Fault Diagnosis Method Of Rotating Machinery Based On Fractional Calculus Full Vector Spectrum

This paper is in the National Natural Science Foundation of China(51261024,51075372,51265039,50775208), Jiangxi Province Education Department Science and technology project(No. GJJ12405), mechanical transmission State Key Laboratory Open Fund(No. SKLMT-KFKT-201514) and Jiangxi Provincial Department of Education Science and technology project(No. GJJ12405) funded expansion research, combined with the spectrum analysis of the respective advantages of the technology and the fractional Fourier transform, the fractional vector power spectrum, fractional vector Wigner distribution, fractional vector wavelet analysis, fractional vector wavelet packet analysis method, and applied to rotating machines so fault diagnosis, and achieved good innovative achievements. Its main research contents are as follows:The first chapter, expounds the fractional vector spectrum theory put forward the necessity and significance of the research, discusses the full vector spectrum theory and in fault diagnosis of domestic and foreign research status. At the same time, the paper also discusses research status at home and abroad of the fractional Fourier transform. On this basis, the paper puts forward the content and innovation of this paper.In the second chapter, the theory and algorithm of the full vector spectrum are discussed in detail, and the definition, algorithm, character and unique advantage of the fractional Fourier transform are discussed. Combined with the full vector spectrum technology theory and fractional Fourier transform, the fractional full vector spectrum analysis method, the characteristics of the method is inherited the fractional Fourier transform of energy aggregation properties and the full vector spectrum technology can to ensure the maximum degree of information integrity, comprehensive advantages, according to the characteristics of the fault signal, select the appropriate rotation angle to calculate, in the direction of maximum energy to implement full information fusion. To rotor system with looseness fault as an example, the experimental study. The experimental results show that the method can not only realize the fault feature extraction, and rotor homologous double channel information integration, also can accurately reflect the vibration characteristics of the rotor system. Finally, the definition and algorithm of fractional power spectrum are given, and the fractional power spectrum analysis is successfully applied to the fault diagnosis of rotating machinery.The third chapter, discusses the vector Wigner distribution is defined and an algorithm is presented based on, similar vector Wigner distribution defined, combined with the characteristics of each of the vector Wigner distribution and the fractional Fourier transform, fractional vector Wigner distribution is proposed, and gives the corresponding definitions and algorithms. Based on the proposed method of rotating machinery fault diagnosis based on fractional vector Wigner distribution, the method fully absorb the full vector spectrum to ensure information integrity, comprehensiveness and spinning characteristics of Wigner distribution of high time-frequency resolution and fractional Fourier transform, effectively reduced low Wigner distribution cross term interference, etc.. Simulation results show that. The proposed fractional order Wigner distribution is effective and can effectively integrate the information of different channels. Finally, the proposed method is applied to the base of the rotor system, and the effectiveness of the method is verified.Chapter four, discusses in detail the theory and algorithm of vector wavelet analysis based on, similar vector wavelet analysis method of definition, combined with the vector wavelet analysis technology and fractional Fourier transform of the respective characteristics, fractional vector wavelet analysis technology, and gives the corresponding definitions and algorithms is proposed. On this basis, put forward to fractional vector wavelet analysis as the basis of rotating machinery fault diagnosis method, the method fully absorb the full vector spectrum to ensure information integrity, comprehensiveness and wavelet analysis of the localization analysis of characteristics and fractional order Fourier transform characteristics of rotating signal processing, and increase the transform coefficient, namely order p, making in determining the fractional wavelet coefficient is more flexible. And the wavelet analysis theory is extended to the generalized time frequency domain, which makes the analysis field of the signal becomes larger. Finally, the proposed method is applied to the analysis of rotor loose fault, and the effectiveness of the proposed method is verified.In the fifth chapter, this chapter discusses the theory and algorithm of vector wavelet packet analysis. The definition of similar dyadic wavelet packet analysis, the wavelet packet analysis and the respective characteristics of the fractional Fourier transform, the fractional order vector wavelet packet analysis is proposed, and the corresponding definition and algorithm are given. And based on this proposed method of rotating machinery fault diagnosis based on fractional vector wavelet packet analysis. The method fully absorb the full vector spectrum to ensure information integrity, comprehensiveness, and wavelet packet analysis can better the detail information of the signal characteristics and fractional Fourier transform, the rotation of the characteristics, effectively reduces the interference in rotating machinery noise to signal analysis and wavelet packet analysis extension to generalized time frequency domain, the signal analysis field larger detailed finally. The proposed method is applied to the rotor looseness fault in, further verify the effectiveness of this method.In the sixth chapter, the content of this paper is summarized and analyzed, and the direction of further research is put forward.