基于互信息的PCA方法及其在过程监测中的应用

摘要

Principal component analysis (P monitoring CA) is a classical algorithm for feature extraction and has been widely used in multivariate statistical process. The essence of the PCA algorithm is to extract the correlation between process variables. However, the correlation matrix defined in the traditional PCA algorithm is limited to consider the linear relationship between variables, which cannot be employed to analyze the mutual dependence between two measured variables. With recognition of this lack, a novel mutual information based PCA (MIPCA) method is proposed for process monitoring. Distinct from the traditional PCA, MIPCA defines the relationship between variables by calculating the mutual information, and the original correlation matrix is replaced by the resulting mutual information matrix. The eigenvectors of the mutual information matrix can thus be utilized as the directions of feature extraction. On the basis of MIPCA, a statistical process monitoring model can then be constructed. Finally, the feasibility and effectiveness of the MIPCA-based monitoring method are validated by a well-known chemical process.%主元分析（PCA）是一种经典的特征提取方法，已被广泛用于多变量统计过程监测，其算法的本质在于提取过程数据各变量之间的相关性。然而，传统PCA算法中定义的相关性矩阵局限于计算变量间的线性关系，无法衡量两个变量间相互依赖的强弱程度。为此，提出一种新的基于互信息的 PCA 方法（MIPCA）并将之应用于过程监测。与传统PCA所不同的是，MIPCA通过计算两两变量间的互信息来定义相关性，将原始相关性矩阵取而代之为互信息矩阵，并利用该互信息矩阵的特征向量实现对过程数据的特征提取。在此基础上，可以建立相应的统计监测模型。最后，通过实例验证MIPCA用于过程监测的可行性和有效性。