Research On Rolling Bearing Fault Diagnosis Method Based On Dictionary Learning And Sparse Optimization

In order to solve the problem of feature extraction and diagnosis of mechanical signals under complex working conditions and reduce the influence of redundant information in data on signal transmission and storage.Mechanical fault diagnosis methods based on dictionary learning and sparse optimization theory are studied in this paper.The main contents include:sparse optimization model construction based on proximal operator theory,signal matrix separation method and compression method based on dictionary learning,fault feature extraction and compound fault signal diagnosis based on group sparsity.The specific content is as follows:(1)The construction of sparse optimization model based on the proximal operator is studied.Combined with sparse representation and proximal operator theory,a novel scale LP norm sparse proximal operator for bearing fault diagnosis was proposed by studying the Iterative Reweighted Least Square IRLS.The fault features were enhanced by reducing the time-domain redundancy of the signals.Experimental results show that,compared with the traditional non-convex proximal operator,such as the Logarithmic penalty proximal operator with the same sparse balance parameters,it has stronger feature extraction ability.At the same time,Combined with proximal operator theory and traditional total variational method this paper proposes a proximal operator based on least square method is used to simplify the filtering process,the algorithm can reduce the redundant information of frequency domain and enhance the fault features,The method is introduced into bearing fault diagnosis and the experimental results show that the method can effectively reduce the redundancy information in frequency domain and enhance the fault features.Finally,combining sparse optimization theory and L1 norm sparse proximal operator,a sparse representation model based on Fourier transform(FFT-Lasso)was proposed for fault diagnosis,which was solved by forward-backward Splitting(FBS).The basic idea of this algorithm is to highlight fault features by removing redundant information in frequency domain.First,based on FBS theory,Fast Fourier transform(FFT)and gradient descent are used to obtain the temporary value of the current iteration.Finally,sparse representation is realized by L1 norm proximal operator.Experimental results show that FFT-Lasso has stronger fault feature extraction compared with the traditional Lasso model based on FBS.(2)The fault diagnosis and signal compression method based on sparse dictionary learning are studied.A matrix separation algorithm based on dictionary learning and nonlinear programming was proposed for weak fault diagnosis of bearings.First,signals were separated by empirical wavelet transform(EWT),and the kurtosis of different intrinsic mode function(IMF)was analyzed to obtain dictionary atoms containing fault features.Then the matrix separation method based on nonlinear programming is used to separate the noise from the original signal.Finally,the harmonic components are monitored by the envelope spectrum and the fault types are determined by comparing with the theoretical values.The experimental results show that the proposed method is superior to the traditional sparse representation method in fault diagnosis.An online compressed sensing strategy is proposed.The model is based on both Improved Online Dictionary Learning Method and Alternating Direction Multiplier Method ADMM matrix reconstruction method.First of all,at the data acquisition end,due to the slow update speed of Lasso sparse code for line dictionary learning,it is replaced by the Forward Stagewise method,which greatly accelerates the speed of feature learning and effectively realizes signal compression and feature extraction.At the same time,save transmission and storage costs.Finally,considering the problem of unsatisfactory reconstruction caused by the traditional coefficient reconstruction method requiring preset sparsity.The ADMM_L1 matrix reconstruction method based on the idea of base pursuit is proposed to realize the high precision reconstruction of signals without sparsity.Simulation results show that this method can effectively extract features and achieve high precision reconstruction.(3)A sparse fault diagnosis method for overlapping groups based on frequency domain optimization is developed.A denoising method of non-convex sparse overlap group with frequency domain priority is proposed to represent the spectral group sparsity of signals.Firstly,the bearing fault signals were converted into frequency domain signals by using the Fast Fourier Transform(FFT),and the overlap group sparse mathematical model was established by IRLS.At the same time,the group threshold was processed by using the sparsity and energy concentration in frequency domain combined with the filter proximal.operator.Finally,the signal is converted into time domain signal and the fault is diagnosed by envelope spectrum of reconstructed signal.Experimental results show that the proposed method has better feature extraction capability and faster computation speed than the traditional sparse representation methods,such as Laplace correlation filtering and the traditional overlap group sparse algorithm.A composite fault signal separation method based on overlapping sparse group was studied.Based on the periodic characteristics of rotating machinery fault signals at constant speed,the energy detection of periodic group signals is carried out to achieve signal separation.Firstly,the binary cycle group is constructed by prior knowledge,and the sparse mathematical model of the group is constructed by ADMM framework.Then,the fault signals of different frequencies are extracted according to the signal characteristics.Finally,the fault signals are diagnosed by envelope spectrum analysis.Experimental results show that the proposed method is fast in calculation and can effectively separate the signals and noises of different periods in the blind source separation of bearing fault signals,which is superior to the traditional variational mode decomposition(VMD)and independent component analysis(ICA).