Nonlinear Parameteric Health Monitoring for Vibrating Structures Under Non-Stationary Excitation

Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


Nonlinear system identification has been used to predict and monitor cracks as they form, propagate, and eventually cause the catastrophic failure of a vibrating cantilevered beam. The Continuous Time based system identification technique allows for estimation of model parameters based on collected stimulus and response data. For this study the estimated cubic stiffness term in the model is mapped as a function of time. The purpose of this investigation is to strengthen results from a previous study [1] through repetition, and to expand the scope of this system identification technique. This study mainly explores the effectiveness of using nonstationary excitation in the identification process, with an understanding that in implementation on real systems the selection input amplitude and frequency may not be readily controlled. Additionally, the robustness of this method is demonstrated in direct comparison to a wellaccepted linear-based approach. The results show this method to be successful with little prior knowledge of the accurate model form or parametric values for the systems being studied.


Mode Shape Cantilever Beam Excitation Amplitude Crack Detection Nonlinear System Identification 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Doughty, T. A. and Higgins, N. S., “Effect of Nonlinear Parametric Model Accuracy in Crack Prediction and Detection”, SEM Annual Conference & Exposition on Experimental and Applied Mechanics, Indianapolis, 2010.Google Scholar
  2. 2.
    Doebling, Scott W., Farrar, C. R., and Prime, M. B., “A Summary of Vibration-Based Damage Identification Methods,” Shock Vibration Digest 30, 1998, pp. 91–105.CrossRefGoogle Scholar
  3. 3.
    Khiem, N.T., Lien, T.V., “Multi-Crack Detection for Beam by the Natural Frequencies,” Journal of Sound & Vibration 273, May 2004, pp.175-185.CrossRefGoogle Scholar
  4. 4.
    Loutridis, S. Douka, E., Hadjileontiadis, L.J., “Forced Vibration Behavior and Crack Detection of Cracked Beams Using Instantaneous Frequency,” NDT & E International 38, July 2005: 411–419.CrossRefGoogle Scholar
  5. 5.
    Lee, YY, Liew K. M., “Detection of Damage Locations in a Beam using the Wavelet Analysis,” International Journal of Structural Stability and Dynamics 1, 2001, pp. 455–465.MATHCrossRefGoogle Scholar
  6. 6.
    Gudmundson, P., “Changes in Modal Parameters Resulting from Small Cracks,” Proceedings of the International Modal Analysis Conference and Exhibit 2, 1984, pp. 690–697.Google Scholar
  7. 7.
    Kim, Jeong-Tae, Ryu, Yeon-Sun, Cho Hyun-Man, Stubbs, N., “Damage Identification in Beam-Type Structures: Frequency-Based Method vs. Mode-shape Based Method,” Engineering Structures 25, 2003, pp. 57–67.CrossRefGoogle Scholar
  8. 8.
    Leonard, F., Lanteigne, J., Lalonde, S., Turcotte, Y., “Free-Vibration of a Cracked Cantilever Beam and Crack Detection,” Mechanical Systems and Signal Processing 15, May 2001, pp. 529–548.CrossRefGoogle Scholar
  9. 9.
    Saavedra, P.N., Cuitino, L.A., “Crack Detection and Vibration Behavior of Cracked Beams,” Computers and Structures. 79 (2001): 1451–1459.CrossRefGoogle Scholar
  10. 10.
    Kim, J.T., Stubbs, N., “Crack Detection in Beam-Type Structures Using Frequency Data,” Journal of Sound and Vibration 259, January 2003, pp.145-161.CrossRefGoogle Scholar
  11. 11.
    Ding, J.L., Pazhouh, J., Lin, S.B., Burton, T.D., “Damage Characterization by Vibration Test,” Scripta Metallurgica et Materialia 30, 1994, pp. 839–834.CrossRefGoogle Scholar
  12. 12.
    Sih, G.C., Tzou, D.Y., “Mechanics of Nonlinear Crack Growth: Effects of Specimen Size and Loading Step,” Martinus Nijhoff Publications, 1984, pp. 155–169.Google Scholar
  13. 13.
    Bovsunovsky, A. and Bovsunovsky, O., “Crack Detection in Beams by Means of the Driving Force Parameters Variation at Non-Linear Resonance Vibrations”, Key Engineering Materials, v 347, Damage Assessment of Structures VII, 2007, pp. 413–420.Google Scholar
  14. 14.
    Andreaus, U., Casini, P., Vestroni, F., “Nonlinear Features In The Dynamic Response of a Cracked Beam Under Harmonic Forcing,” Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005, v 6 C, 5th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2005, pp. 2083–2089.Google Scholar
  15. 15.
    Wowk, V., Machinery Vibration Measurement and Analysis, McGraw Hill, Inc. New York, 1991.Google Scholar
  16. 16.
    Crespo da Silva, M. R. M. and Glynn, C. C., “Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams, II. Forced Motions,” International Journal of Solids and Structures 6, 1978, pp. 449–461.Google Scholar
  17. 17.
    Doughty, Timothy A., Davies, P., Bajaj, A. K., “A Comparison of Three Techniques Using Steady-State Data to Identify Nonlinear Modal Behavior of an Externally Excited Cantilever Beam,” Journal of Sound and Vibration, 249(4), 2002, pp. 785–813.CrossRefGoogle Scholar
  18. 18.
    Doughty, Timothy A., System Identification of Modes in Nonlinear Structures. PhD Thesis, Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, 2002.Google Scholar
  19. 19.
    Doughty, T. A. and Leineweber, M. J., “Investigating Nonlinear Models for Health Monitoring in Vibrating Structures”, ASME International Mechanical Engineering Congress and Exposition, November 2009.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.University of PortlandPortlandUSA

Personalised recommendations