The New Second and Higher Order Spectral Technique for Damage Monitoring of Structures and Machinery
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Published
Nov 1, 2020
Len Gelman
Abstract
The new second and higher order spectral technique, the cross-covariance of complex spectral components, is proposed for monitoring damage of structure and machinery Normalization of the proposed technique is also developed. It is shown by simulation that the proposed technique provides effectiveness gain for detecting of damage compared to the higher order spectra.
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Keywords
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References
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Brush, E. & Adams, D. (2010). Development of a dynamic model for subsurface damage in sandwich composite materials, Proceedings of the IMAC-XXVIII, 1-4 February, Jacksonville, Florida, pp. 129-136
Collis, W. B, White, P. R, & Hammond, J. K. (1998). High order spectra: the bispectrum and trispectrum. Mechanical Systems and Signal Processing, Vol. 12(3), pp. 375-394.
Fackrell, J. W, White, P. R, Hammond, J. K, & Pinnington, R. J. (1995). The interpretation of the bispectra of vibration signals. Mechanical Systems and Signal Processing, Vol. 9(3), pp. 267-274.
Gelman, L. (2007). Piecewise model and estimated of damping and natural frequency for a spur gear, Mechanical Systems and Signal Processing, Vol. 21, pp. 1192-1196.
Gelman, L. (2007). Adaptive time-frequency transform for non-stationary signals with nonlinear polynomial frequency variation, Mechanical Systems and Signal Processing, Vol. 21(6), pp. 2684-2687.
Gelman, L., & Gorpinich, S. (2000). Non-Linear Vibroacoustical Free Oscillation Method for Crack Detection and Evaluation, Mechanical Systems and Signal Processing, Vol. 14(3), pp. 343-351.
Gelman, L., & Ottley, M. (2006). New processing techniques for transient signals with nonlinear variation of the instantaneous frequency in time, Mechanical Systems and Signal Processing, Vol. 20(5), pp. 1254-1262.
Gelman, L., & Petrunin, I. (2007). The new multidimensional time/multi-frequency transform for higher order spectral analysis. Multidimensional Systems and Signal Processing, Vol. 18 (4), pp. 317-325.
Gelman, L., White, P., & Hammond, J. (2005). Fatigue crack diagnostics, A comparison of the use of the complex bicoherence and its magnitude. Mechanical Systems and Signal Processing, Vol. 19(4), pp. 913–918.
Hanssen, A, & Scharf, L. (2003). A theory of polyspectra for nonstationary stochastic processes. IEEE Transactions on Signal Processing, Vol. 51(5), pp. 1243-1252.
Hickey, D., Worden, K., Platten, M., Wright, J., & Cooper, J. (2009). Higher-order spectra for identification of nonlinear modal coupling, Mechanical Systems and Signal Processing, Vol. 23(4), pp. 1037-1061.
Hillis, A., Neild, S., Drinkwater, B., & Wilcox, P. (2006). Global crack detection using bispectral analysis. Proc. Royal Soc. A, Vol. 462, pp. 1515-1530.
Hsu, C. (1975). The response of a parametrically excited hanging string in fluid. ASME Journal of Sound and Vibration, Vol. 39, pp 305-316.
Jefferys, E. & Patel, M. (1982). Dynamic analysis models of the tension leg platform. ASME Journal of Energy Resources Technology, Vol 104, pp 317-323.
Kim, Y. C., & Powers, E. J. (1979). Digital bispectral analysis and its applications to non-linear wave interactions. IEEE Transactions on Plasma Science, Vol. 7(2), pp. 120-131.
McCormick, A. C., & Nandi, A. K. (1999). Bispectral and trispectral features for machine condition diagnosis. IEE Proc. of the Vision, Image and Signal Processing, Vol. 146 (5), pp. 229–234.
Mendel, J. M. (1991). Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proc. of the IEEE, Vol. 79 (3), pp. 278–305.
Narsiavas, S. (1990). On the dynamics of oscillators with bilinear damping and stiffness. International Journal of Non-linear Mechanics, Vol 25(5), pp 535-554.
Nikias, C. L, & Mendel, J. M. (1993). Signal processing with higher-order spectra. IEEE Signal Processing Magazine, Vol. 10 (3), pp. 10–38.
Oppenheim A., Schafer, R., & Buck, J. (1999). Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, pp. 468.
Patel, M., Brown, D. & Witz, J. (1986). Operability analysis for a mono-hull crane barge. Proc. of the RINA, spring meeting.
Rivola, A., & White, P. (1998). Detecting system non-linearities by means of higher order statistics. Proceedings of the 3rd International Conference on Acoustical and Vibratory Surveillance Methods and Diagnostic Techniques, 13-15/10/1998, Senlis, France, Vol. 1, pp. 263-272.
Sachs, L. (1984). Applied Statistics – A Handbook of Techniques, Springer-Verlag, New York.
Schreier, P. J, & Scharf, L. L. (2006). Higher-order spectral analysis of complex signals. Signal Processing, Vol. 86 (11), pp. 3321-3333.
