Research On The Fault Diagnosis Method For Gearbox Based On Graph Signal Processing

With the rapid development of science and technology and modern industry,mechanical equipment has become more complex,sophisticated and compact.Once a certain link of the mechanical equipment fails,it will affect the normal production of the equipment,and even cause casualties.Therefore,it has very critical realistic meanings to study effective mechanical equipment condition monitoring and fault diagnosis technology to judge and prevent the occurrence of equipment failures in a timely manner.Gearbox is important parts of the mechanical syst em,and ensuring their good running status is directly associated with the normal production of the entire mechanical equipment.However,because of the complexity of mechanical equipment and the harsh working conditions,the collected vibration signals ar e often complex and non-linear.It is difficult to extract fault features from such complex signals using traditional signal processing methods,which affects the id entification of failure modes.Therefore,it is necessary to study new methods of mechanical fault diagnosis.This paper,with the funding of the National Natural Science Foundation of China（No.51875182）,takes rolling bearings and gearboxes as the research objects,introduces graph signal processing into the field of mechanical fault diagnosi s,and carries out research on feature extraction,fault component separation and pattern recognition,etc.And a series of fault diagnosis methods based on graph signal processing have been proposed.The main research work of this paper includes:（1）In order to extract the non-stationary and non-linear fault features of rolling bearing vibration signals more accurately and effectively,complex network and graph signal processing（GSP）was introduced into the field of mechanical fault diagnosis,and a method of rolling bearing fault diagnosis based on the graph spectrum amplitude entropy of visibility graph(GSAE_VG)was proposed.Firstly,the vibration signal of rolling bearing was transformed into visibility graph signal;then,the visibility graph signal was transformed from vertex domain to graph spectrum domain by graph Fourier translation（GFT）,and graph spectrum amplitude entropy was calculated as the fault characteristic parameter.Finally,Mahalanobis distance discriminant function is used as classifier to recognize different types of faults.From the analysis results of actual rolling bearing vibration signals,it can be seen that the fault diagnosis method based on the graph spectrum amplitude entropy of visibility graph can not only effectively extract the fault features of rolling bearing,but also accurately identify the multi-type bearing faults,and it is a simple and effective method for feature extraction without considering the problem of parameter selection.（2）In order to solve the problem that it is difficult to accurately identify the fault components by directly enveloping the composite fault vibration signal of the gearbox,a method of gearbox compound fault diagnosis based on adaptive threshold windowed graph Fourier transform（WGFT）of visibility graph is proposed.Firstly,the simulation signals of gear and bearing faults were analyzed by WGFT,and the order distributions of different signal vertex-graph spectrum coefficients were studied:the vertex-graph spectrum coefficients of gear fault simulation signals were projected to the low-order region,and the vertex-graph spectrum coefficients of bearing fault simulation signals were projected to the high-order region.Combined with this characteristic,the feasibility of reconstructing each fault component is analyzed.Then,the order threshold of the reconstructed fault components was optimized by combining the artificial fish swarm algorithm and the change rate of si gnal kurtosis.Each fault component was reconstructed according to the vertex-graph spectrum coefficients within the range of the optimized order threshold.Finally,the envelope demodulation analysis of each fault component was carried out.The experiment al results show that this method can effectively separate the vibration signal components of the gearbox composite fault,and then diagnose the gearbox composite fault accurately.（3）Aiming at the problem of pattern recognition for multiple types of gearbox faults under limited label samples,the idea of semi-supervised classification is combined with graph convolutional networks,and an intelligent fault diagnosis method for gearboxes based on semi-supervised graph convolution networks（SSGCN）is proposed.In order to obtain satisfactory diagnostic results,in this proposed method,an undirected k-nearest neighbor graph weighted by thermonuclear is constructed and expressed in the form of adjacency matrix to fully reflect the local geometric characteristics of each signal.Secondly,some key hyper-parameters were optimized by grid search method,and the frequency domain signals and graph adjacency matrix were input into the two-layer SSGCN model to train the parameters of the model.Finally,the unlabeled fault samples are classified.The application examples show that,compared with the supervised deep learning method,the proposed method can not only adaptively extract the available fault features from the frequency domain signals,but also effectively identify different types of gearbox with compound faults.It is an effective and feasible end-to-end semi-supervised method.Based on the graph signal processing method,this paper conducts in-depth research on the new methods of feature extraction,f ault component extraction and pattern recognition in the field of Gearbox fault diagnosis,and proposes a series of mechanical fault diagnosis method based on graph signal processing.Algorithm simulation and experimental results show that the method propo sed in this paper has certain application prospects in Gearbox fault diagnosis.