基于高维空间流形变化的设备状态趋势分析方法  

Trend Analysis Method via Manifold Evolution in High Dimensional Space for State of Machinery Equipment

作　　者：黎敏[1] 阳建宏[1] 徐金梧[1] 杨德斌[1] 

机构地区：[1]北京科技大学机械工程学院,北京100083

出　　处：《机械工程学报》2009年第2期213-218,共6页Journal of Mechanical Engineering

基　　金：国家高技术研究发展计划(863计划;2007AA04z169);国家自然科学基金(50674010);北京市自然科学基金(3062012);机械传动与制造工程湖北省重点实验室开放基金(2007A19)资助项目

摘　　要：以机械设备的运行状态为研究对象,提出一种基于高维空间流形变化的趋势分析方法。该方法将一维时间序列重构到高维相空间中,利用相点邻域的切空间信息逼近流形的局部几何结构,从而得到描述流形变化的切方向矩阵;通过多向主元分析方法对不同状态下的流形切方向矩阵进行计算,获得各个状态的权重得分,从而实现对设备状态变化的趋势分析。对混沌信号添加幅值大小不同的冲击进行数值仿真试验,与LYAPUNOV指数、近似熵等传统非线性分析方法相比,该方法能够更有效地描述系统状态变化的过程。将该方法应用于轴承外圈故障的振动信号分析中,成功地刻画了轴承疲劳劣化的趋势。A new trend analysis method based on the manifold evolution for the running state of machinery equipment is presented. A one-dimensional time series is embedded into a high dimensional phase space to reconstruct a dynamical manifold. The tangent direction of each phase point in the manifold is approximated by extracting the local geometric information within the neighborhood. Then the tangent direction matrix, which contains the information of the manifold evolution, is obtained. Finally the weight score of each state, which serves as a feature index of the trend analysis, is calculated by perform ing multi-way principal component analysis to all states in the form of tangent direction matrices. The method is validated by using data measured from chaotic system with additive GAUSSIAN white noise and periodical impacts with increasing amplitude. The experiments indicate that the new method has advantage over the traditional features such as LYAPUNOV exponents and approximate entropy in terms of the noise robustness. In addition, the method is applied to the analysis of vibration signals measured from a bearing test-bed. In the experiment, the outer races of the bearings are made with some pits on purpose, representing different levels of fault. The experimental results show that the proposed method based on the manifold evolution is able to reveal the fatigue deterioration trend of mechanical system.

关 键 词：流形变化 高维空间 多向主元 趋势分析 

分 类 号：TH165[机械工程—机械制造及自动化] TH133