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Empirical Slow-Flow Identification for Structural Health Monitoring and Damage Detection

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Topics in Modal Analysis, Volume 7

Abstract

We utilize the nonlinear system identification (NSI) methodology, which was recently developed based on the correspondence between analytical and empirical slow-flow dynamics. Performing empirical mode decomposition on the simulated or measured time series to extract intrinsic mode oscillations, we establish nonlinear interaction models, which invoke slowly-varying forcing amplitudes that can be computed from empirical slow-flows. By comparing the spatio-temporal variations of the nonlinear modal interactions for structures with defects and those for the underlying healthy structure, we will demonstrate that the proposed NSI method can not only explore the smooth/nonsmooth nonlinear dynamics caused by structural damage, but also the extracted vibration characteristics can directly be implemented for structural health monitoring and detecting damage locations. Starting with traditional tools such as the modal assurance criterion (MAC) and the coordinate MAC are utilized.

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References

  1. Lee YS, Tsakirtzis S, Vakakis AF, Bergman LA, McFarland DM (2009) Physics-based foundation for empirical mode decomposition. AIAA J 47:2938–2963

    Google Scholar 

  2. Lee YS, Tsakirtzis S, Vakakis AF, McFarland DM, Bergman LA (2010) A time-domain nonlinear system identification method based on multiscale dynamic partitions. Meccanica 46:625–649

    Google Scholar 

  3. Lee YS, Vakakis AF, McFarland DM, Bergman LA (2010) A global local approach to system identification: a review. Struct Control Health Monit 17:742–760

    Google Scholar 

  4. Lee YS, Vakakis AF, McFarland DM, Bergman LA (2010) Nonlinear system identification of the dynamics of aeroelastic instability suppression based on targeted energy transfers. Aeronaut J 114:61–82

    Google Scholar 

  5. Tsakirtzis S, Lee YS, Vakakis AF, Bergman LA, McFarland DM (2010) Modeling of nonlinear modal interactions in the transient dynamics of an elastic rod with an essentially nonlinear attachment. Commun Nonlinear Sci Numer Simul 15:2617–2633

    Google Scholar 

  6. Huang N, Shen Z, Long S, Wu M, Shih H, Zheng Q, Yen N-C, Tung C, Liu H (1998) The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc R Soc Lond Ser A. Math Phys Sci 454:903–995

    Google Scholar 

  7. Brandon JA (1998) Some insights into the dynamics of defective structures. Proc Inst Mech Eng Part C: J Mech Eng Sci 212:441–454

    Google Scholar 

  8. Ewins DJ (1990) Modal testing: theory and practice. Research Studies Press, UK

    Google Scholar 

  9. Kerschen G, Golinval J-C, Vakakis AF, Bergman LA (2005) The method of proper orthogonal decomposition for order reduction of mechanical systems: an overview. Nonlinear Dyn 41:147–170

    Google Scholar 

  10. Feeny BF, Kappagantu R (1998) On the physical interpretation of proper orthogonal modes in vibrations. J Sound Vib 211:607–616

    Google Scholar 

  11. Kerschen G, Golinval JC (2002) Physical interpretation of the proper orthogonal modes using the singular value decomposition. J Sound Vib 249:849–865

    Google Scholar 

  12. Ma X, Azeez MFA, Vakakis AF (2000) Non-linear normal modes and non-parametric system identification of non-linear oscillators. Mech Syst Signal Process 14:37–48

    Google Scholar 

  13. Georgiou I (2005) Advanced proper orthogonal decomposition tools: using reduced order models to identify normal modes of vibration and slow invariant manifolds in the dynamics of planar nonlinear rods. Nonlinear Dyn 41:69–110

    Google Scholar 

  14. Galvanetto U, Surace C, Tassotti A (2008) Structural damage detection based on proper orthogonal decomposition: experimental verification. AIAA J 46:1624–1630

    Google Scholar 

  15. Cusumano JP, Bae B-Y (1993) Period-infinity periodic motions, chaos, and spatial coherence in a 10 degree of freedom impact oscillator. Chaos Solitons Fractals 3:515–535

    Google Scholar 

  16. Cusumano JP, Sharkady MT, Kimble BW (1994) Experimental measurements of dimensionality and spatial coherence in the dynamics of a flexible-beam impact oscillator. Philos Trans R Soc Ser A 347:421–438

    Google Scholar 

  17. Ritto TG, Buezas FS, Sampaio R (2011) A new measure of efficiency for model reduction: application to a vibroimpact system. J Sound Vib 330:1977–1984

