Studied The Mechanical Fault Diagnosis Method Based On Kernel Function Method

Kernel function method is a strong technology to promote linear method to non-linear method,which is a non-linear data treatment method.This thesis makes more advanced research on the application of kernel function method to the mechanical fault diagnosis,which combines the National Natural Science Foundation of China(No.50775208) and the Natural Science Foundation of He'nan Educational Committee,China(No.2006460005,2008C460003).The content of each chapter of the dissertation is as follows:In the first chapter,the subject and the meaning of this thesis is set forth.This chapter summarizes the development and application of kernel function method in mechanical fault diagnosis up to now,and then states the main points and the innovation of this thesis.The second chapter states the basis theory of kernel function method,and then makes further research on kernel space,kernel function and its nature,the necessary and sufficient condition for the selection of kernel function,and non-linear map of kernel function.The content of this chapter is the basis of the dissertation.In the third chapter,the kernel principle component analysis(KPCA) reserves the merit of principle component analysis and can process nonlinear problem,a fault diagnosis method based on KPCA is proposed.The proposed method can transform a nonlinear problem into the higher dimensional linear feature space by kernel function map.Then the PCA method is used to this dimensional space to extract the nonlinear features.The fault patterns can be recognized by this nonlinear features,then applies it to rotor fault and Roller Bearing fault.At the same time,the recognition effect of the PCA and KPCA is compared.The experiment result shows that the KPCA method can better recognize the fault patterns.Combined the advantages of the full vector spectrum and kernel principle component analysis(KPCA),a new fault diagnosis method of rotating machinery based on the full vector spectrum and KPCA is proposed.The proposed method makes full use of t he integrality and completeness of the rotor information extracted by the full vector spectrum method,and the capability of nonlinear problem processed by the KPCA method.The proposed method is compared with the KPCA method,the experiment result shows that the proposed method is very effective,this method can better extract the nonlinear feature of the fault in the rotating machine,and recognize the fault patterns effectively.The fourth chapter focuses on the disadvantage of KPCA mechanical fault diagnosis method,namely KPCA can't separate from every training sample,which will increases the complexity and quantity of calculations.A new fault diagnosis method of machine based on the sparse kernel principle component analysis(SKPCA) is proposed.The proposed method can transform a nonlinear problem into the higher dimensional linear feature space by kernel function mapping.The covariance matrix of the mapping data is sparse by the adjustable weights.The weights are optimized using a maximum-likelihood approach.Then the PCA method is used to this feature space to extract the nonlinear features.The sparse kernel principle component analysis(SKPCA) reserves the merit of kernel principle component analysis(KPCA), at the same time the speed of pattern recognition is greatly enhanced under the recognized efficiency is not reduced.The simulation shows that SKPCA and KPCA almost have the same recognition effectiveness.However SKPCA reduce the computational overhead of the kernel matrix,so the recognition speed of SKPCA is greatly accelerated.The fifth chapter elaborates the basic theory and calculation of kernel independent component analysis,does a simulation experiment,and applies the method into the source separation of mechanical fault.An experiment is taken by using roller bearing fault as example,and the result is compared with that of independent component analysis.The result shows that this method gets a better effect on the fault source separation of roller bearing.The characteristic of this method is that it adapts the distribution of sub-Gaussian and sup-Gauss.It also suits for signal source separation of non-linear characteristics data and provides a mean for source separation of mechanical fault.In the sixth chapter,the conclusions of the dissertation are summarized.Future research of kernel methods is prospected.