基于互信息的PCA方法及其在过程监测中的应用

doi:10.11949/j.issn.0438-1157.20150374

化工学报 ›› 2015, Vol. 66 ›› Issue (10): 4101-4106.DOI: 10.11949/j.issn.0438-1157.20150374

基于互信息的PCA方法及其在过程监测中的应用

童楚东, 史旭华

宁波大学信息科学与工程学院, 浙江宁波 315211

收稿日期:2015-03-23 修回日期:2015-05-29 出版日期:2015-10-05 发布日期:2015-10-05
通讯作者: 史旭华
基金资助:
浙江省自然科学基金项目(LY14F030004);浙江省科技厅公益项目(2015C31017)。

Mutual information based PCA algorithm with application inprocess monitoring

TONG Chudong, SHI Xuhua

Faculty of Electrical Engineering &Computer Science, Ningbo University, Ningbo 315211, Zhejiang, China

Received:2015-03-23 Revised:2015-05-29 Online:2015-10-05 Published:2015-10-05
Supported by:
supported by the Natural Science Foundation of Zhejiang Province, China (LY14F030004).

摘要/Abstract

摘要：

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。

关键词: 主元分析, 数值分析, 过程系统, 互信息, 故障检测, 统计过程监测

Abstract:

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.

Key words: principal component analysis, numerical analysis, process systems, mutual information, fault detection, statistical process monitoring

中图分类号:

TP277

童楚东, 史旭华. 基于互信息的PCA方法及其在过程监测中的应用[J]. 化工学报, 2015, 66(10): 4101-4106.

TONG Chudong, SHI Xuhua. Mutual information based PCA algorithm with application inprocess monitoring[J]. CIESC Journal, 2015, 66(10): 4101-4106.

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基于互信息的PCA方法及其在过程监测中的应用

Mutual information based PCA algorithm with application inprocess monitoring

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