Detection and Characterization of Cracks in Beams via Chaotic Excitation and Statistical Analysis

  • Chandresh Dubey
  • Vikram KapilaEmail author
Part of the Understanding Complex Systems book series (UCS)


Vibration-based damage detection methods are widely used to identify hidden damages in beam or structural components. This chapter presents a novel approach to detect and characterize cracks in beam type structures. Specifically, a chaotic signal is used to excite a beam and statistical properties of the resulting time series of beam response are analyzed to detect and characterize the crack. Initially, a single degree of freedom (SDOF) approximation of the beam with opening and closing crack is analyzed to establish that salient statistical parameters, e.g., standard deviation, skewness, and kurtosis are strongly influenced by crack properties. Next, using a finite element model of a cracked cantilever beam, spatio-temporal responses are produced for chaotic excitation and different crack characteristics. An extensive numerical study reveals that, as in the case of SDOF model, standard deviation and kurtosis of response data can yield information about the location and severity of crack. Finally, an experimental study is performed to systematically collect responses corresponding to the SDOF approximation of the cantilever beam with a crack of varying depth at a fixed location. This experimental study validates the results of the numerical study. Specifically, a careful analysis of the experimental data validates that statistical parameters such as standard deviation, skewness, and kurtosis can accurately predict crack severity.


Time Series Data Cantilever Beam Crack Depth Crack Location Crack Detection 
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.



This work is supported in part by the National Science Foundation under an RET Site grant 0807286, a GK-12 Fellows grant 0741714, and the NY Space Grant Consortium under grant 48240-7887.


  1. [1].
    Andreausa, U., Casinib, P., Vestronia, F.: Non-linear dynamics of a cracked cantilever beam under harmonic excitation. Int. J. Non. Lin. Mech. 42, 566–575 (2007)CrossRefGoogle Scholar
  2. [2].
    Bouraou, N., Gelman, L.: Theoretical bases of free oscillation method for acoustical non-destructive testing. Proceedings of Noise Conference, The Pennsylvania State University. 519–524 (1997)Google Scholar
  3. [3].
    Bamnios, Y., Douka, E., Trochidis, A.: Crack identification in beam structures using mechanical impedance. J. Sound Vib. 256(2), 287–297 (2002)CrossRefGoogle Scholar
  4. [4].
    Bamnios, G., Trochidis, A.: Dynamic behavior of a cracked cantilever beam. Appl. Acoust. 45, 97–112 (1995)CrossRefGoogle Scholar
  5. [5].
    Chati, M., Rand, R., Mukherjee, S.: Modal analysis of a cracked beam. J. Sound Vib. 207, 249–270 (1997)zbMATHCrossRefGoogle Scholar
  6. [6].
    Cawley, P., Ray, R.: A comparison of natural frequency changes produced by cracks and slots. Trans. ASME. 110, 366–370 (1998)Google Scholar
  7. [7].
    Duane, C.H., Bruce, L.L.: Mastering Matlab 7. Prentice Hall, Upper Saddle River, NJ (2005)Google Scholar
  8. [8].
    Douka, E., Bamnios, G., Trochidis, A.: A method for determining the location and depth of crack in double-cracked beams. Appl. Acoust. 65, 997–1008 (2004)CrossRefGoogle Scholar
  9. [9].
    Jensen, A., Anders la, C.H.: Ripples in Mathematics: The Discrete Wavelet Transform. Cambridge University Press, New York, NY, (2001)zbMATHCrossRefGoogle Scholar
  10. [10].
    Moaveni, S.: Finite Element Analysis Theory and Application with ANSYS. Prentice Hall, Upper Saddle River, NJ, (2007)Google Scholar
  11. [11].
    Meirovitch, L.: Fundamentals of Vibrations. McGraw-Hill, New York, NY, (2001)Google Scholar
  12. [12].
    Nichols, J.M., Trickey, S.T., Virgin, L.N.: Structural health monitoring through chaotic interrogation. Meccanica. 38, 239–250 (2003)zbMATHCrossRefGoogle Scholar
  13. [13].
    Nichols, J.M., Virgin, L.N., Todd, M.D., Nichols, J.D.: On the use of attractor dimension as a feature in structural health monitoring. Mech. Syst. Signal Process. 17(6), 1305–1320 (2003)CrossRefGoogle Scholar
  14. [14].
    Orhan, S.: Analysis of free and forced vibration of a cracked cantilever beam. NDT&E International. 40, 443–450 (2007)CrossRefGoogle Scholar
  15. [15].
    Peng, Z.K., Lang, Z.Q., Billings, S.A.: Crack detection using nonlinear output frequency response functions. J. Sound Vib. 301, 777–788 (2007)CrossRefGoogle Scholar
  16. [16].
    Ryue, J., White P.R.: The detection of crack in beams using chaotic excitations. J. Sound Vib. 307, 627–638 (2007)CrossRefGoogle Scholar
  17. [17].
    Rizos, P.F., Aspragathos, N., Dimarogonas, A.D.: Identification of crack location and magnitude in a cantilever beam from the vibration modes. J. Sound Vib. 138(3), 381–388 (1990)CrossRefGoogle Scholar
  18. [18].
    Spiegel, M., Stephens, L.: Statistics. McGraw-Hill, New York, NY (2008)Google Scholar
  19. [19].
    Sundermeyer, J.N., Weaver, R.L.: On crack identification and characterization in a beam by non-linear vibration analysis. J. Sound Vib. 183(5), 746–760 (1995)CrossRefGoogle Scholar
  20. [20].
    Sprott, J.C.: Chaos and Time-Series Analysis. Oxford University Press, New York, NY, (2003)zbMATHGoogle Scholar
  21. [21].
    Vakil-Baghmisheh, M.-T., Peimani, M., Sadeghi, M.H., Ettefagh, M.M.: Crack detection in beam like structures using genetic algorithms. Applied Soft Computing. 8, 1150–1160 (2008)CrossRefGoogle Scholar
  22. [22].
    Trendafilova, I., Manoach, E.: Vibration-based damage detection in plates by using time series analysis. Mech. Syst. Signal Process. 22, 1092–1106 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Polytechnic Institute of NYUBrooklynUSA

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