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Meccanica

, Volume 38, Issue 2, pp 239–250 | Cite as

Structural Health Monitoring Through Chaotic Interrogation

  • J.M. Nichols
  • S.T. Trickey
  • M.D. Todd
  • L.N. Virgin
Article

Abstract

The field of vibration based structural health monitoring involves extracting a ‘feature’ which robustly quantifies damage induced changes to the structure in the presence of ambient variation, that is, changes in ambient temperature, varying moisture levels, etc. In this paper, we present an attractor-based feature derived from the field of nonlinear time-series analysis. Emphasis is placed on the use of chaos for the purposes of system interrogation. The structure is excited with the output of a chaotic oscillator providing a deterministic (low-dimensional) input. Use is made of the Kaplan–Yorke conjecture in order to ‘tune’ the Lyapunov exponents of the driving signal so that varying degrees of damage in the structure will alter the state space properties of the response attractor. The average local attractor variance ratio (ALAVR) is suggested as one possible means of quantifying the state space changes. Finite element results are presented for a thin aluminum cantilever beam subject to increasing damage, as specified by weld line separation, at the clamped end. Comparisons of the ALAVR to two modal features are evaluated through the use of a performance metric.

Chaos Damage detection Attractor Lyapunov spectrum 

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References

  1. 1.
    Bishop, C.M., ‘Novelty detection and neural network validation’, IEE Proceedings: Vision, Image, and Spectral Processing, Vol. 141, 1994.Google Scholar
  2. 2.
    Brincker, R., Anderson, P., Martinez, M.E. and Tallavo, F., ‘Modal analysis of an offshore platform using two different ARMA approaches’, in: Proc. 14th International Modal Analysis Conference, 1994.Google Scholar
  3. 3.
    Broomhead, D.S. and King, G.P., ‘Extracting qualitative dynamics from experimental data’, Physica D 20 (1986) 217-236.Google Scholar
  4. 4.
    Cook, R.D., Malkus, D.S. and Plesha, M.E., Concepts and Applications of Finite Element Analysis, Wiley, New York, 1989.Google Scholar
  5. 5.
    Craig, C., Neilson, R.D. and Penman, J., ‘The use of correlation dimension in condition monitoring of systems with clearance’, J. Sound Vibr. 231(1) (2000) 1-17.Google Scholar
  6. 6.
    Farrar, C.R., Cornwell, P.J., Doebling, S.W. and Prime, M.B., Structural Health Monitoring Studies of the Alamosa Canyon and I-40 Bridges, Technical Report LA-13635-MS, Tech. Rep., Los Alamos National Laboratory Report, 2000.Google Scholar
  7. 7.
    Farrar, C.R., Doebling, S.W. and Nix, D.A., ‘Damage identification with linear discriminant operators’, in: Proc. 17th International Modal Analysis Conference, 1999a.Google Scholar
  8. 8.
    Farrar, C.R., Duffey, T.A., Doebling, S.W. and Nix, D.A., ‘A statistical pattern recognition paradigm for vibration-based structural health monitoring’, in: Structural Health Monitoring 2000, 1999b, pp. 764-773.Google Scholar
  9. 9.
    Fraser, A.M. and Swinney, H.L., ‘Independent coordinates for strange attractors from mutual information’, Phys. Rev. A 33 (1986) 1134-1140.Google Scholar
  10. 10.
    Garcia, G.V. and Osegueda, R., ‘Combining damage index method and ARMA method to improve damage’, in: Proc. IMAC XVIII: A Conference on Structural Dynamics, 2000, pp. 668-673.Google Scholar
  11. 11.
