| Gearbox is an important part of rotating machinery,which covers a wide range of mechanical equipment and plays an important role in industrial applications.Gearboxes generally operate under harsh working conditions,and their key components,rolling bearings and gears,are prone to failure,so ensuring their normal operation is of great significance to reduce economic losses and avoid catastrophic accidents.Using effective signal processing methods to analyze vibration signals and reveal fault features is one of the common strategies for mechanical fault diagnosis.With the progress of science and technology and the development of modern industry,the fault vibration signals of mechanical equipment become more and more complex.Coupled with the non-linearity and non-stationary of gearbox fault vibration signals,the traditional signal processing methods will still cause the“misdiagnosis”and“missed diagnosis”of gearbox faults.Therefore,it is necessary to explore the new fault diagnosis methods for gearbox.Supported by the National Natural Science Foundation of China(No.51875182),this paper takes the vibration signals of gearbox as the research object,introduces the graph signal proc essing methods into the field of mechanical fault diagnosis,and makes a deep and systematic study on the fault feature extraction and pattern recognition of gearbox.This paper has carried out and completed the following research works:(1)Aiming at the problem that it is difficult to extract the fault impulse components from rolling bearing vibration signals under strong background noise and other interference components,a rolling bearing fault diagnosis method is proposed based on horizontal visibility graph and graph Fourier transform(GFT).In the proposed method,the vibration signal collected from a faulty rolling bearing is first converted into a horizontal visibility graph.Then,the GFT is performed on the graph signal to obtain the corresponding graph spectrum.Since most of the fault impulse components are clustered in the high-order region of graph spectrum,only the last few graph spectrum coefficients are selected for the inverse analysis of GFT to extract the fault impulse components in the original vibration signal.Finally,the extracted fault impulse components are subjected to the envelope demodulation analysis to diagnose the rolling bearing fault.Simulation and experimental results indicate that compared with the GFT based on path graph and the spectral kurtosis,the GFT based on horizontal visibility graph can extract the fault impulse components of rolling bearings more effectively and has stronger anti-noise performance.(2)Aimed at the characteristic that vibration signals of gearb ox with different faults have horizontal visibility graphs with different structures,a gearbox fault diagnosis method is proposed based on the index of total variation on graph(TV _G)and Mahalanobis distance.In the proposed method,the vibration signals of gearbox are also converted into horizontal visibility graphs.Then,the TV _G index of the graph signals is extracted as the single fault feature of gearbox.Finally,Mahalanobis distance is used to identify the gearbox states.Experimental results show t hat the proposed method can accurately diagnose the gearbox faults with different types and degrees,and the TV_G index is obviously better than the classical time-domain indexes including approximate entropy,permutation entropy,kurtosis and root mean squ are in distinguishing different states of gearbox.(3)In order to extract the nonlinear and non-stationary fault features of gearbox vibration signals accurately and effectively,a gearbox fault diagnosis method is proposed based on graph spectral indexes and K-means clustering.After converting the vibration signals of gearbox into path graphs,multiple graph spectral indexes are extracted.The graph spectral indexes are sorted by the Fisher score algorithm,and several of the most sensitive graph spectral indexes are selected as the fault features of gearbox.The K-means clustering algorithm is used to identify different faults of gearbox.Experimental results indicate that the graph spectral indexes can not only effectively distinguish different types of rolling bearing faults,but also effectively distinguish different degrees of inner and outer ring faults,and the distinguishing ability is obviously superior to the traditional time-domain indexes and frequency-domain indexes.(4)Laplacian regularization(Lap R)is a semi-supervised classification method based on undirected graph,which can obtain more classification information by using not only a small number of known samples,but also a large number of unknown samples.Aiming at the problem of multi-fault pattern recognition with a small number of known samples,a gearbox fault diagnosis method is proposed based on Lap R.The vibration dataset or feature dataset is first constructed into an undirected and weighted k-nearest neighbor graph.Then,the labels of samples in the dataset are regarded as graph signals indexed by vertices of the nearest neighbor graph,and the smoothness of graph signals is measured by the TV _G index based on Laplacian matrix.Finally,the states of all unknown sample are determi ned by finding the smoothest graph signal under the condition of satisfying the labeled constraint given by known samples as far as possible.Experimental results indicate that whether in the analysis of vibration datasets or feature datasets,the Lap R cla ssification method is superior to K-nearest neighbor classifier,support vector machine and other commonly used classification methods in gearbox fault diagnosis,and the advantage is more obvious with less known samples.(5)Graph shift regularization(GSR)is a semi-supervised classification method based on arbitrary graph.Aiming at the problem that the Lap R classification method is only applicable to undirected graphs,an intelligent fault diagnosis method for gearbox is proposed based on directed GSR.The vibration dataset of gearbox is directly constructed into a more appropriate,directed and weighted k-nearest neighbor graph.Then,the labels of samples in the vibration dataset are regarded as graph signals indexed by vertices of the nearest neighbor graph,and the smoothness of graph signals is measured by the TV_G index based on graph shift.Finally,the states of all unknown sample are determined by finding the smoothest graph signal under the condition of satisfying the labeled constraint given by known samples as far as possible.Experimental results show that the directed GSR is better and more stable than the undirected GSR,convolutional neural network and support vector machine in gearbox fault diagnosis,and it has only two adjustable paramete rs which are easy to determine the optimal value.In this paper,the application of graph signal processing methods in gearbox fault diagnosis is studied deeply.The graph signal processing methods are respectively applied to the fault feature extraction and pattern recognition of gearbox,and complete and systematic gearbox fault diagnosis methods are proposed based on graph signal processing.The research results show that the proposed methods have a good application prospect in gearbox fault diagnosis. |
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