图信号处理方法是近年来随着图谱理论发展而出现的新研究领域，该方法能有效提取隐藏在数据集内部的特征信息。本项目拟将图信号处理与复杂网络引入机械故障诊断领域，建立起完整、系统的图谱域机械故障诊断方法。主要研究工作包括：（1）根据各类典型机械故障振动信号的特点，研究建立振动信号与图结构的转换算法；（2）以图离散信号处理、图傅里叶变换、图短时傅里叶变换、图小波变换和图经验模态分解为基础，研究提出图谱域上振动信号的滤波、去噪、变换与分解方法；（3）基于图信号的矩阵谱与图谱域振动信号分析处理方法，研究建立各类典型机械故障的图谱域特征指标；（4）对各类典型机械故障，以提取振动信号中的故障特征和分离振动信号中的故障分量为基础，提出有效的图谱域诊断方法。本项目研究工作是时域、频域和时-频域机械故障诊断方法的重要拓展，将为机械故障诊断提供新的有效途径，具有重要的理论意义和工程应用价值。

The graph signal processing (GSP) is a new research field with the development of the spectral graph theory in recent years, which can effectively extract the feature information hidden in the data set. The purpose of this project is to establish a new kind of methodology for mechanical fault diagnosis from the graph spectral domain by introducing the GSP and complex network into the field of mechanical fault diagnosis. The research work of this project mainly includes: (1) building the conversion algorithm between the graph structure and the vibration signal of various typical mechanical faults according to the characteristics of the vibration signal; (2) proposing the methods for filtering, denoising, transformation and decomposition of the vibration signal in the graph spectral domain by using the discrete signal processing on graphs, the graph Fourier transform, the graph short-time Fourier transform, the graph wavelet transform and the graph empirical mode decomposition; (3) establishing the graph spectral feature indices of various typical mechanical faults based on the matrix spectrums of graph signal and GSP; (4) presenting effective diagnosis methods for various typical mechanical faults by extracting fault features and separating fault components in the graph spectral domain. This project is an important extension of the traditional mechanical fault diagnosis methods from the time domain, frequency domain and time-frequency domain, which can provide new and effective ways for mechanical fault diagnosis. Therefore, this project is of great significance to both theoretical research and engineering application.