Wavelet-based multi-fractal spectrum for machine defect identification

ASME International Mechanical Engineering Congress and Exposition, Proceedings

Volumn 10 PART A, Issue , 2008, Pages 673-679

  Yan, Ruqiang ^a   Gao, Robert X ^a  

^a University of Massachusetts   (United States)

Author keywords

Defect identification; Health monitoring; Multi fractal spectrum; Wavelet transform

Indexed keywords

ACCELEROMETERS; FRACTALS; IDENTIFICATION (CONTROL SYSTEMS); WAVELET TRANSFORMS; BEARINGS (MACHINE PARTS); DEFECTS; FREQUENCY BANDS; ROLLER BEARINGS; SIGNAL PROCESSING; WAVELET ANALYSIS;

MULTI-FRACTAL SPECTRUM; SUB-FREQUENCY BAND; CONTINUOUS WAVELET TRANSFORMS; DEFECT IDENTIFICATION; HEALTH MONITORING; SIGNAL PROCESSING TECHNIQUE; SINGULARITY SPECTRUM; TIME-FREQUENCY RESOLUTION; WAVELET COEFFICIENTS;

MACHINERY; WAVELET TRANSFORMS;

EID: 44349137503     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/IMECE2007-41984     Document Type: Conference Paper

References (22)

1. Kiral, Z., and Karagülle, H., 2003, "Simulation and analysis of vibration signals generated by rolling element bearing with defects", Tribology International, Vol. 36, pp. 667-678.
2. Wang, C. and Gao, R., 2003, "Wavelet transform with spectral post-processing for enhanced feature extraction", IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 4, pp. 1296-1301.
3. Grassberger, P. and Procacia I., 1983, "Measuring the strangeness of strange attractors", Physica D, Vol. 9, No. 1-2, pp. 189-208.
4. Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I., and Shraiman, B. I., 1986, "Fractal measures and their singularities: The characterization of strange sets", Physical Review A, Vol. 33, No. 2, pp. 1141-1151.
5. Kobayashi, T., Madokoro, S., and Wada, Y., 2001, "Human sleep EEG analysis using the correlation dimension", Clinical Electroencephalography, Vol.32, No.3, pp.112-118.
6. Jiang, J.D. and Chen, J., 1999, "The application of correlation dimension in gearbox condition monitoring", Journal of Sound and Vibration, Vol.224, No.5, pp.529-541.
7. Logan, D. and Mathew, J., 1996, "Using the correlation dimension for vibration fault diagnosis of rolling element bearings-I. Basic concepts", Mechanical Systems and Signal Processing, Vol.10, No.3, pp.241-250.
8. Shimizu, Y., Thurner, S., and Enrenberger, K, 2002, "Multi-fractal Spectra as a measure of complexity in human posture", Fractals, Vol. 10, No.1, pp. 103-116.
9. Stošić, T. and Stošić, B.D., 2006, "Multi-fractal analysis of human retinal vessels", IEEE Transactions on Medical Imaging, Vol. 25, No. 8, pp. 1101-1107.
10. Struzik, Z. R. and Siebes, A., 2002, "Wavelet transform based multi-fractal formalism in outlier detection and localization for financial time series", Physica A, Vol. 309, pp. 388-402.
11. Parrainello, T. and Vaughan R. A., 2002, "Multi-fractal analysis and feature extraction in satellite imagery", International Journal of Remote Sensing, Vol. 23, No. 9, pp. 1799-1825.
12. Peng, Z., He, Y, Guo, D., and Chu, F., 2003, "Wavelet multi-fractal approaches for singularity analysis of the vibration signals", Key Engineering Materials, Vol. 245-246, pp. 565-570.
13. Arneodo, A., Grasseau, G., and Kostelich, E.J., 1987, "Fractal dimensions and f(α) spectrum of the hénon attractor", Physics Letters A, Vol. 124, No. 8, pp. 426-432.
14. Grassberger, P., Badii, R., and Politi, A., 1988, "Scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors", Journal of Statistical Physics, Vol. 51,No. 1-2, pp. 135-178.
15. Arneodo, A., Bacry, E., and Muzy, J.F., 1991, "Wavelets and multi-fractal formalism for singular signals: application to turbulence data", Physical Review Letters, Vol. 67, No. 25, pp. 3515-3518.
16. Muzy, J.F., Bacry, E., and Arneodo, A., 1993, "Multi-fractal formalism for fractal signals: The structure-function approach versus the wavelet-transform modulus-maxima method", Physical Review E, Vol. 47, No. 2, pp. 875-884.
17. Arneodo, A., Bacry, E., and M-zy, J.F., 1995, "The thermodynamics of fractals revisited with wavelets", Physica A, Vol. 213, No. 1, pp. 232-275;
18. Mandelbrot, B.B., 1986, "Fractals and multi-fractals: noise, turbulence and non-fractal patterns in physics", On Growth and Form: Fractal and Non-fractal Pattern in Physics, Editors: Stanley H.E. and Ostrowski, N., Springer-Verlag.
19. Mallat S. and Hwang, W.L., 1992, "Singularity detection and processing with wavelets", IEEE Transactions on Information Theory, Vol. 38, No. 2, pp. 617-643.
20. Meneveau, C. and Sreenivasan, K.R., 1989, "Direct determination of the f(a) singularity spectrum and its application to fully developed turbulence", Physical Review A, Vol. 40, pp. 5284-5294.
21. Mallat, S., 1999, A Wavelet Tour of Signal Processing, Academic Press.
22. Wavelab, http://www-stat.stanford.edu/~wavelab