    Google Scholar 

  18. Azeez MFA, Vakakis AF (2001) Proper orthogonal decomposition (POD) of a class of vibro-impact oscillations. J Sound Vib 240:859–889

    Google Scholar 

  19. Kurt M, Chen H, Lee YS, McFarland DM, Bergman LA, Vakakis AF (2012) Nonlinear system identification of the dynamics of a vibro-impact beam: numerical results. Arch Appl Mech 82:1461–1479

    Google Scholar 

  20. Chen H, Kurt M, Lee YS, McFarland DM, Bergman LA, Vakakis AF (2012) Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection. Mech Syst Signal Process, in review

    Google Scholar 

  21. Yao R, Pakzad SN (2012) Autoregressive statistical pattern recognition algorithms for damage detection in civil structures. Mech Syst Signal Process 31:355–368

    Google Scholar 

  22. Le J, Law SS Substructural damage detection with incomplete in formation of the structure. J Appl Mech Trans ASME 79:041003-1–10

    Google Scholar 

  23. Flynn EB, Todd MD, Wilcox PD, Drinkwater BW, Croxford AJ (2011) Maximum-likelihood estimation of damage location in guided-wave structural health monitoring. Proc R Soc Lond Ser A. Math Phys Sci 467:2575–2596

    Google Scholar 

  24. Doebling SW, Farrar dR, Prime MB, Shevitz DW (1996) Damage identification and health monitoring of structural and mechanical systems form changes in their vibration characteristics: a literature review, Los Alamos National Laboratory Report (LA-13070-MS)

    Google Scholar 

  25. Kim B-H, Stubbs N, Sikorsky C (2002) Local damage detection using incomplete modal data. In: Proceedings of IMAC-910 XX 202, 4–7 Feb 2002, the Westin Los Angeles Airport, Los Angeles, CA

    Google Scholar 

  26. Wang L, Yang Z, Waters TP (2010) Structural damage detection using cross correlation functions of vibration response. J Sound Vib 329: 5070–5086

    Google Scholar 

  27. Messina A, Williams EJ, Contursi T (1998) Structural damage detection by a sensitivity and statistical-based method. J Sound Vib 216:791–808

    Google Scholar 

  28. Fan W, Qiao P (2011) Vibration-based damage identification methods: a review and comparative study. Struct Health Monit 10:83–111

    Google Scholar 

  29. Farrar CR, Doebling SW, Nix DA (2001) Vibration-based structural damage identification. Proc R Soc Lond Ser A. Math Phys Sci 359:131–149

    Google Scholar 

  30. Lieven NAJ, Ewins DJ (1988) Spatial correlation of mode shapes, the coordinate modal assurance criterion (COMAC). In: Proceedings of the 4th international modal analysis conference, Los Angeles, CA, pp 690–695

    Google Scholar 

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Acknowledgements

This work was supported in part by the National Science Foundation of the United States through Grants CMMI-0927995 and CMMI-0928062.

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Authors and Affiliations

  1. New Mexico State University, Las Cruces, NM, 88003, USA

    Young S. Lee

  2. University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    Michael McFarland, Lawrence A. Bergman & Alexander F. Vakakis

Authors
  1. Young S. Lee
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  2. Michael McFarland
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  3. Lawrence A. Bergman
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  4. Alexander F. Vakakis
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Corresponding author

Correspondence to Young S. Lee .

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Editors and Affiliations

  1. University of Cincinnati, Cincinnati, 45221-0018, Ohio, USA

    Randall Allemang

  2. , The Enterprise Program, Michigan Technological University, Townsend Drive 1400, Houghton, 49931, Mississippi, USA

    James De Clerck

  3. , Dept. of Mechanical Engineering, University of Massachusetts Lowell, Riverside St. 197, Lowell, 01854, Massachusetts, USA

    Christopher Niezrecki

  4. & State University, Department of Mechanical Engineering, Virginia Polytechnic Institute, Randolph Hall 114 T, Blacksburg, 24060, Virginia, USA

    Alfred Wicks

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© 2014 The Society for Experimental Mechanics

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Lee, Y.S., McFarland, M., Bergman, L.A., Vakakis, A.F. (2014). Empirical Slow-Flow Identification for Structural Health Monitoring and Damage Detection. In: Allemang, R., De Clerck, J., Niezrecki, C., Wicks, A. (eds) Topics in Modal Analysis, Volume 7. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6585-0_59

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  • DOI: https://doi.org/10.1007/978-1-4614-6585-0_59

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-6584-3

  • Online ISBN: 978-1-4614-6585-0

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