Research On Application Of Fractal Theory In Fault Diagnosis

Fractal is an essential feature of a class of things that are ubiquitous in nature and human society.Fractal theory,as an important branch of nonlinear disciplines,is particularly suitable for the analysis of various complex signals.The purpose of this paper is to study the application of fractal theory in fault diagnosis.The vibration signals collected when the equipment is running in different states will have different fractal characteristics.By using the method of measuring the fractal dimension of vibration signals,it can effectively identify the different operating states of the equipment to achieve the purpose of fault diagnosis.In terms of fractal dimension types,the focus is on in-depth discussion of correlation dimension and generalized dimension.1.The G-P correlation dimension algorithm is introduced.We propose a method to calculate the squared sum of the fitting deviations for its algorithm steps,determine the linear region of the double logarithmic graph,and improve the accuracy of the calculation results.By adding different signal-to-noise ratio white noise to the Lorenz attractor simulation signal and then calculating the correlation dimension,the ability of the correlation dimension to resist the influence of noise is studied.2.In this paper,the generalized dimensional calculation method based on point center is studied.The correlation dimension algorithm is extended,and the properties of generalized dimension are analyzed.The generalized dimension spectrum of Chen's attractor signal and Brownian motion trajectory signal is used.The comparison verifies its signal measurement capability.3.Combined with bearing fault data,this paper studies the single-fractal fault diagnosis based on correlation dimension and the general method of multi-fractal fault diagnosis based on generalized dimension.Single-fractal fault diagnosis uses the fractal dimension and state space to classify the fault diagnosis,which has the advantages of fast and small data volume.Multi-fractal fault diagnosis uses sample sequences to characterize different states,and performs state according to the correlation between sequences.The identification makes the fault diagnosis method more flexible and expands the application range of the fractal fault diagnosis method.