Full Vector’s Higher-order Statistics And Its Applicationin Fault Diagnosis

Higher-order statistics analysis is widely adopted in the rotor fault diagnosis because it can extract the nonlinear properties of the signals. But general higher-order statistics analysis is used to regard single channel signal as the research objects, it cannot embody the characteristics completely, and furthermore the analysis conclusions obtained may be different coming from the double channels’ signals at the same cross section. In order to solve this problem, two new developed approaches of higher order statistics is proposed based on the full vector-spectrum analysis method, namely vector bispectrum and vector wigner higher-order spectrum. The definition and algorithm process of vector higher-order statistics are given. The new approaches are applied to the recognition to the rotor fault diagnosis. The main research work is as follows:1. The theory and numerical algorithms of vector spectrum analysis method are expounded in this thesis. It proves that vector spectrum can be totally compatible to the signals at the same cross section and accurately describe the actual state of the rotors. And it overcomes the differences in spectrum structures coming from different directions at the same cross section of general frequency spectrum analysis, then the unique spectrum structure is obtained, which would provide a reliable basis to the next feature extraction and fault diagnosis.2. The advantages and the deficiencies of traditional bispectrum analysis and traditional wigner higher order spectrum are studied, which are verified by experiments. The conclusion that the characters from single channel analysis are not complete is reached, and it’s high time for information fusion.3. Vector bispectrum slices method is proposed combining vector spectrum with bispectrum analysis. The algorithm is given; also the simulation and the fault diagnosis experiment are studied. The results show that vector bispectrum slices can reflect the nonlinear properties of the signals thoroughly and give a consistent conclusion, which could promote the accuracy of fault diagnosis.4. The effect of vector bispectrum slices becomes worse dealing with non–Gaussian signals. So wavelet packet analysis is introduced for its particulates in local optimization. Wavelet packet-vector spectrum is put forward. It not only inherits the extraction of nonlinear properties of vector bispectrum and double channels infusion, but also realizes the wavelet packet’s inhibition of non-Gaussian noise.5. Vector wigner higher-order spectrum is proposed based on vector spectrum and wigner higher-order spectrum, and the definition and algorithm are expounded as well. In order to inhibit cross terms, the filter of Choi-Williams kernel is adopted, which greatly promotes the performance of this method. Through simulation and experiments, it is verified that vector wigner higher-order spectrum performs better than traditional wigner higher-order spectrum.