Research On The Application Of Graph Signal Processing In Rolling Bearing Fault Diagnosis

Rolling bearing is an important part of mechanical systems.Continuous and normal running of rolling bearing is essential to fully utilize the performance of the equipment.Therefore,it is of great theoretical significance and engineering value to diagnose the bearing fault effectively and timely when the rolling bearing fails with local flaw.At present,the analysis of equipment's vibration signals collected by sensors is the main means to realize condition monitoring and fault diagnosis.Because,the characteristic information in the bearing vibration signal changes when the fault occurs.So it is also a hotspot focused by many researchers in the field of fault diagnosis to realize the bearing fault pattern recognition by extracting the effective feature.Bearing fault diagnosis technology based on new methods and new theories emerges endlessly.And it enables some problems which are difficult to deal with by traditional signal processing or pattern recognition methods can be effectively solved.Supported by the project of Natural Science Foundation of China “Research on Mechanical Fault Diagnosis Methods from the Graph Spectral Domain”(Project Approval Number: 51875182),this thesis takes rolling bearing as the research object,and combines the graph signal processing(GSP)and algebraic method to solve the problems of bearing fault extraction feature extraction,dimension reduction and pattern recognition.The main research contents of this thesis are listed as follows:(1)Aiming at the problem of missed diagnosis of rolling bearing faults by directly performing envelope demodulation with vibration signals in the presence of background noise interference or other interference components,graph signal processing method is introduced into bearing fault diagnosis.Take into account the impulse feature of path graph Laplacian matrix eigenvectors under Gaussian function weight,an optimal weighted graph Fourier transform(GFT)impulse extraction method based on particle swarm optimization algorithm is proposed.In this proposed method,the vibration signal is firstly transformed into path graph under Gaussian function weighted.Then,the amplitude at the fault frequency of the reconstructed impulse signal's envelope spectrum is used as the fitness function in the particle swarm algorithm to get the optimal thermonuclear width.Subsequently,the Laplace matrix eigenvectors within the algebraic connectivity can be used to reconstruct the impulse signal components by using the graph inverse Fourier transform method.Finally,the reconstructed impulse signal is demodulated by envelope demodulation method for the bearing faults diagnosis.The analysis results demonstrate that the proposed method can effectively reconstruct impulse component of rolling bearing fault and diagnose the bearing fault.(2)Because of the redundancy of high-dimensional time and frequency domain feature,the result of fault diagnosis usually is poor.To solve this problem,the eigenvectors corresponding to the zero eigenvalues of the neighbor graph Laplacian matrix is used for the dimension reduction of rolling bearing fault features,and an adaptive spectral clustering algorithm combined with modularity indicators is proposed to diagnose rolling bearing fault.In this method,the high-dimensional time and frequency domain features are extracted from vibration signal to form the initial sample feature set.Then,a neighbor graph is constructed using the feature samples.To solve the problem that the total number of clusters is unknown,the modularity indicators are used to determine it adaptively.After that,the eigenvectors corresponding to the finite zero eigenvalues are used as the dimension reduction feature set of the initial feature sample.Finally,the k-means method is used to cluster the samples to diagnose the fault of the rolling bearing.The results show that the proposed method effectively improves the fault recognition accuracy rate for the pattern recognition problems of different rolling bearing fault.(3)Graph convolution networks(GCN)can automatically extract features and utilize local geometric information of unlabeled samples.So,a fault classification method of rolling bearings based on semi-supervised GCN is proposed to solve the problem of bearing fault semi-supervised classification under low label ratio.In this method,the k-nearest neighbor graph is firstly used to link up the labelled training samples with the unlabelled samples through the distance measurement,as a consequence,the feature information of the labelled samples spread to the unlabelled samples by the edge connection.Then,the deep features of the nodes on the graph structure are extracted by the convolution operation defined on the graph structure.The cross entropy function of the labelled samples is regarded as the loss function and the network parameters are updated by back propagation method.Finally,the fault of unlabelled samples are recognized.This method does not need manual feature extraction and feature selection steps to realizes end to end feature learning and fault classification.The various types of rolling bearing fault signals are used to verify the effectiveness of the proposed method.The analysis results demonstrate that the proposed method can also effectively identify rolling bearing faults.Based on the theory of graph signal processing,this thesis conducts a deep research on the application of correlation methods in fault diagnosis of rolling bearings,such as the fault impulse signal extraction,the feature dimension reduction,the fault clustering,the semi-supervised classification,and proposes some rolling bearing fault diagnosis methods based on graph signal processing.The research results show that the proposed method can effectively diagnose the type of rolling bearing faults,which has certain practical significance and engineering value.