变分模态分解方法及其在机械故障诊断中的应用研究

Variational mode decomposition (VMD) is a newly developed methodology for adaptive signal decomposition, which can non-recursively decompose a multi-component signal into a number of quasi-orthogonal and band-limited intrinsic mode functions (BLIMF). VMD is theoretically well founded and a non-recursive algorithm which allows for backward error correction. Wiener filtering is embedded into the VMD algorithm that makes it be much more robust to sampling and noise. A convex optimization technique is used in the VMD which can effectively reduce the confusion of the mode. As such, VMD is very applicable for processing mechanical vibration signal and extracting fault signatures. Since VMD is just developed, this project is devoted to its theoretical research and is firstly adopted it into the fields of mechanical fault diagnosis. Aiming at the key problems of VMD, solutions for the core optimization and instantaneous frequency of the decomposed BLIMF are proposed. For the study of the key parts in rotating machines, an iterative VMD interval-thresholding denoising technique and instantaneous time-frequency spectrum for VMD are developed for the mechanical fault prognosis and feature extraction under time-varying conditions, respectively. Based on the above research, complex VMD (CVMD) is newly proposed for the analysis of 2-dimensional signals and it is then used for the multi-source coupling fault diagnosis in rotor systems. The project research results have important meaning to the improvement of the adaptive signal analysis as well as mechanical fault diagnosis technology.

变分模态分解(Variational Mode Decomposition，VMD)是一种新的信号自适应处理方法，它采用非递归方式自适应分解信号为准正交带限内禀模态函数，具备误差反向纠错能力和完整数学基础。VMD所内嵌维纳滤波使其对噪声和采样不敏感，而固有凸优化算法可有效减小模态混淆，因此非常适合于机械振动信号处理与故障特征提取。由于VMD提出不久，本项目将完善VMD理论并首次应用于机械故障诊断。拟解决VMD核心优化算法全局收敛性、瞬时频率求解等关键问题。以旋转机械关键部件为研究对象，提出VMD循环区间阈值降噪方法、VMD瞬时时频谱等技术，为机械故障早期预示、时变工况特征提取提供新途径。在此基础上，拓展基本VMD算法，提出复数变分模态分解方法；融合VMD降噪与瞬时时频谱，提出转子系统耦合故障诊断新方法。本项目研究对于自适应信号处理的发展、机械故障诊断技术水平的提高都具有重要意义。

变分模态分解(Variational Mode Decomposition，VMD)是一种新的信号自适应处理方法，它采用非递归方式自适应分解信号为准正交带限内禀模态函数，具备误差反向纠错能力和完整数学基础。VMD所内嵌维纳滤波使其对噪声和采样不敏感，而固有凸优化算法可有效减小模态混淆，因此非常适合于机械振动信号处理与故障特征提取。本项目完善VMD理论并首次应用于机械故障诊断。以旋转机械关键部件为研究对象，①提出了齿轮点蚀故障二维高斯分布新模型与时变啮合刚度计算方法；②研究了变分模式分解的在不规则采样、脉冲响应、分数高斯噪声和tone分离等方面的滤波带特性；③基于变分模式分解和总变差的信号降噪方法；④计算阶比分析和变分模态分解结合的滚动轴承变转速故障诊断方法；⑤VMD的调制谱强度分布在齿轮故障诊断中的应用研究，为机械故障早期预示、时变工况特征提取提供新途径。在此基础上，拓展基本VMD算法，提出复数变分模态分解方法，并应用于转子系统碰摩故障正交双路诊断中国。本项目研究对于自适应信号处理的发展、机械故障诊断技术水平的提高都具有重要意义。