Concluding Remarks

A broad range of techniques are presented in this chapter. The varying methods will be useful in different circumstances and hence there is no golden rule on which approach to use when. The suitability will depend on the type of data and the features to be extracted.


  • 8.1 A uniform steel rotor, 1 m in length, is supported at each end on bearings, each of which has constant stiffness 5х10э N/m with damping od 150 Nsec/m . There are two discs mounted 250 mm from either end and both of these are steel with thickness 20 mm and diameter 100 mm. The first disc has an imbalance of 0.04 kg mm, while the second has an imbalance of 0.02 kg mm, both at zero phase. The shaft passes through a clearance of 10pm at midspan. Calculate the response and determine the speed at which the shaft will contact the stator.
  • 8.2 A time signal has the form

Determine the maximum instantaneous frequency and velocity, and the time at which these occur.

8.3 A vibration trace has the form

The white noise has amplitude of 10. Determine the autocorrelation function and identify the main frequencies.

8.4 A time-limited signal has the form

For 0 300 sec.

Determine an empirical mode decomposition for this signal. (Note this may be achieved either manually or with freely available MATLAB routines.)

8.5 Taking the matrix

determine the SVD of both U and its transpose and explain the relationship between the two.


Antoni, J., 2007, Cyclic spectral analysis of rolling-element bearing signals: Facts and fictions, Journal of Sound and Vibration, 304, pp. 497-529.

Baydar, N., Chen, Q., Ball, A. and Kruger, U., 2001, Detection of incipient tooth defect in helical gears using multivariate statistics, Mechanical Systems and Signal Processing, 15(2), pp. 303-321.

Bogert, B.P., Healey, M.J.R. and Tukey, J.W., 1963, The quefrequency analysis of time series for echoes: Cepstrum, psuedo-autocvariance, cross-cepstrum and saphe cracking, Proceeding of the Symposium on Time Series Analysis, pp. 209-243, Providence, RI ProvidePP.

Collis, W.B., White, P.R. and Hammond, J.K., 1998, Higher order spectra: The bi-spectrum and tri-spectrum, Mechanical Systems and Signal Processing, 12(3), pp. 375-394.

Cooley, J.W. and Tukey, J.W., 1965, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, 19(90), pp. 297-301.

Fackerell, J.W.A., White, P.R., Hammond, J.K. and Pinnington, R.J., 1995, The interpretation of the bispectra of vibration signals - 1. Theory, Mechanical Systems and Signal Processing, 9(3), pp. 257-266.

Feldman, M., 2011, Hilbert transform in vibration analysis, Mechanical Systems and Signal Processing, 25, pp. 735-802.

Flitter, D.W., Hewitt, G. and Mayes, I.W., (1991). Remote monitoring and processing of large quantities of on-line vibration data by an expert system, Institution of Electrical Engineers, Colloquium on Advanced Condition Monitoring Systems for Power Generation, pp. 1011-1018, IEEE, London.

Golub, G.H. and van Loan, C.F., 1996, Matrix Computations, The John Hopkins University Press, Charles Village, Baltimore, MA.

Huang, N.E., Shen, Z„ Long, S.R., Wu, M.C., Shi, H.H., Zheng, Q„ Yen, N.-C., Tunf, C.C. and Liu, H.H., 1998, The empirical mode decomposition and the Hilbert Spectrum for nonlinear and non-stationary time series analysis, Proceedings of the Royal Society, A, 454, pp. 903-995.

Lawson, C.L. and Hanson, R.J., 1974, Solving least square problems, Prentice-Hall Inc., Eaglewood Cliffs, NJ. Republished in 1995 by the Society for Industrial and Applied Mathematics.

Ma, H., Pang, F.R., Song, R. and Wen, B., 2015, Fault feature analysis of cracked gear considering the effects of the extended tooth contact, Engineering Failure Analysis, 48, pp. 105-120.

Nabney, I.T., 2003, Netlab, Algorithms for Pattern Recognition, Springer-Verlag, London.

Peng, Z.K., Tse, P.W. and Chu, F.L., 2005, A comparison study of improved Hilbert-Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing, Mechanical Systems and Signal Processing, 19, pp. 974-988.

Randall, R.B., 2013, A history of Cepstrum analysis and its application to mechanical problems, Conference 'Surveilance 7', Chatres, France, (October).

Silverman, B.W., 1986, Density Estimation for Statistics and Data Analysis, London, Chapman and Hall.

Worden, K. and Tomlinson, G.R., 2001, Non-Linearity in Structural Dynamics, CRC Press, Boca Raton, FL (originally published by IOP Publishing, London, UK).

Wu, F. and Qu, L., 2009, Diagnosis of subharmonic faults of large rotating machinery, Mechanical Systems and Signal Processing, 23, pp. 467-475.

Yunusa-Kaltungo, A. and Sinha, J.K., 2014, Coherent composite HOS analysis of rotating machines with different support flexibilities, Vibration Engineering and Technology of Machinery, Proceedings of VETOMAC-X, pp. 145-153, Manchester, UK.

< Prev   CONTENTS   Source   Next >