Complex three-order cumulant has different definition forms. Different forms conclude different information. For studying the effection of frequency in the coupled signals to fault diagnosis, the differential method to the three order cumulants of coupled signals is adopted. By using the differential of complex three order cumulants before and after respectively, then their ？dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.
References
[1]
Feng, Y.X., Zhang, W.P., Yang, T., et al. (2015) Wind Turbine Planetary Gearbox Fault Analysis Based on Bispectrum. Advanced Materials Research, 1070-1072, 1861-1868.
[2]
Zhang, R.G. and Tan, Y.H. (2014) Intelligent Fault Diagnosis of Rolling Element Bearings Based on Bispectrum Principal Components Analysis. Zhendong Gongcheng Xuebao/Journal of Vibration Engineering, 27, 763-769.
[3]
Wang, H., Deng, G., Li, Q., et al. (2016) Research on Bispectrum Analysis of Secondary Feature for Vehicle Exterior Noise Based on Nonnegative Tucker3 Decomposition. Eksploatacja i Niezawodnosc (Maintenance and Reliability), 18, 291-298. https://doi.org/10.17531/ein.2016.2.18
[4]
Kesler, S.B. (1986) Modern Spectrum Analysis. IEEE Press, Piscataway, New Jersey.
[5]
Marple, S.L. (1987) Digital Spectral Analysis with Applications. Prentice-Hall, Upper Saddle River, New Jersey.
[6]
Raughveer, M.R. (1990) Time-Domain Approaches to Quadratic Phase Coupling Estimation. IEEE Transactions on Automatic Control, 35, 48-56. https://doi.org/10.1109/9.45142
[7]
Zhang, Y. and Wang, S.X. (1998) The Slice Spectra Approach to Nonlinear Phase Coupling Analysis. Acta Electronica Sinica, 26, 104-109.
Wu, W.B., Yang, S.Q., Zhou, T.G. (2013) Application of Complex Three-Order Cumulants to Fault Diagnosis of Hydraulic Valve. Journal of Tianjin University (Science and Technology), 46, 590-595.
[10]
Wu, W.B., Huang, Y.J. and Chen, W.X. (2012) High Order Spectrum’s Coupling Performance Based on Mechanical Fault Diagnosis. Journal of Vibration, Measurement & Diagnosis, 32, 130-134.
[11]
Hinich, M.J. (1990) Higher Order Cumulants and Cumulant Spectra. 5th ASSP Workshop on Spectrum Estimation and Modeling, Rochester, NY, 10-12 October 1990, 391-402. https://doi.org/10.1109/SPECT.1990.205534
[12]
Wu, W.B., Huang, Y.J. and Chen, W.X. (2013) The Impact of Complex Cumulants’ Conpling Properties on the Results of Fault Diagnosis. Machine Design and Research, 29, 14-17.
![\"\"](\"Edit_2105131d-e3cd-4d2c-9651-674df1289104.bmp\")
？dimensional spectrum is calculated, and the results are used to fault diagnosis. The experimental results show that, the increase frequency item in three order cumulants after differentiated impacts on the results of fault diagnosis and the degree of effection is relative to the differential times. And the correct rate of fault diagnosis can be raised by changing the differential times of three order cumulants.
