| The mechanical fault diagnosis is very important to ensure the normal operation of the rotating machinery and has important theoretical significance and practical value. When a local failure occurs in mechanical equipment, the fault information will be contained in its vibration signal. Therefore, how to extract the fault feature information from the vibration signal and how to conduct pattern recognition are hotspots in the area of machinery condition monitoring and fault diagn osis.Gearbox is the most commonly used key component of machinery. Meanwhile, ensure the safe and stable operation of gearbox is an important part of the equipment maintenance.But the working condition of the gearbox is very complex, the rotaing speed is varied greatly, and the load carrying capacity is various. These factors would adversely affect gearbox fault diagnosis, thereby reducing the performance of traditional diagnosis methods. Through the analysis of the eigenvalues and eigenvectors of the graph matrix, the graph spectrum theory can effectively extra ct the fault information hidden in the data. Supported by National Natural Science Foundation(No. 51275161), this dissertation focuses on the gearbox fault signal, and combines the graph spectrum theory with modern signal processing theory to study a series of questions in the process of gearbox fault diagnosis, such as the feature extraction, the feature selection, the pattern recognition, and the component extraction. On this basis, this dissertation establishes a complete and systematic gearbox fault diagnosis method based on graph spectrum theory.The main works and innovative achievements of this dissertation are as follows:(1) The path graph is introduced into the time series analysis, and the Graph Fourier Transform(GFT) of the path graph signal under different weights are investigated from the graph spectrum domain. For the case that the traditional definitions of weights are hard to reflect the differences among the vertices, a new weight is defined by the Euclidean distance. The investigation results show that: in the case of the weights are defined as 1, the amplitude characteristics of the GFT graph spectrum domain are more obvious than that of Fourier Transform(FT), the eigenvectors of Laplacian behaves like the harmonic form and there is a corresponding relationship between the order and the frequency; in the case of the weights are defined by the Euclidean distance, the eigenvectors of Laplacian have obvious local characteristics, namely, the higher the order of a eigenvector, the more the eigenvector like an impulse. This also means that the impulse characteristics of the signal are reflected by the spectrum lines in the high-order region of GFT graph spectrum.(2) To solve the problem that the sensitivity fault features of the initial feature set are difficult to distinguish, the Laplaian Score(LS) is applied to the fault feature selection of the rolling bearing vibration signals and then a fault diagnosis method of rolling bearing is proposed using LS and Fuzzy CMeans(FCM) clustering. In addition, in order to avoid the problem of setting the neighbor graph parameters k in the LS method, a supervised Laplaian Score(SLS) feature selection method is proposed and then a fault diagnosis method of rolling bearing is put forward by combining SLS and Principal Component Analysis(PCA). The vibration signals of rolling bearings are analyzed by the above methods, and the results show that: these two feature selection methods can effectively extract fault related features, reduce the irrelevant or redundant features, and then improve the accuracy of the fault diagnosis. For the feature selection method, unsupervised LS measures the characteristics by the locality preserving ability, while supervised SLS takes into account the data label information and the local geometric structure. As a new supervised feature selection method, the classification effect of SLS is more concentrated than that of LS.(3) In order to apply the graph spectrum method to the pattern recognition of the mechanical fault diagnosis, the correlation spectrum of Laplaian eigenvector is proposed and applied to the fault diagnosis of rolling bearings. The definition of the correlation spectrum of Laplaian eigenvector is the absolute value of cosine of the angle between two Laplaian eigenvectors which are calculated by the standard orthogonal decomposition of the Laplacian of a feature set. Based on the correlation spectrum of Laplaian eigenvector, a method for the fault diagnosis of rolling bearings is proposed. The characteristic of this method is that the fault pattern recognition problem is transformed into the problem of solving eigenvalues. Application examples show that this method can be used to diagnosis the fault of rolling bearing s effectively with simple calculation process, fast calculation speed and high classification accuracy.(4) Based on the characteristics that vibration signals of rolling bearings with different faults have different path graph structures, a fault diagnosis method based on the Laplacian energy(LE) feature extraction and Mahalanobis distance(MD) criterion function is proposed. Experimental analysis results show that the proposed method can identify the rolling bearing faults accurately and effectively, and has the characteristics of requiring only minute amounts of sampling points and training samples.(5) According to the GFT graph spectrum defined by weight 1, the fault diagnosis method based on the GFT feature extraction and the K-means clustering is proposed. The proposed method is used to identify the work condition and fault patterns of the rolling bearing. Results show that the diagnosis method based on the GFT feature extraction can capture the frequency variation characteristics of the graph signal and identify the fault pattern of the rolling bearing effectively. Moreover, the result obtained from the proposed method is much better than the method based on the FT feature extraction.(6) Based upon the GFT graph spectrum with the weight defined by the Euclidean distance, the GFT of simulation signals of the gear and the bearing with localized faults are analyzed. The results show that the GFT graph spect rum of the simulation signal of gear fault is mainly distributed in the lower-order region and the GFT graph spectrum of the simulation signal of bearing fault is concentrated in the high-order region. Therefore, the spectrum lines in the low-order region can be used to reconstruct the gear fault components. Meanwhile, the spectrum lines in the high-order region can be used to reconstruct the bearing fault components. Thus, a fault diagnosis method based on GFT fault component extraction and Hilbert envelope analysis are proposed and applied to the fault diagnosis of rolling bearing and compound fault diagnosis of gearbox, respectively. The analysis results of simulation signals and experimental signals indicate that the proposed method can effectively filter the noise component and highlight the fault characteristics in the envelope spectrum.This dissertation conducts a systematic research on the graph spectrum theory and its applications to gearbox fault diagnosis, such as the feature extraction, the feature selection, the pattern recognition and the fault component extraction, and proposes a complete and systematic gearbox fault diagnosis method based on graph spectrum theory. The research ideas and proposed approaches of this dissertation have a good application prospect in the field of rotating machinery fault diagnosis. |
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