Rolling Bearing Fault Diagnosis Based On The Variational Mode Decomposition And Generalized Fractal Dimension

The development of modern industrial equipment is increasingly large, complex, high-speed and full automatic. Bearing is one of the most common and most easily damaged parts in rotating machinery. The status of their work directly affects the performance of the whole equipment. The service life of each bearing is greatly different, so make periodic maintenance according the service life might cause the waste of resources and it is difficult to detect the sudden failure. So it is very important to detect and diagnose the fault. In this paper, a method of feature extraction and fault diagnosis about the vibration signal of a rolling bearing is put forward and make a study of the application of fractal theory and variational mode decomposition in rolling bearing fault.First of all, the common forms of bearing fault and its formation mechanism is introduced. Then the paper describes the bearing vibration signal feature extraction method and the basic process of rolling bearing fault diagnosis in detail.Secondly, the fractal theory and fractal dimension are described in detail and analyze the fractal characteristic of the bearing vibration signal, mainly including the selfsimilarity, scale invariance and multifractal characteristics. It is proved that the fractal method can be used to analyze the complexity of the bearing vibration signal, and the fractal characteristic of the signal can be quantitatively described. Then, the fractal dimension and the generalized fractal dimension of the fractal dimension are selected as the characteristic to achieve the status of the fault signal. In addition, the advantages and disadvantages of fractal and multifractal fault diagnosis methods are also analyzed in detail.Then, a method of bearing fault diagnosis based on the generalized fractal dimension matrix is proposed. The method is an extension of the generalized fractal dimension, and it requires that the signal is decomposed by the variational method. The VMD mtheod is a kind of non recursive and variational method. It obtains the decomposition components by iteratively searching the optimal solution of the variational model to get the frequency center and bandwidth of each component. The signal can be decomposed into several modal functions(Function Mode, MF) by the method of VMD. Then obtain the generalized fractal dimension of each modal component to construct the generalized fractal dimension matrix as the feature and identify the state of the equipment by the correlation analysis.Finally, the rolling bearing fault data of Case Western Reserve University is studied as the research object to analysis the different part of rolling bearing fault and different degree of damage. Then, make a comparison between the generalized fractal dimension matrix method and the generalized fractal dimension method to demonstrate that the generalized fractal dimension matrix method has a better feasibility and accuracy.