Double Spectral Analysis Of The New Method, Its Application In Engineering

Bispecturm analysis is one of the useful tools for the non-linear systems, non-Gaussian processes and nonminimum phase, and was applied in many fields, such as radar, sonar, physical geography, biomedicine, image reconstruction, mechanical fault diagnosis, harmonic retrieval, array processing etc. However, bispectrum has the limitation, for instance, it is incapable of avoiding the disturbance of non-Gaussian noise. In addition the definition of bispectrum is on the basis of the random stationary signals, but in fact, a lot of time-varying signals are obtained, so its application is restricted to great extent. Based on the deficiency of traditional bispectrum, bispectrum analysis is developed. The theory is developed and perfected, and applied to mechanical fault diagnosis. Following are the primary contributions:1. The definition, character, algorithm and physical meaning of traditional bispectrum analysis were introduced, then the deficiency was analyzed, and the start and the necessity of further study are pointed out.2. Based on the deficiency of traditional bispectrum, which has good insensitivity to independent Gaussian noise. However, it is incapable of avoiding the disturbance of non-Gaussian noise, Combining wavelet transform with bispectrum, a new method based on bispectrum analysis in the wavelet transform domain is proposed, and applied in the fault diagnosis of rolling bearing. The experiment results show that the proposed method is superior to the traditional bispectrum, especially in the exist of non-Gaussian noise.3. The choice of threshold in the wavelet threshold denoising has no the unitive standard, so the denoising threshold is chose through the subject or experience, and the application of wavelet threshold denoising is blocked. Based on it, the method based on wavelet packet bispectrum analysis was introduced, using multi-resolution analysis to extract the frequency band and the band of noise and eigenfrequency is different. The method not only can denoise, but also can escape threshold denoising, and was applied to the fault diagnosis of rolling bearing. The experiment results show the proposed method is effective.4. Aiming at engineering cyclostationary signals, higher order cyclic-statistics (HOCS) was applied to mechanical engineering field. The definition, algorithm and characteristic of cyclic bispectrum analysis were introduced. Using third-order cyclic cumulant is capable of avoiding the disturbance of any Gaussian and non-Gaussian noise, a simple diagnosis method based on the slice spectrum of cycle bispectrum was...