动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 of mechanical equipment has the characteristics of weak dynamic response and complex transmission path and so on. The fault characteristic signal is often submerged in strong background and noise signals, which makes it difficult to extract and identify. The essence of dynamic model decomposition (DMD) is a decomposition algorithm that reveals the spatial-temporal evolution of complex systems, and decompose the time series into a series of single-frequency modes including modes which can represent early fault characteristics. After systematically studied DMD theory, this project proposes adaptive multiscale DMD, high-order DMD and high-dimensional DMD theory. The main research contents are as follows: .① Sparse optimization and multiscale are used to fully extract fault feature information and build adaptive multiscale DMD theory. .② Constructing causal model to approximate the time-varying system, the similarity matrix is expanded to a high-order data structure by increasing the time dimension and the number of channels, and the high-order DMD decomposition of the fault signal is performed to capture time varying information..③ The phase space reconstruction technique is used to reconstruct the signal into the high-dimensional phase space. Manifold learning is used to determine the main direction of the high-dimensional data to segment the slices and the high-dimensional DMD decomposition of the matrixed slices, to extract early weak fault characteristic..④ The above theories are applied to the feature extraction, identification and trend prediction of early fault signals of equipment to provide new methods and technical support for the early fault diagnosis of equipment.

机械设备的早期故障具有动态响应微弱，传递路径复杂等特点，故障特征信号通常淹没在强背景和强噪声信号中，难以提取和识别。动模式分解（DMD）的本质是一种揭示复杂系统时空演变规律的分解算法，能将时间序列分解成含表征早期故障特征的系列单频模态。本项目在系统研究DMD的基础上提出自适应多尺度DMD，高阶DMD及高维DMD理论，主要研究内容如下：①采用稀疏优化和多尺度化来充分提取故障特征信息，建立自适应多尺度DMD理论。②构建因果关系模型对时变系统进行近似表达，通过增加时间维度将相似矩阵拓展为高阶数据结构，对故障信号进行高阶DMD分解，捕捉时变信息。③采用相空间重构技术将信号重构到高维相空间中，采用流形学习确定高维数据体主方向进行切片分割，对矩阵化的切片进行高维DMD分解，提取早期微弱故障。④将上述理论应用于设备早期故障信号的特征提取、识别和趋势预测，以期为设备早期故障诊断提供一种新的方法和技术支撑。

在设备的运行过程中，振动信号包含丰富的设备运行状况信息。通过分析振动信号来了解设备运行状况是目前机械设备在线监测以及故障诊断的重要手段。然而，机械设备通常工作在复杂的工况下，采集到的信常常与噪声耦合呈现强非线性、非平稳特征，导致故障特征难以被有效识别。本项目提出的动模式分解理论通过将一维振动信号构造为高维动力学系统矩阵以反映原始动力学系统，并将其分解为一系列动力学模态以提取原始信号中内蕴的动力学特征，在此基础上实现齿轮和轴承早期故障特征提取与故障分类。本项目的研究思路如下：（1）针对DMD进行了深入的理论研究及应用研究。提出了特征增强的DMD、自适应多分辨率DMD，并利用这些改进算法对故障特征进行增强。（2）采用局部最低秩DMD实现高维空间中早期微小故障的特征提取。提出了局部最秩DMD，周期性的低秩DMD，并将上述理论应用于设备的早期故障诊断中。（3）采用多元DMD实现了多元信号的信息融合及故障特征同步提取。对DMD的理论基础进行深入研究，在一维DMD的基础上，利用张量奇异值分解理论提出了多元DMD，并将其应用于多元信号的信息融合与特征提取。（4）采用压缩感知DMD实现了信号的高保真小样本存储与故障诊断模型的轻量化。提出了一种自适应压缩感知DMD的轴承信号特征提取与信号传输新方法。采用自适应DMD字典来进行轴承故障特征提取，并利用压缩感知对信号进行压缩处理。并将其输入轻量化迁移学习神经网络中，实现了低运行效率设备的高精度故障诊断。