基于核函数PCA的齿轮箱状态监测研究

讨论核函数PCA(principal analysis component，主元分析)的算法原理，提出基于核函数PCA的齿轮箱状念监测方法。该方法借助于核函数计算得到原始特征的非线性主元，并根据非线性主元构建特征子空间，实现对齿轮箱运行状态的分类识别，并监测其状态变化。实例研究表明，核函数PCA分类效果比PCA好，能有效识别出齿轮箱的不同状念，并及时监测到齿轮箱工作状态的变化。

GEARBOX CONDITION MONITORING BASED ON KERNEL PRINCIPAL COMPONENT ANALYSIS

The kernel principal component analysis (KPCA) is discussed, where the inner integral operator kernel functions is used to realize the nonlinear map from the raw feature space to high dimensional feature space, and then standard principal analysis component (PCA) is performed in the high dimensional space. An approach for gearbox condition monitoring based on KPCA is presented, in which the nonlinear principal components of original feature space are calculated by means of kernel function, in succession feature subspace are constructed based upon these selected nonlinear principal components, and gearbox condition classification and recognition and condition monitoring are realized. The experimental data sets of gearbox working under normal, tooth cracked and tooth broken conditions are analyzed, and the results indicate that the KPCA can classify and recognize different gearbox conditions more efficiently than the PCA method, and then monitor the developments and variation of gearbox conditions in time.