Quadratic phase coupling detection in harmonic vibrations via an order-recursive AR bispectrum estimation

Nonlinear Dynamics

Volumn 19, Issue 3, 1999, Pages 273-294

  Gallego, Antolino ^a   Urdiales, Cristina ^b   Ruiz, Diego P ^a  

^a UNIVERSITY OF GRANADA   (Spain)

^b UNIVERSITY OF MÁLAGA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; HARMONIC ANALYSIS; MATHEMATICAL MODELS; MATRIX ALGEBRA; REGRESSION ANALYSIS; VIBRATIONS (MECHANICAL); WHITE NOISE;

AUTOREGRESSIVE (AR) BISPECTRUM; QUADRATIC PHASE COUPLING (QPC) DETECTION;

SIGNAL DETECTION;

EID: 0032687256     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008398026872     Document Type: Article

References (27)

1. Nikias, C. L. and Petropulu, A. P., Higher-Order Spectra Analysis. A Nonlinear Signal Processing Framework, Prentice Hall, Englewood Cliffs, NJ, 1993.
2. Nikias, C. L. and Raghuveer, M., 'Bispectrum estimation: A digital signal processing framework', Proceedings of the IEEE 75, 1985, 869-891.
3. Nikias, C. L. and Mendel, J. M., 'Signal processing with higher-order spectra', IEEE Signal Processing Magazine 7, 1993, 10-37.
4. Swami, A., Giannakis, G. B., and Zhou, G., 'Bibliography on higher-order statistics', Signal Processing 60(1), 1997, 65-126.
5. Elgar, S., Van Atta, C. W., and Gharib, M., 'Bispectral analysis of ordered and chaotic vortex shedding from vibrating cylinders', Physica D 39, 1989, 281-286.
6. Shimizu, H. and Inoue, T., 'Machine fault diagnosis by vibrational analysis. Exploratory introduction of the bispectrum method', Bulletin of the Faculty of Engineering, Yokohama National University 27, 1978, 52-60.
7. Barker, R. W., Hinich, M. J., and Klutke, G. A., 'Higher-order statistics and spectral estimation for vibration signal pattern recognition', in Proceedings of the International Workshop on Higher-Order Statistics, Chamrousse, France, July, 1991, pp. 183-186.
8. Collis, W. B., White, P., and Hammond, J., 'Bispectrum and trispectrum of mechanical systems', in Proceedings of the International Workshop on Higher-Order Statistics, Begur-Gerona, Spain, June, 1995, pp. 124-128.
9. Bendat, J. S. and Piersol, A. G., 'Spectral analysis of nonlinear systems involving square-low operations', Journal of Sound and Vibration 81, 1982, 199-213.
10. Lutes, L. D., 'Trispectrum for the response of a non-linear oscilator', International Journal of Non-Linear Mechanics 26(2), 1991, 893-909.
11. Kim, Y. C., Beall, J. M., Powers, E. J., and Miksad, R. W., 'Bispectrum and nonlinear wave coupling', Physics of Fluids 23, 1980, 258-263.
12. Wu, D. W. and Liu, C. R., 'An analytical model of cutting dynamics, Parts I and II', Transactions of the American Society of Mechanical Engineering, Journal of Engineering for Industry, 1985, 107-118.
13. Billings, S. A. and Tsang, K. N., 'Spectral analysis for non-linear systems, Part I: Parametric non-linear spectral analysis', Mechanical Systems and Signal Processing 3(4), 1991, 319-339.
14. Billings, S. A. and Tsang, K. N., 'Spectral analysis for non-linear systems, Part III: Case study examples', Mechanical Systems and Signal Processing 4(1), 1991, 3-21.
15. Balachandran, B. and Khan, K., 'Spectral analyses of nonlinear interactions', Mechanical Systems and Signal Processing 10(6), 1996, 711-727.
16. Huber, P. J., Kleiner, B., Gasser, T., and Dummermuth, G., 'Statistical methods for investigation phase relations in stationary stochastic processes', IEEE Transactions on Audio Electro acoustic AU-19, 1971, 78-86.
17. Sato, T., Sasaki , K., and Nakamura, Y., 'Real-time bispectral analysis of gear noise and its applications to contactless diagnosis', Journal of the Acoustical Society of America 62, 1977, 382-387.
18. Sato, T., Kishimoto, T., and Sasaki, K., 'Laser Doppler particle measuring system using nonsinusoidal forced vibration and bispectral analysis', Applied Optics 17, 1978, 667-670.
19. Kim, Y. C. and Powers, E. J., 'Digital bispectral analysis and its applications to nonlinear wave interactions', IEEE Transactions on Plasma Science 7, 1979, 120-131.
20. Raghuveer, M. and Nikias, C. L., 'Bispectrum estimation: A parametric approach', IEEE Transactions on Acoustic, Speech and Signal Processing 33, 1985, 1213-1230.
21. Raghuveer, M. and Nikias, C. L., 'Bispectrum estimation via AR modeling', Signal Processing 9(1), 1986, 35-48.
22. Kim, Y. C., Beall, J. M., Powers, E. J., and Miksad, R. W., 'Bispectrum and nonlinear wave coupling', Physics of Fluids 23(2), 1980, 258-263.
23. Gallego, A., Carrión, M. C., Ruiz, D. P., and Medouri, A., 'Prewindowed and postwindowed methods for bispectrum estimation via AR modelling', IEE Electronics Letters 29(2), 1993, 181-182.
24. Gallego, A., Carrión, M. C., Ruiz, D. P., and Medouri, A., 'The relationship between AR-modelling bispectral estimation and the theory of linear prediction', Signal Processing 37(3), 1994, 381-388.
25. Makhoul, J., 'Linear prediction: A tutorial review', Proceedings of the IEEE 63(4), 1975, 561-580.
26. Zohar, S., 'The solution of a Toeplitz set of linear equations', Journal of the Association for Computing Machinery 21, 1974, 272-276.
27. Marple, S. L., Digital Spectral Analysis with Applications, Prentice Hall, Englewood Cliffs, NJ, 1987.