article  Google Scholar 

  20. Y. Lu, Z.Tu, Artificial boundary condition approach for structural identification: a laboratory perspective, 26th International Modal Analysis Conference, Orlando, Florida USA (2008).

    Google Scholar 

  21. A. Berman, System identification of structural dynamic models -theoretical and practical bounds, Proceedings of the AIAA/ASME/ASCE/AHS 25th Structures, Structural Dynamics, & Materials Conference, (1984) 123-128.

    Google Scholar 

  22. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Oxford University Press, 1965.

    Google Scholar 

  23. D.A. Rade, G. Lallement, A strategy for the enrichment of experimental data as applied to an inverse eigensensitivity-based FE model updating method, Mechanical Systems and Signal Processing, 12(2). (1998) 293-3078.

    Article  Google Scholar 

  24. C. Fernandez, Artificial boundary conditions in sensitivity based finite element model updating and structural damage detection, Master's Thesis. Naval Postgraduate School. Monterey, CA. 2004.

    Google Scholar 

  25. S. Boyd, Lecture 8 Least-norm solutions of underdetermined equations, EE263 Autumn Stanford University 2007-08.

    Google Scholar 

  26. G.H. Golub, C.F. Van Loan, Matrix Computations, The Johns Hopkins University Press, 3rd Ed. 1996.

    Google Scholar 

  27. MATLAB® R2010A, The Mathworks, Inc. Natick, MA.

    Google Scholar 

  28. M.J. Lai, On sparse solutions of underdetermined linear systems, Journal of Concrete and Applicable Mathematics. 2009.

    Google Scholar 

  29. D.L. Donoho, For Most Large Underdetermined Systems of Linear Equations the Minimal L1-norm Solution is also the Sparsest Solution, Communications on Pure and Applied Mathematics, Vol. LIX (2006) 0797–0829.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mechanical & Aerospace Engineering - Code ME/Go, Naval Postgraduate School, 700 Dyer Road Bldg. 245 Room 313, Monterey, CA, 93943-5146, USA

    Joshua H. Gordis

  2. LT Konstantinos Papagiannakis, Hellenic Navy, Athens, Greece

    Joshua H. Gordis

Authors
  1. Joshua H. Gordis
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joshua H. Gordis .

Editor information

Editors and Affiliations

  1. Society for Experimental Mechanics, School Street 7, Bethel, 06801-1405, USA

    Tom Proulx

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this paper

Cite this paper

Gordis, J.H. (2011). Optimal Selection of Artificial Boundary Conditions for Model Update and Damage Detection. In: Proulx, T. (eds) Sensors, Instrumentation and Special Topics, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9507-0_15

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-9507-0_15

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-9506-3

  • Online ISBN: 978-1-4419-9507-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation