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Time and frequency domain nonlinear system characterization for mechanical fault identification

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Abstract

Mechanical systems are often nonlinear with nonlinear components and nonlinear connections, and mechanical damage frequently causes changes in the nonlinear characteristics of mechanical systems, e.g. loosening of bolts increases Coulomb friction nonlinearity. Consequently, methods which characterize the nonlinear behavior of mechanical systems are well-suited to detect such damage. This paper presents passive time and frequency domain methods that exploit the changes in the nonlinear behavior of a mechanical system to identify damage.

In the time domain, fundamental mechanics models are used to generate restoring forces, which characterize the nonlinear nature of internal forces in system components under loading. The onset of nonlinear damage results in changes to the restoring forces, which can be used as indicators of damage. Analogously, in the frequency domain, transmissibility (output-only) versions of auto-regressive exogenous input (ARX) models are used to locate and characterize the degree to which faults change the nonlinear correlations present in the response data. First, it is shown that damage causes changes in the restoring force characteristics, which can be used to detect damage. Second, it is shown that damage also alters the nonlinear correlations in the data that can be used to locate and track the progress of damage. Both restoring forces and auto-regressive transmissibility methods utilize operational response data for damage identification. Mechanical faults in ground vehicle suspension systems, e.g. loosening of bolts, are identified using experimental data.

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Abbreviations

ARX:

Auto-regressive exogenous

DFM:

Discrete frequency model

FRF:

Frequency response function

OEM:

Original equipment manufacturer

References

  1. Siebert, W.M.: Signals and Systems. McGraw Hill, New York (1986)

    Google Scholar 

  2. Bracewell, R.N.: The Fourier Transform and its Applications, 2nd edn. WCB/McGraw-Hill, Boston, MA (1986)

    Google Scholar 

  3. Thrane, N.: The Hilbert Transform. Hewlett Packard Application Notes (1984)

  4. Chui, C.K.: An Introduction to Wavelets. Academic Press, San Diego, CA (1992)

    MATH  Google Scholar 

  5. Leontaritis, I., Billings, S.A.: Input–output parametric models for non-linear systems. Part I: Deterministic non-linear systems. Int. J. Control 41(2), 303–328 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  6. Storer, D.M., Tomlinson, G.R.: Recent developments in the measurement and interpretation of higher order transfer functions from non-linear structures. Mech. Syst. Signal Process. 7(2), 173–189 (1993)

    Article  Google Scholar 

  7. Collis, W.B., White, P.R., Hammond, J.K.: Higher-order spectra: the bispectrum and trispectrum. Mech. Syst. Signal Process. 12, 375–394 (1998)

    Article  Google Scholar 

  8. Surace, C., Worden, K., Tomlinson, G.R.: On the nonlinear characteristics of automotive shock absorbers. Proc. Inst. Mech. Eng.: Part D 206(D1), 3–16 (1992)

    Google Scholar 

  9. Audenino, A.L., Belingardi, G.: Modeling the dynamic behavior of a motorcycle damper. J. Automobile Eng.: Part D 209, 249–262 (1995)

    Google Scholar 

  10. Haroon, M., Adams, D.E., Luk, Y.W., Ferri, A.A.: A time and frequency domain approach for identifying non-linear mechanical system models in the absence of an input measurement. J. Sound Vib. 283, 1137–1155 (2005)

    Article  Google Scholar 

  11. Haroon, M., Adams, D.E., Luk, Y.W.: A technique for estimating linear parameters using nonlinear restoring force extraction in the absence of an input measurement. ASME J. Vib. Acoustics 127(5), 483–492 (2005)

    Article  Google Scholar 

  12. McGee, C.G., Haroon, M., Adams, D.E.: A frequency domain technique for characterizing nonlinearities in a tire-vehicle suspension system. ASME J. Vib. Acoustics 127(1), 61–76 (2005)

    Article  Google Scholar 

  13. Adams, D.E., Allemang, R.J.: Residual frequency autocorrelation as an indicator of nonlinearity. Int. J. Non-Linear Mech. 36, 1197–1211 (2000)

    Article  Google Scholar 

  14. Adams, D.E., Allemang, R.J.: Discrete frequency models: a new approach to temporal analysis. ASME J. Vib. Acoustics 123(1), 98–103 (2001)

    Article  Google Scholar 

  15. Masri, S.F., Caughey, T.K.: A nonparametric identification technique for nonlinear dynamic problems. J. Appl. Mech. 46, 433–447 (1979)

    MATH  Google Scholar 

  16. Masri, S.F., Sassi, H., Caughey, T.K.: Nonparametric identification of nearly arbitrary nonlinear systems. J. Appl. Mech. 49, 619–628 (1982)

    MATH  Google Scholar 

  17. Masri, S.F., Miller, R.K., Saud, A.F., Caughey, T.K.: Identification of nonlinear vibrating structures: Part I – Formulation. J. Appl. Mech. 54, 918–922 (1987)

    MATH  Google Scholar 

  18. Masri, S.F., Miller, R.K., Saud, A.F., Caughey, T.K.: Identification of nonlinear vibrating structures: Part II – Applications. J. Appl. Mech. 54, 923–930 (1987)

    Article  MATH  Google Scholar 

  19. Adams, D.E.: Frequency domain ARX model and multi-harmonic FRF estimators for non-linear dynamic systems. J. Sound Vib. 250(5), 935–950 (2002)

    Article  Google Scholar 

  20. Adams, D.E., Farrar, C.R.: Classifying linear and non-linear structural damage using frequency domain ARX models. Struct. Health Monit. 1(2), 185–201 (2002)

    Article  Google Scholar 

  21. Zhang, H., Schulz, M.J., Naser, A., Ferguson, F., Pai, P.F.: Structural health monitoring using transmittance functions. Mech. Syst. Signal Proc. 13(5), 765–787 (1999)

    Article  Google Scholar 

  22. Johnson, T.J., Adams, D.E.: Transmissibility as a differential indicator of structural damage. ASME J. Vib. Acoustics 124(4), 634–641 (2002)

    Article  Google Scholar 

  23. Jiang, Y., Zhang, M., Lee, C.H.: A study of early stage self-loosening of bolted joints. ASME J. Mech. Des. 125, 518–526 (2003)

    Article  Google Scholar 

  24. Bickford, J.H.: An Introduction to the Design and Behavior of Bolted Joints. Marcel Dekker Inc., New York (1990)

    Google Scholar 

  25. Hess, D.P., Davis, K.: Threaded components under axial harmonic vibration, Part I: Experiments. ASME J. Vib. Acoustics 118(3), 417–422 (1996)

    Google Scholar 

  26. Hess, D.P., Sudhirkashyap, S.V.: Dynamic loosening and tightening of a single-bolt assembly. ASME J. Vib. Acoustics 119, 311–316 (1997)

    Google Scholar 

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Authors and Affiliations

  1. Ray W. Herrick Laboratories, School of Mechanical Engineering, Purdue University, 140 S. Intramural Drive, West Lafayette, IN, 47907-2031, USA

    Muhammad Haroon & Douglas E. Adams

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  1. Muhammad Haroon
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  2. Douglas E. Adams
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Correspondence to Douglas E. Adams.

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Haroon, M., Adams, D.E. Time and frequency domain nonlinear system characterization for mechanical fault identification. Nonlinear Dyn 50, 387–408 (2007). https://doi.org/10.1007/s11071-006-9183-0

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