Improvement in accuracy of natural frequency determination based on the envelope of cross-correlation function

This paper presents a method of improvement of the accuracy in natural frequency determination when having impulse responses from impact testing. A new method is used for obtaining impulse response spectrum. The improvement in natural frequency determination is a result of improving the spectral resolution. For this, the new method uses calculation of surface area under the envelope of the cross-correlation function. This process is repeated by single-harmonic signal generated step-by-step with frequency changed iteratively. Thus the frequency resolution of determined spectrum is independent of length of analysed impulse response.

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1. Palacz M., Krawczuk M.: Vibration parameters for damage detection in structures, J. Sound Vibration, 249 (2002) 999-1010.
2. Salawu O.S.: Detection of structural damage through changes in frequency:
   a review, Eng. Structures, 19 (1997) 718-723.
3. Patil D.P., Maiti S.K.: Detection of multiple cracks using frequency measurements, Eng. Fracture Mech., 70 (2003) 1553-1572.
4. Dilena M., Dell’Oste M.F., Morassi A.: Detecting cracks in pipes filled with fluid from changes in natural frequencies, Mech. Systems Signal Processing, 25 (2011) 3186-3197.
5. Choubey A., Sehgal D.K., Tandon N.: Finite element analysis of vessels to study changes in natural frequencies due to cracks, Int. J. Pressure Vessels Piping, 83 (2006) 181-187.
6. Bendat J.S., Piersol A.G.: Engineering applications of correlation and spectral analysis, Wiley Interscience, New York 1980.
7. Gasior M.: Improving Frequency Resolution of Discrete Spectra, PhD thesis, AGH University of Science and Technology, Kraków 2006.
8. Gasior M.: Improving Frequency Resolution of Discrete Spectra - Algorithms of Three-Node Interpolation, LAP LAMBERT Academic Publishing, 2010.
9. Cawley P., Adams R.D.: Improved frequency resolution from transient tests with short record lengths. Journal of Sound and Vibration, Vol. 64, No. 1, 1979,
   pp. 123-132.
10. Quinn B.G. Recent advances in rapid frequency estimation. Digital Signal Processing, Vol. 19, No. 6, 2009, pp. 942-948.
11. Dunne J.F. A fast time-domain integration method for computing non-stationary response histories of linear oscillators with discrete-time random forcing.
    J. Sound Vibration, 254 (2002) 635-676.
12. Thrane N.: The Hilbert Transform, Technical Review 3, Brüel&Kjær, Naerum, Denmark 1984.
13. Thrane N., Wismer J., Konstantin-Hansen H., Gade S.: Practical use of the “Hilbert transform”, Application Note, Brüel&Kjær, Naerum, Denmark 1999.
14. Ahn S.J., Jeong W.B., Yoo W.S.: Improvement of impulse response spectrum and its application, J. Sound Vibration, 288 (2005) 1223-1239.
15. Katunin A.: Localization of damage in beam-like structures applying time-frequency distributions to modal shapes of vibration, Diagnostyka, 17 (2016)
    53-58.