Kernel Methods For Nonlinear System Identification,Equalization,Separation Of Signals And Its Application In Fault Diagnosis

This paper is supported by the National Natural Science Foundation of China (50775208、51075372), the Mechanical Equipment Health Maintenance Foundation of Hunan Province Key Laboratory (200904) and the Natural Science Foundation of Henan Education Department (2008C460003), nonlinear system identification, equalization and signal separation method based on kernel function is studied, and successfully applied to the mechanical fault diagnosis, some innovative achievements are obtained. The main content of this paper is as follows:The first chapter introduces the research significance of this topic, reviews the research status of the kernel function method and its application in mechanical fault diagnosis at home and abroad, as well as its application in fault diagnosis. At last, summarizes the main content and innovation of this paper.The second chapter introduces the basic idea of the kernel space theory, on this basis, and shows some commonly used kernel functions and their properties, the necessary and sufficient conditions to choose the kernel function and the nonlinear mapping of the kernel function. The content of this chapter is the theoretical foundation of the whole thesis.The third chapter discusses the identification principle of the kernel recursive least square method and its three classic algorithm, they are ALD-KRLS, SW-KRLS and FB-KRLS. Through a simulation study, I have made a comparion with the traditional RLS algorithm and the KRLS algorithm for nonlinear system identification. Simulation result shows that, the KRLS identification algorithm is superior to the traditional RLS identification algorithm in the performance of identification precision, stability and anti-jamming. SW-KRLS algorithm obtains the best identification than the other. The SW-KRLS algorithm is especially suitable for time varying nonlinear system identification. On this foundation, I put forward mechanical fault identification method based on KRLS, and apply it to the rotor system fault diagnosis. The experiment result shows that the proposed method is effective. The fourth chapter, in view of limitation of the traditional adaptive equalization method, a new adaptive equalization method based on KRLS is proposed. By introducing the kernel function, the original nonlinear data is mapped into high dimensional feature space, then implementing standard least square algorithm. In the following, the proposed method and the traditional method are contrasted and analysised, the simulation result shows that the proposed method is superior to the traditional method. It can eliminate the transmission channel, and extract the weak impact resistance components effectively. Finally, the proposed method is applied to extracting weak resistance fault of rotor system. The experiment result shows that this method is effective.The fifth chapter discusses the basic idea and algorithm of the independent component analysis and the kernel independent component analysis in detail. KICA is a nonlinear algorithm. It is the extension of the ICA in high dimensional feature space. Its performance is more excellent. It can solve many problems which can not be solved by classic ICA method, such as nonlinear mixed blind signal separation. In view of the traditional independent component in dealing with nonlinear mixed fault source separation insufficiency, I propose a new nonlinear mixed mechanical fault source blind separation method based on KICA. This method using the advantage of the kernel function, the signal from the low dimensional nonlinear space is transformed into high dimensional feature space, where they can be separated by linear ICA method. The simulation result shows that, compared with traditional ICA method, the KICA method has obvious advantage in dealing with nonlinear mixted blind source separation problem. Finally, the proposed method is applied to the problem of bearing fault signal blind separation, the experiment result shows that this method is effective.The sixth chapter is the summary of the whole thesis, and put forward some issue for further research.