Fault Diagnosis Based On Sparse Representation And Dictionary Learning

On-line monitoring of mechanical equipment will bring mass data transmission and processing pressure.So,data should be represented to sparse and extracted the essential characteristics of the signal,then achieved dimensional analysis and transmission of massive data.The core problem in sparse representation is the construction of sparse dictionaries and the solution of sparse vectors.Therefore,this topic carries out research on dictionary construction and sparse decomposition method based on sparse representation theory and applies it to fault diagnosis.The main contents are as follows:(1)To analyze the sparse representation algorithm theory,the research on the performance of typical sparse decomposition algorithm was developed.Constructing the simulation signal and verifying the orthogonal matching pursuit and least angle regression algorithm by simulation signal.The results show that Orthogonal Matching Pursuit(OMP)can obtain more sparse solutions,and Least Angle Regression Stagewise(LARS)can get a more accurate solution.Therefore,OMP is chosen as the sparse decomposition algorithm in the sparse representation process of this paper,and LARS is chosen as the dictionary updating method in the online dictionary learning process.(2)The method of fault feature extraction and signal reconstruction based on adaptive correlation Laplace dictionary was developed.Firstly,Laplace wavelet is selected as the dictionary atom that represents the impact feature through theoretical study.Then the parameters of Laplace basis function are filtered from the signal by adaptive cross-correlation method;the constructed wavelet is expanded into a complete sparse dictionary through column cycle.Finally,the sparse dictionary is used for the signal sparse representation process,and signal impact features are analyzed from sparse coefficients.Using the experimental verification method for rolling bearing failures,the results show that the sparse representation based on Laplace dictionary can effectively extract the signal impact components.By laminating the Laplace dictionary and the Discrete Cosine Transform(DCT)dictionary,sparse representation and high-precision reconstruction of signals can be realized.(3)The sparse representation fault diagnosis method based on online dictionary learning was proposed.First,segmenting the signal into the learning dictionary,then applying LARS to sparse coding and the block coordinate descending to dictionary update to alternately perform dictionary learning.Finally,the resulting overcomplete dictionary is combined with the segmentation error threshold OMP to solve the sparse representation problem.Sparse representation of the signal can be found.Through using simulation signals and rolling bearing experimental to verify methods,the results show that the sparse representation method based on online dictionary learning can achieve sparse representation of the rolling bearing signal and combine with sparse dictionary to reconstruct the signal,which can effectively extract the fault features of the signal.