Thomson, J. & Stewart, H. (1986). Nonlinear dynamics and chaos. John Willey.
Young, T., & Fu, K. S. (1986). Handbook of pattern recognition and image processing. New York, Academic.
Brush, E. & Adams, D. (2010). Development of a dynamic model for subsurface damage in sandwich composite materials, Proceedings of the IMAC-XXVIII, 1-4 February, Jacksonville, Florida, pp. 129-136
Collis, W. B, White, P. R, & Hammond, J. K. (1998). High order spectra: the bispectrum and trispectrum. Mechanical Systems and Signal Processing, Vol. 12(3), pp. 375-394.
Fackrell, J. W, White, P. R, Hammond, J. K, & Pinnington, R. J. (1995). The interpretation of the bispectra of vibration signals. Mechanical Systems and Signal Processing, Vol. 9(3), pp. 267-274.
Gelman, L. (2007). Piecewise model and estimated of damping and natural frequency for a spur gear, Mechanical Systems and Signal Processing, Vol. 21, pp. 1192-1196.
Gelman, L. (2007). Adaptive time-frequency transform for non-stationary signals with nonlinear polynomial frequency variation, Mechanical Systems and Signal Processing, Vol. 21(6), pp. 2684-2687.
Gelman, L., & Gorpinich, S. (2000). Non-Linear Vibroacoustical Free Oscillation Method for Crack Detection and Evaluation, Mechanical Systems and Signal Processing, Vol. 14(3), pp. 343-351.
Gelman, L., & Ottley, M. (2006). New processing techniques for transient signals with nonlinear variation of the instantaneous frequency in time, Mechanical Systems and Signal Processing, Vol. 20(5), pp. 1254-1262.
Gelman, L., & Petrunin, I. (2007). The new multidimensional time/multi-frequency transform for higher order spectral analysis. Multidimensional Systems and Signal Processing, Vol. 18 (4), pp. 317-325.
Gelman, L., White, P., & Hammond, J. (2005). Fatigue crack diagnostics, A comparison of the use of the complex bicoherence and its magnitude. Mechanical Systems and Signal Processing, Vol. 19(4), pp. 913–918.
Hanssen, A, & Scharf, L. (2003). A theory of polyspectra for nonstationary stochastic processes. IEEE Transactions on Signal Processing, Vol. 51(5), pp. 1243-1252.
Hickey, D., Worden, K., Platten, M., Wright, J., & Cooper, J. (2009). Higher-order spectra for identification of nonlinear modal coupling, Mechanical Systems and Signal Processing, Vol. 23(4), pp. 1037-1061.
Hillis, A., Neild, S., Drinkwater, B., & Wilcox, P. (2006). Global crack detection using bispectral analysis. Proc. Royal Soc. A, Vol. 462, pp. 1515-1530.
Hsu, C. (1975). The response of a parametrically excited hanging string in fluid. ASME Journal of Sound and Vibration, Vol. 39, pp 305-316.
Jefferys, E. & Patel, M. (1982). Dynamic analysis models of the tension leg platform. ASME Journal of Energy Resources Technology, Vol 104, pp 317-323.
Kim, Y. C., & Powers, E. J. (1979). Digital bispectral analysis and its applications to non-linear wave interactions. IEEE Transactions on Plasma Science, Vol. 7(2), pp. 120-131.
McCormick, A. C., & Nandi, A. K. (1999). Bispectral and trispectral features for machine condition diagnosis. IEE Proc. of the Vision, Image and Signal Processing, Vol. 146 (5), pp. 229–234.
Mendel, J. M. (1991). Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications. Proc. of the IEEE, Vol. 79 (3), pp. 278–305.
Narsiavas, S. (1990). On the dynamics of oscillators with bilinear damping and stiffness. International Journal of Non-linear Mechanics, Vol 25(5), pp 535-554.
Nikias, C. L, & Mendel, J. M. (1993). Signal processing with higher-order spectra. IEEE Signal Processing Magazine, Vol. 10 (3), pp. 10–38.
Oppenheim A., Schafer, R., & Buck, J. (1999). Discrete-Time Signal Processing. Upper Saddle River, NJ: Prentice Hall, pp. 468.
Patel, M., Brown, D. & Witz, J. (1986). Operability analysis for a mono-hull crane barge. Proc. of the RINA, spring meeting.
Rivola, A., & White, P. (1998). Detecting system non-linearities by means of higher order statistics. Proceedings of the 3rd International Conference on Acoustical and Vibratory Surveillance Methods and Diagnostic Techniques, 13-15/10/1998, Senlis, France, Vol. 1, pp. 263-272.
Sachs, L. (1984). Applied Statistics – A Handbook of Techniques, Springer-Verlag, New York.
Schreier, P. J, & Scharf, L. L. (2006). Higher-order spectral analysis of complex signals. Signal Processing, Vol. 86 (11), pp. 3321-3333.
Thomson, J. & Stewart, H. (1986). Nonlinear dynamics and chaos. John Willey.
Young, T., & Fu, K. S. (1986). Handbook of pattern recognition and image processing. New York, Academic.
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Technical Briefs