高维经验模式分解理论及其在设备早期故障诊断中的应用研究

The early fault signals of the mechanical equipment are usually weak signals which are submerged in the strong background signal and strong noise, nonlinear and non-stationary characteristics of the weak signals are obvious, so the traditional methods are difficult to identify and extract them from the collected signals. The High-dimensional Empirical Mode Decomposition (HEMD) algorithm is proposed in this project. One dimensional signal would be reconstructed in the high-dimensional phase space through the phase-space reconstruction method. The high-dimensional signal is decomposed into a series of Intrinsic Mode Function (IMFS) by HEMD. And the attractor mainstream recognition technology and local projection method are used to bring the high-dimensional signal down to the one dimension signal. The gear and bearing fault signal feature extraction and fault classification are researched based on this method. The research ideas are as follows: （1）The multivariate empirical mode decomposition (MEMD) principle is researched and its application to the field of mechanical fault diagnosis. （2）The multiple empirical mode decomposition is promoted to the high-dimensional empirical mode Decomposition (HEMD) by phase-space reconstruction method, researching the HEMD decomposition principle and exploring the effective method of calculating the local average of the high-dimensional signals. （3）The available means of inhibition of endpoint effect and modal aliasing phenomenon in the HEMD decomposition are researched, in order to increase the effectiveness of HEMD decomposition. （4）Research on the fault feature extraction and the fault classification based on decomposition of HEMD , which would provide a new method for early fault diagnosis and technical support of the equipment.

机械设备的早期故障信号通常为淹没在强背景和强噪声中的微弱信号，非线性和非平稳性特征明显，采用传统的方法难以识别和提取。本项目提出了高维经验模式分解（HEMD）理论，通过将一维信号重构到高维相空间中，对高维信号进行HEMD分解，分解成一系列高维固有模态函数，利用吸引子主流识别技术和局部投影算法，将高维信号降为一维信号，在此基础上实现齿轮和轴承早期故障信号的特征提取与故障分类。该项目的研究思路如下：（1）研究多元经验模式分解原理，并将其应用到机械故障诊断领域中。（2）结合相空间重构技术，将多元经验模式分解推广到高维经验模式分解（HEMD），研究HEMD的分解原理，探索计算高维信号局部均值的有效方法。（3）寻求HEMD分解理论中有效抑制端点效应和模态混叠现象的方法，提高HEMD分解的有效性。（4）研究基于HEMD分解的故障特征提取算法和故障分类算法，以期为设备早期故障诊断提供新的方法和技术支撑。

本项目按照计划完成了既定研究内容，在课题组原有故障诊断研究的基础上，针对采用多个传感器采集到的多元信号，通过多元EMD分解及高维EMD分解进行特征提取和故障分类，完成设备的早期故障诊断。首先，针对EMD进行了深入的理论及应用研究。提出了自适应噪声辅助完全集合EMD，再生相移正弦辅助EMD，及类似EMD的衍生算法自适应局部迭代滤波。并利用特征IMF进行早期故障特征提取与故障演化追踪。其次，采用多元EMD进行多元信号的早期故障特征提取与分类。提出了多元EMD，噪声辅助多元EMD，自适应噪声辅助多元EMD，及自适应投影本征变换多元EMD等方法，并将上述理论应用于设备的早期故障诊断中。并对多元EMD进行凸优化，更好的进行设备早期故障的特征提取。最后，采用高维EMD在高维相空间中实现早期故障分类及特征提取。对采用相空间重构的多种熵及张量分解等高维算法进行深入理论研究，在已有的对传统一维EMD研究的基础上，将EMD推广到二维EMD，三维EMD及高维EMD中，实现信号的高维EMD分解。通过对一维信号重构到高维相空间中后的分析，提取出一维空间中不易识别的隐含信息，从而更好的进行故障识别及分类。

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