    George, D., Hunter, N., Farrar, C. and Deen, R., ‘Identifying damage sensitive features using nonlinear time series and bispectral analysis’, in: Proc. IMAC XVIII: A Conference on Structural Dynamics, 2000, pp. 1796-1802.Google Scholar
  12. 12.
    Hughes, T., The Finite Element Method: Linear, Static, and Dynamic Analysis, Prentice-Hall, New York, 1987.Google Scholar
  13. 13.
    Kaplan, J.L. and Yorke, J.A., ‘Chaotic behavior of multidimensional difference equations’, in: Peitgen, H.-O. and Walther, H.-O. (eds), Functional Difference Equations and Approximations of Fixed Points, Vol. 730 of Lecture Notes in Mathematics, Berlin, 1979.Google Scholar
  14. 14.
    Lopez, F.P. and Zimmerman, D.C., ‘A pattern recognition approach for damage localization using incomplete measurements’, in: Proceedings of the 17th International Modal Analysis Conference, 1999, pp. 579-585.Google Scholar
  15. 15.
    Meirovitch, L., Principles and Techniques of Vibrations, Prentice-Hall, New York, 1997.Google Scholar
  16. 16.
    Ni, Y.Q., Wang, B.S. and Ko, J.M., ‘Selection of input vectors to neural networks for structural damage identification’, in: Proc. SPIE 3671, 1999, pp. 270-280.Google Scholar
  17. 17.
    Nichols, J.M. and Nichols, J.D., ‘Attractor reconstruction for nonlinear systems: a methodological note’, Math. Biosci. 171 (2001) 21-32.Google Scholar
  18. 18.
    Nichols, J.M. and Virgin, L.N., ‘Practical evaluation of invariant measures for the chaotic response of a two-frequency excited mechanical oscillator’, Nonlinear Dyn. 26(1) (2001) 67-86.Google Scholar
  19. 19.
    Okafor, A.C., Chandrashekhara, K. and Jiang, Y.P., ‘Location of impact in composite plates using waveform-based acoustic emission and Gaussian cross-correlation techniques’, in: Proc. SPIE 2718, 1996, pp. 291-302.Google Scholar
  20. 20.
    Pandey, A.K. and Biswas, M., ‘Damage detection in structures using changes in flexibility’, J. Sound Vibr. 169 (1994) 3-17.Google Scholar
  21. 21.
    Pecora, L.M. and Carroll, T.L., ‘Discontinuous and nondifferentiable functions and dimension increase induced by filtering chaotic data’, Chaos 6(3) (1996) 432-439.Google Scholar
  22. 22.
    Sampaio, R.P., Maia, N.M.M. and Silva, J.M.M., ‘Damage detection using the frequency-response-function curvature method’, J. Sound Vibr. 226(6) (1999) 1029-1042.Google Scholar
  23. 23.
    Stubbs, N., Kim, J.T. and Topole, K., ‘Efficient and robust algorithm for damage localization in offshore platforms’, in: ASCE 10th Structures Congress, 1992.Google Scholar
  24. 24.
    Takens, F., ‘Detecting strange attractors in turbulence’, in: Rand, D. and Young, L.-S. (eds), Dynamical Systems and Turbulence, Vol. 898 of Lecture Notes in Mathematics, Springer, New York, 1981, pp. 366-381.Google Scholar
  25. 25.
    Theiler, J., ‘Spurious dimension from correlation algorithms applied to limited time-series data’, Phys. Rev. A 34 (1986) 2427.Google Scholar
  26. 26.
    Virgin, L.N., Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration, Cambridge University Press, Cambridge, 2000.Google Scholar
  27. 27.
    Wolf, A., Swift, J.B., Swinney, H.L. and Vastano, J.A., ‘Determining Lyapunov exponents from a time series’, Physica D 16 (1984) 285-317.Google Scholar
  28. 28.
    Worden, K., ‘Structural fault detection using a novelty measure’, J. Sound Vibr. 201 (1997) 85-101.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • J.M. Nichols
    • 1
  • S.T. Trickey
    • 1
  • M.D. Todd
    • 1
  • L.N. Virgin
    • 2
  1. 1.Naval Research LaboratoryWashingtonU.S.A
  2. 2.Pratt School of EngineeringDuke UniversityU.S.A

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